Reconstruction of B-hadron final states at D

a rXiv:h ep-ph/211190v113Nov22Recent status of polarized parton distributions M.Hirai (Asymmetry Analysis Collaboration )1Radiation Laboratory,RIKEN (The institute of Physics and Chemical Research),Wako,Saitama 351-0198,Japan Abstract.We study an influence of precise data on uncertainty of polarized parton distribution functions.This analysis includes the SLAC-E155proton target data which are precise measure-ments.Polarized PDF uncertainties are estimated by using the Hessian matrix.We examine cor-relation effect between the antiquark and gluon uncertainties.It suggests that reducing the gluon uncertainty is needed to determine the polarized antiquark distribution clearly.INTRODUCTION Polarized parton distribution functions (polarized PDF’s)have so far been optimized from polarized deep inelastic scattering (polarized DIS)world data [1,2].We could obtain only a slight piece of information about polarized antiquark and gluon distribu-tions.At this stage,the antiquark SU(3)f flavor symmetry is assumed in most of the polarized PDF analyses.The SU(3)f symmetry breaking is already known as the Got-tfried sum rule violation in the unpolarized case.In principle,the polarized PDF analysis should take account of the symmetry breaking.However,we must not only determine a shape but also a sign of each polarized antiquark distribution.It needs more precise data to improve the current status.Semi-inclusive DIS experiments [3]are also expected to separate antiquark flavor distributions.However,the separated distributions may not be credible due to ambiguity of the fragmentation functions.Then,antiquark flavor dis-tributions cannot be decomposed clearly.The current knowledge of the polarized gluondistribution is still poor.The polarized gluon distribution is suggested as the positive distribution;however,there is large difference between various parameterization results.We would like to know ambiguity of polarized PDF’s quantitatively.PDF uncertainty plays an important role in illustrating the ambiguity.Furthermore,it is important to show the phenomenological uncertainty of predicted physical quantities (e.g.,scattering cross-sections and spin asymmetries)with parameterized PDF’s and their uncertainties in our work.A purpose of this analysis is to clarify the current knowledge about the polarized PDF’s from the polarized DIS world data by using their PDF uncertainty.In this analysis,the polarized PDF’s are optimized including precise SLAC-E155proton target data [4].Then,we examine an influence of the precise data on the polarized PDF uncertainty,which is estimated by the Hessian method.PARAMETERIZATION OF THE POLARIZED PDF’SThe polarized PDF’s are determined by using spin asymmetry A1of the polarized DIS experiments from the EMC,SMC,SLAC-E130,E142,E143,E154,E155,and HERMES:A1(x,Q2)=2x[1+R(x,Q2)]2n f∑i=1e2i ∆C q(x,αs)⊗[∆q i(x,Q2)+∆¯q i(x,Q2)]+∆C g(x,αs)⊗∆g(x,Q2) ,(2)where e i is the electric charge of quarks,and∆C q,∆C g are Wilson’s coefficient functions. The convolution⊗is defined by f(x)⊗g(x)= 1x dy/y f(x/y)g(y).The polarized PDF’s ∆f(≡f↑−f↓)are defined as helicity distributions in the nucleon.In the AAC analysis, the polarized PDF∆f(x)is defined at initial Q2by the weight function form:∆f(x)=Axα(1+λxγ)f(x),(3)where f(x)is the unpolarized PDF,and A,α,λ,andγare free parameters.Optimized PDF’s are four distributions;∆u v(x),∆d v(x),∆¯q(x),and∆g(x),and these are evolved from the initial Q2(=1GeV2)to the same Q2of experimental data by the DGLAP equation[7].In particular,the gluon distribution∆g(x)contributes to the structure function with the non-zero coefficient function∆C g in the NLO case.This analysis uses two constraint conditions.First,the positivity condition is used to restrict large-x behavior of the polarized PDF’s.This condition corresponds to the probabilistic interpretation of the parton distributions in the LO:|∆f(x)|≤f(x).It needs not to be satisfied strictly in the NLO analysis.However,the polarized antiquark and gluon distributions tend to badly break the positivity limit:|∆f(x)|≫f(x).Such excessive behavior is due to the large experimental errors in the large-x region.Hence, this behavior should be limited by this condition.Next,the SU(3)fflavor symmetry is assumed:∆¯u(x)=∆¯d(x)=∆¯s(x)=∆s(x).Using this assumption,one canfix thefirst moments of the valence quarks with hyperon decay constants,then∆u v=0.926and∆d v=−0.341are obtained.Note that the Bjorken sum rule is satisfied automatically byfixingfirst moments.Furthermore,the spin content∆Σis obtained by∆ΣNf =3=∆u v+∆d v+6∆¯q.Since,the antiquark contribution isemphasized,then the spin content determination is susceptible to the antiquark behavior. In the analysis,we choose the modified minimal subtraction(UNCERTAINTY ESTIMATIONFortunately PDF uncertainty estimation method has been developed in the last several years(see a brief review[6]).The polarized PDF uncertainty comes from several error sources,e.g.,experimental errors,unpolarized PDF,ΛQCD,and so on.However,it is difficult to incorporate these errors into uncertainty estimation simultaneously.In the present analysis,the polarized PDF uncertainty is estimated from experimental errors by using the Hessian matrix H i j which is defined as a second order derivative matrix in the expandedχ2(a i)function around its minimum point.The PDF uncertaintyδ∆f(x) can be obtained easily by the inverse matrix of the Hessian and linear error propagation:[δ∆f(x)]2=∆χ2∑i,j ∂∆f(x)∂a j,(4)where∆χ2(=χ2(a i)−χ2min)is defined as the difference from the minimumχ2.It deter-mines a confidence level of the PDF uncertainty,and it depends on theχ2distributionK(s)with N degrees of freedom.Here,N is the number of optimized parameters.In our estimation,the value of∆χ2is obtained by the following equation: ∆χ20K(s)ds=σ, whereσ(=0.683)corresponds to1σerror of a standard distribution in order to com-pare with general experimental errors.The statistical and systematic errors are added in quadrature,so that it could be overestimation.The proper estimation exists between the overestimated uncertainty and the uncertainty from only the statistical error.RESULTS AND DISCUSSIONSThe bestfitting result isχ2(/d.o.f.)=346.33(0.90).Thefirst moments of new results and the AAC pervious results(AAC00,NLO set2)[1]are shown in Table.1.A correla-tion coefficientρ¯qg between thefirst moment of the antiquark and gluon distributions is ρ¯qg=−0.836,and there is strong correlation between two distributions.The uncertain-ties of the new results become smaller than those of the previous results.The gluonfirst moment and spin content∆Σstill have large uncertainty.Thefixedfirst moments∆u v and ∆d v do not have uncertainty,then the∆Σuncertainty is six times as large as the antiquark uncertainty.Thus,the spin content is subject to the uncertainty of the antiquark distri-bution.Figure1shows the uncertainty of the new antiquark distribution.The antiquark uncertainty becomes rather large in the region x<0.01,however the experimental datascarcely exist.The polarized DIS spin asymmetries A p,d1(x)approaches rapidly to zeroin the rang x<0.004.It is insufficient to clarify small-x behavior of the antiquark dis-tribution.Therefore,the antiquark determination has extrapolating ambiguity in small-x region.It is needed tight constraint condition or other experiment.In addition,Figure1shows comparison between the PDF uncertainties of new results and the previous results.There are no significant improvements of the valence quark uncertainties.On the SU(3)f symmetry assumption,thefixingfirst moments strongly restricts the behavior of valence quark distributions.In contrast,the antiquark and gluon uncertainties are reduced in the range0.01<x<0.5,where the E155proton data exist.TABLE 1.First moments of the polarized antiquark,gluon,andspin content ∆Σwith their uncertainties at Q 2=1GeV 2.∆¯q ∆g ∆Σ−0.062±0.023,0.499±1.268,0.213±0.138AAC00The precise polarized DIS data can reduce the antiquark uncertainty mainly.On the other hand,the gluon uncertainty changes in response to antiquark uncertainty reduction due to a strong correlation between two distributions.Since the gluon contribution to the structure function g 1(x )is smaller than the quark and antiquark contributions,we can extract only a little information of the gluon distribution in spite of the NLO analysis.Actually,the gluon uncertainty is still large.It indicates the difficulty of determining the gluon distributions from the polarized DIS data.Therefore,the uncertainty reduction of the gluon distribution is due to the strong correlation rather than the NLO contribution.In order to examine the correlation effect on the parameterization,we re-analyzed the ∆g (x )=0case in which the fixed gluon distribution does not have uncertainty.The polarized PDFuncertainties of the ∆g (x )=0case are compared to those of the ∆g (x )=0case in Figure 2.The gluon distribution slightly exists at high-Q 2due to Q 2evolution of the singlet type DGLAP equation.The valence quark uncertainties scarcely change.Drastic improvement of the antiquark uncertainty is due to vanished the large gluon uncertainty.the obscure gluon distribution brings about the larger antiquark uncertainty by the complementary relation.x x xx FIGURE 1.Polarized PDF’s with their uncertainties at Q 2=1GeV 2.Dashed curves are the uncertain-ties of previous results (AAC NLO-2)-0.3-0.2-0.1x Preliminary !-1.5-1-0.500.511.520.00010.0010.010.11x200 GeV 2∆g(x )=0 at 1 GeV 2FIGURE 2.Polarized antiquark and gluon distributions with their uncertainties at Q 2=1GeV 2.The shaded portion shows the uncertainty of ∆g (x )=0results,and the dashed curves are the uncertainties of new results (∆g (x )=0).SUMMARYBy this analysis,the polarized PDF’s were optimized from the polarized DIS world data which included the SLAC-E155proton target data.The polarized PDF uncertain-ties were estimated by the Hessian method.The E155precise measurements scarcely improve the valence quark uncertainties,but they can reduce the antiquark and gluon uncertainties.These,however,are still wrapped in large uncertainty.The SU(3)f sym-metry,which we are obliged to assume,restricts strongly the valence quark behavior by fixing first moments,and the spin content determination depends on the antiquark behavior.Additionally,there is the strong correlation between the antiquark and gluon distributions.If the gluon distribution is clarified by RHIC-Spin at BNL,the uncertainty of the antiquark distribution can be reduced to some extent.Similarly,the complemen-tary relation can reduce the large uncertainty of the spin content which comes from the extrapolating issue of the antiquark behavior.Then,we will be able to investigate the antiquark flavor dependence in detail.REFERENCES1.AAC,Y .Goto et al .,Phys.Rev.D62(2000)034017.2.De Florian and R.Sassot,Phys.Rev.D62(2000)094025;M.Glück,E.Reya,M.Stratmann,and W.V ogelsang,Phsy.Rev.D63(2001)09400;E.Leader,A.V .Sidorov,and D.B.Stamenov,Eur.Phys.J.C23(2002)479-485;J.Blümlein and H.Böttcher,Nucl.Phys.B B636(2002)225-263.Fortran pro-gram librarys of polarized PDF’s are available from /hepdata/pdf.html.3.SMC,B.Adeva et al .,Phys.Lett.B420,180(1998);HERMES,K.Ackerstaff et al .,Phys.Lett.B464123(1999).4.SLAC-E155,P.L.Anthony et al .,Phys.Lett.B493(2000)19.5.L.W.Whitlow,S.Rock,A.Bodek,S.Dasu and E.M.Riordan,Phys.Lett.B250,193(1990);SLAC-E143,K.Abe et al .,Nucl.Phys B452(1999)1946.M.Botje ,J.Phys.G 28(2002)779-790.7.V .N.Gribov and L.N.Lipatov,Sov.J.Nucl.Phys.15(1972)438and 675;G.Altarelli and G.Parisi,Nucl.Phys.B 126(1977)298;Yu.L.Dokshitzer,Sov.Phys.JETP 46(1977)641.8.M.Glück,E.Reya,and A.V 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SAT阅读题目练习:二战后布雷顿森林货币体系SAT阅读题目练习On July 22, 1944, as allied troops were racing across Normandy to liberate Paris, representatives of 44 nations meeting at the Mount Washington resort in Bretton Woods, New Hampshire, created a financial and monetary system for the postwar era. It had taken three weeks of exhausting diplomacy. At the closing banquet, the assembled delegates rose and sang “For He’s a Jolly Good Fellow.” The fellow in question was John Maynard Keynes, leader of the British delegation and intellectual inspiration of the Bretton Woods design.Lord Keynes, the world’s most celebrated economist, was playing a tricky dual role. He had proposed a radical new monetary system to free the world from the deflationary pressures that had caused and prolonged the Great Depression. Bretton Woods, he hoped, would be the international anchor for the suite of domestic measures that came to be known as Keynesian—the use of public spending to cure depression and the regulation of financial markets to prevent downturns caused by failed private financial speculation.Keynes was also hoping to restore Britain’s prewar position as a leading industrial and financial power. His two roles overlapped, but far from perfectly. The Americans shared the British desire to restore world growth, but not to preserve Britain’s empire or its protectionist system of preferential trade deals for nations that settled their accounts in pounds sterling.Writing to a colleague after the conference ended, Keynes professed to be pleased. He wrote that in the new International Monetary Fund, “we have in truth got both in substance and in phrasing all that we could reasonably hope for.” The new World Bank, Keynes declared, offered “grand possibilities. … The Americans are virtually pledging themselves to quite gigantic untied loans for reconstruction and development.”Yet in many respects, Bretton Woods was a rout for Keynes and the British. America today is often described as the sole surviving superpower, but in 1944 U.S. supremacy was towering. Germany and Japan were on the verge of ruin. Britain had gone massively into debt to prosecute the war, sacrificing more than a quarter of its national wealth. The Russians had lost tens of millions of soldiers and civilians. America was unscathed, its casualties were modest by comparison, it held most of the world’s financial reserves, and its industrial plant was mightier than ever.Though Keynes inspired Bretton Woods, the Americans won the day. As leverage, Keynes had only his own brilliance and a fast-fading appeal to Anglo-American wartime solidarity. In most matters, a rival design by Keynes’s American counterpart, Harry Dexter White, prevailed. White, a left-wing New Dealer serving as No. 2 man at the Treasury, shared Keynes’s basic views on money. But the White planprovided a far more modest fund and bank. Instead of the generous extension of wartime lend-lease aid that Keynes was promoting, the British had to settle for an American loan, to be repaid with interest.(两人的观点是不太一样的，White希望温和的经济政策，凯恩斯比较激进) The Bretton Woods system was hailed as a vast improvement over both the rigid gold standard of pre-1914 and the monetary anarchy of the interwar period. For a quarter-century, Bretton Woods undergirded a rare period of steady growth, full employment, and financial stability. But in many respects, the vaunted role of the World Bank, the International Monetary Fund, and the Bretton Woods rules specifying fixedexchange rates was a convenient mirage. (学生回忆这里有题目，我没有看到题目，这里说这些组织的作用被夸大，如同海市蜃楼。

Epileptiform Activity and Cognitive De ficits in SNAP-25+/−Mice are Normalized by Antiepileptic DrugsIrene Corradini 1,3,†,Andrea Donzelli 1,†,Flavia Antonucci 1,2,Hans Welzl 3,Maarten Loos 4,5,Roberta Martucci 1,Silvia De Astis 1,2,Linda Pattini 6,Francesca Inverardi 7,David Wolfer 4,Matteo Caleo 8,Yuri Bozzi 8,11,Claudia Verderio 2,Carolina Frassoni 7,Daniela Braida 1,Mario Clerici 9,Hans-Peter Lipp 4,Mariaelvina Sala 1and Michela Matteoli 1,101Dipartimento di Biotecnologie Mediche e Medicina Traslazionale,Universitàdegli Studi di Milano,20129Milan,Italy 2CNRInstitute of Neuroscience,20129Milan,Italy 3Fondazione Filarete,20139Milan,Italy 4Institute of Anatomy,University of Zurich,CH-8057Zurich,Switzerland 5Sylics,Synaptologics BV,1008Amsterdam,The Netherlands 6Department of Bioengineering (LP),Politecnico di Milano,20133Milan,Italy 7Clinical Epileptology and Experimental Neurophysiology Unit,Fondazione I.R.C.C.S.Istituto Neurologico "C.Besta",20133Milan,Italy 8CNR Institute of Neuroscience,56124Pisa,Italy 9Fondazione IRCCS Don Gnocchi,20148Milan,Italy 10Humanitas Clinical and Research Center,20089Rozzano,Italy 11Laboratory of Molecular Neuropathology,CIBIO,University of Trento,38123Trento,ItalyAddress correspondence to Dr Michela Matteoli,Dipartimento di Biotecnologie Mediche e Medicina Traslazionale,Universitàdegli Studi diMilano Via Vanvitelli,20129Milan,Italy.Email:michela.matteoli@unimi.it †equal contributors.Synaptosomal-associated protein of 25kDa (SNAP-25)is a protein that participates in the regulation of synaptic vesicle exocytosis through the formation of the soluble NSF attachment protein recep-tor complex and modulates voltage-gated calcium channels activity.The Snap25gene has been associated with schizophrenia,attention de ficit hyperactivity disorder,and bipolar disorder,and lower levels of SNAP-25have been described in patients with schizophrenia.We used SNAP-25heterozygous (SNAP-25+/−)mice to investigate at which extent the reduction of the protein levels affects neuronal network function and mouse behavior.As interactions of genotype with the speci fic laboratory conditions may impact behavioral results,the study was performed through a multilaboratory study in which behavioral tests were replicated in at least 2of 3distinct European laboratories.Reductions of SNAP-25levels were associ-ated with a moderate hyperactivity,which disappeared in the adult animals,and with impaired associative learning and memory.Electroencephalographic recordings revealed the occurrence of frequent spikes,suggesting a diffuse network hyperexcitability.Consistently,SNAP-25+/−mice displayed higher susceptibility to kainate-induced seizures,paralleled by degeneration of hilar neurons.Notably,both EEG pro file and cognitive defects were im-proved by antiepileptic drugs.These results indicate that reduction of SNAP-25expression is associated to generation of epileptiform discharges and cognitive dysfunctions,which can be effectively treated by antiepileptic drugs.Keywords:epilepsy,memory,SNAP-25,valproate IntroductionSynapses are fundamental brain structures that mediate information transfer between neurons.Synaptic dysfunctions contribute to a large number of psychiatric diseases,including schizophrenia,autism,and intellectual disability,which are therefore called “synaptopathies ”(Grant 2012).Synaptosomal-associated protein of 25kDa (SNAP-25)is a soluble NSF at-tachment protein receptor protein,tethered to the plasma membrane via several cysteine-linked palmytoil chains,that participates in synaptic vesicle exocytosis through the for-mation of a complex with syntaxin and with the synaptic vesicle protein synaptobrevin/V AMP (Jahn and Scheller 2006;Südhof and Rothman 2009).SNAP-25also interacts with and modulates the activity of various voltage-gated ion channels(VGCC)(Atlas 2001;Zamponi 2003;Catterall and Few 2008;Condliffe et al.2010).SNAP-25is involved in different psychiatric disorders.Case –control-or family-based studies indicated that the Snap25gene is associated with attention de ficit hyperactivity disorder (ADHD)(Barr et al.2000;Kustanovich et al.2003;Mill et al.2004;Faraone et al.2005;Feng et al.2005).Accord-ingly,Snap25intronic single nucleotide polymorphisms (SNPs)have been linked to inattentive hyperactivity in a group of ADHD children (Zhang et al.2010),and associated with hyperactivity in autism spectrum disorders (Guerini et al.2011).Genome-wide linkage scan analysis for schizo-phrenia susceptibility genes suggested the chromosomal region 20p12.3-11,containing Snap25,as a candidate region for the disease (Lewis et al.2003).Also,SNAP-25levels are lower in the hippocampus (Young et al.1998;Thompson et al.2003)and in the frontal lobe (Thompson et al.1998)of patients with schizophrenia.Finally,modi fications of SNAP-25levels occur in the brain of bipolar patients (Fatemi et al.2001;Scarr et al.2006),while one SNP variant in the promoter region,associated with higher SNAP-25expression in prefrontal cortex,was linked with early onset of bipolar disorder (Etain et al.2010).The demonstration that SNAP-25levels are altered in psy-chiatric diseases suggests that variations in the protein expression may have a pathogenic effect,possibly affecting synaptic function and network activity,and resulting in phe-notype alterations.Indeed,homozygous mutant mice in which Ser187of SNAP-25is substituted with Ala display an altered emotional behavior (Kataoka et al.2011),while repla-cement of the mature SNAP-25b isoform with the SNAP-25a isoform,which is present in early development,results in de-velopmental defects,spontaneous seizures,and impaired short-term synaptic plasticity (Johansson et al.2008).So far,the only evidence that reduction of SNAP-25expression may directly impact the behavioral phenotype derives from the analysis of the coloboma mouse,which is characterized by a hemizygous 2-centimorgan deletion of a segment on chromosome 2q,including the gene region en-coding SNAP-25(Hess et al.1995).The coloboma mice,largely used as a model for ADHD (Wilson 2000;reviewed in Faraone et al.2005;Russell 2007),display a hyperactive phe-notype,which is reduced by the expression of the SNAP-25©The Author 2012.Published by Oxford University Press.All rights reserved.For Permissions,please e-mail:journals.permissions@Cerebral Cortex February 2014;24:364–376doi:10.1093/cercor/bhs316Advance Access publication October 12,2012at Lanzhou University on April 14, 2015/Downloaded fromtransgene(Hess et al.1996).However,coloboma mice may not be suited for investigating the neurophysiological and be-havioral phenotype induced by reduction of SNAP-25levels, because the37genes that are present in the deleted region on chromosome2,including genes for phospholipase C beta-1 (Plcb1),coloboma(cm),Plcb4,and Jag1,may contribute to the mice phenotype(Gunn et al.2011).While SNAP-25homozygous mutant mice die at birth from respiratory failure,heterozygous(SNAP-25+/−)mice are viable (Washbourne et al.2001).We used therefore SNAP-25+/−mice to investigate at which extent selective reduction of the protein levels,as occurring in psychiatric diseases,affects neuronal network function and mouse behavior.The large majority of behavioral tests were carried out in at least2of3 European laboratories and generated reproducible results.We found that SNAP-25+/−mice display hyperactivity and show an abnormal EEG profile associated with cognitive defects, both normalized by treatment with valproate(VLP). Materials and MethodsAnimalsMale SNAP-25+/+and SNAP-25+/−C57BL/6mice,originally from M.C. Wilson(University of New Mexico Health Sciences Center,Albuquer-que,NM,USA),were provided by J.Sorensen(MPI,Goettingen). Mice were maintained and repeatedly backcrossed on C57BL/6back-ground for more than10generations.Zero-to six-month-old age-matched littermate mice were used.All the experimental procedures followed the guidelines established by the Italian Council on Animal Care and were approved by the Italian Government decree No.27/2010.All efforts were made to minimize the number of subjects used and their suffering.Mice were individu-ally housed throughout the testing period with free access to food and water at controlled temperature(20–22°C)with a12-h light/dark cycle(lights on at7:00AM).Genotyping was performed by PCR as described(Washbourne et al.2001).Westen Blot AnalysisHomogenates from cortices of E18,P7,P14,P30,and adult(3months old)mice were analyzed by western blotting using anti-SNAP-25, 1:1000(Chemicon,Temecula,CA.,USA),anti-Calbindin(CB),1:500 (Swant,Bellinzona,Switzerland),anti-beta-III-Tubulin1:4000(Promega Corporation,Madison,USA),anti-alpha-Tubulin1:2000(Sigma-Aldrich, St.Louis,MO),anti-vGlut11:2000(Synaptic System,Gottingen, Germany).Antibodies against SNAP-47,SNAP-29,and SNAP-23were a gift of R.Jahn(MPI,Gottingen).Immunoreactive bands were detected using the Pierce ECL Western Blotting Substrate(Thermo Fisher Scienti-fic Inc.,Rockford,IL),scanned with a Bio-rad GS-800™calibrated den-sitometer,and analyzed with Image J software.Beta-III tubulin or alpha-tubulin was used as loading controls.For each developmentalstage,SNAP-25/beta-III tubulin or SNAP-25/alpha tubulin optical den-sities were normalized to the average of controls.Immunohistochemical AnalysisImmunohistochemistry was performed on5SNAP-25+/+and3 SNAP-25+/−mice at postnatal day(P)2and on3SNAP-25+/+and3 SNAP-25+/−adult(P90)mice.The immunoperoxidase and immuno-fluorescence procedure was performed on free-floating sections (Moroni et al.2008)using the following primary antibodies:anti-CB, 1:5000,anti-nonphosphorylated neurofilaments,1:1000(SMI311; Sternberger Monoclonals Incorporated,Lutherville,USA), anti-calretinin(CR),1:3000,anti-neuropeptide Y(NPY;Peninsula Bachem,Bubendorf,Switzerland),anti-doublecortin,1:800(DCX; Cell Signaling Technology,Danvers,MA,USA),anti-cholecystokinin, 1:100(CCK-8;Neomarkers,Fremont,CA,USA),anti-vGlut1,1:1500 (Synaptic System,Gottingen),anti-vGlut2,1:1000(Synaptic System,Gottingen),and anti-vGat,1:1000(Synaptic System,Gottingen).For cytoarchitectonic analysis,selected sections were stained with thionin(0.1%in distilled water).qRT-PCR AnalysisBrain tissues from P7,P14,P30,and adult mice were used for real-time PCR analysis.Sample was homogenized prior to RNA extractionin800μL of Trizol.Total RNA was isolated using the NucleoSpin miRNA(Macherey-Nagel GmbH&Co.,Düren,Germany)isolation kit according to the manufacturer’s protocol.The RNA was eluted with30-μL Rnase-free water.All RNA was quantified by spectrophotometerand optical density260/280nm ratios were determined.Reverse transcription was performed on2-μg RNA using Superscript III First-Strand Synthesis System and random hexamer primers(Life Technol-ogies,Carlsbad CA,USA).Real-time polymerase chain reaction (qRT-PCR)was performed using7900HT fast-real-time PCR system instrument(Life Technologies,Carlsbad CA,USA).The amplificationwas carried out in a total reaction volume of11μL,using the TaqManGene Expression Master Mix(Life Technologies,Carlsbad CA,USA). Predeveloped TaqMan Assay Reagent(FAM-MGB)for SNAP25andfor GAPDH were purchased from PE Applied Biosystems.Each genewas analyzed in triplicate.Data analysis was performed with theΔΔCt method.All RNA levels were normalized to Gapdh.Spontaneous Motor Activity and Amphetamine Response Spontaneous motor activity was carried out as described in Sup-plementary Materials and Methods.Before the start of the test, SNAP-25+/+and SNAP-25+/−mice(7–9weeks of age)were habituatedto the testing room for at least1h.Cumulative horizontal and vertical movement counts were recorded for4h before and3h after treat-ment.,animals were treated subcutaneous(s.c.)with saline or amphetamine sulfate(4mg/kg)dissolved in0.9%NaCl.Activity measures began immediately after injection and lasted3h,accordingto Hess et al.(1996).ElectroencephalogramAfter surgery(for details see Supplementary Materials and Methods), Electroencephalogram(EEG)activity was recorded,in a Faraday chamber,using a Power-Lab digital acquisition system(AD Instru-ments,Bella Vista,Australia;sampling rate100Hz)in freely moving SNAP-25+/+and SNAP-25+/−mice(n=10mice per genotype).EEG traces were analyzed as described(Manfredi et al.2009)for spike activity.Basal cerebral activity was recorded continuously for24h infreely moving mice.For each24-h EEG recording,the mean numberof spikes was evaluated in both genotypes.After the recordings,theEEG and video(through a video camera put inside the Faraday chamber)were analyzed for the incidence/duration of spontaneous cortical spike activity and the percentage of animals displaying spike activity,as pre-viously described(Zhang et al.2004;Manfredi et al.2009).Kainate-Induced SeizuresSNAP-25+/+and SNAP-25+/−mice(n=10mice per genotype)received intraperitoneal(i.p.)kainic acid(KA,Sigma Aldrich,St.Louis,MO)dis-solved in saline at35-mg/kg body weight.Saline-injected animals ofboth genotypes were used as controls.Seizure severity was determinedas described(Bozzi et al.2000).The rating scale value was scoredevery20min for a maximum of3h,and data were used to calculatethe time-course of seizure severity for each genotype(Schauweckerand Steward1997;Tripathi et al.2008).At the end of behavioral obser-vation(3h after KA),animals were returned to their home cages; animals were killed at14days after KA for histopathological analyses.Quantification of NPY StainingThe quantification method was adapted from that described in Anto-nucci et al.,2008.Four-eight NPY-stained sections through the dorsal hippocampus were analyzed in each KA-treated mouse(wild type [wt],n=5;heterozygous[het],n=5).Images of CA3stratum radiatumCerebral Cortex February2014,V24N2365at Lanzhou University on April 14, 2015/Downloaded fromand of the overlying corpus callosum in each hemisphere were digi-tized(Zeiss Axiovision).Light intensity and microscope settings were optimized initially and then held constant.Care was taken to avoid saturation at either end of the pixel intensity range(0–255).Mean signal intensity in the CA3stratum radiatum was divided by the back-ground labeling in each section(calculated in the callosum of each hemisphere).For each animal,an NPY staining score was obtained by averaging the values obtained in individual sections.The NPY stain-ing score was then correlated to the maximum behavioral seizure score recorded for each mouse following KA treatment.Pearson cor-relation analysis was performed using SigmaPlot11.0.Two-Bottle Preference Tests and Latent InhibitionTwo-bottle preference and latent inhibition test in a conditioned taste aversion(CTA)paradigm were performed as previously described (Bruno et al.2007).For details,see Supplementary Materials and Methods.Conditioned Taste AversionSNAP-25+/+(n=10)and SNAP-25+/−(n=12)mice were individually housed during the CTA test.After mice were adapted to a restricted drinking schedule(20min/day for4days),they were exposed to a saccharin solution(0.5%)followed1h later by a malaise-inducing in-jection of LiCl(0.14M,2%body weight,i.p.).Beginning48h after conditioning,mice could freely choose to drink either saccharin sol-ution or tap water during3daily choice tests(ct1–ct3).The amount of saccharin intake expressed as the percentage of totalfluid con-sumed([saccharin/saccharin+water]×100)was taken as an aversion index.Object RecognitionTen SNAP-25+/+and11SNAP-25+/−mice were used.The novel object recognition task was performed as described in Supplementary Materials and Methods.Sociability and Preference for Social Novelty TestTen SNAP-25+/+and12SNAP-25+/−mice were used.The sociability and preference for social novelty test was performed in a3-chamber transparent polycarbonate box as described in Supplementary Materials and Methods.Pharmacological TreatmentOne week after basal EEG,animals were recorded1h before and for 2h immediately after drug i.p.treatment:VLP sodium salt(250mg/ kg),ethosuximide(ETO;200mg/kg),carbamazepine(CBZ;50mg/ kg),and nimodipine(NIMO;10mg/kg).VLP was given immediately before HCl exposure in the CTA test,20min before T1in the object recognition test,and20min before sociability and social novelty test. All drugs were dissolved in saline,NIMO in10%ethanol,and saline and CBZ in1%Tween80.The doses of ETO,VLP,and NIMO were chosen for their ability to suppress differently induced seizures in mice(Larkin et al.1992;DeLorey et al.1998;Liljelund et al.2005; Shitak et al.2006;Marrosu et al.2007;Chung et al.2009).All the drugs were given i.p.in a volume of0.1mL/10g.Fresh drug solutions were prepared daily.Drugs were purchased from Sigma-Aldrich (St.Louis,MO).Data AnalysisOne-way ANOV A with repeated measures,1-way factorial ANOV A design with genotype(SNAP-25+/+,SNAP-25+/−)or2-way ANOV A as between subject factor were used.Post hoc analysis was done using Tukey’s Bonferroni’s or Holm Sidak’s post hoc tests.Pairwise com-parisons between genotypes or treatments were assessed with Stu-dent’s t-test or Fisher exact probability tests.Correlation between the maximum behavioral seizure score and NPY was performed using SigmaPlot11.0and by Pearson correlation analysis.The significance threshold was set at P<0.05.All statistical analyses were done with software Prism,version5(GraphPad,San Diego,CA).ResultsDevelopmental Expression of SNAP-25in Heterozygous Mice BrainWestern blotting analysis of wild-type and heterozygous mice cortices showed that SNAP-25and syntaxin progressively in-crease during brain development.To validate SNAP-25levels and to minimize development-related artifacts possibly leading to erroneous data interpretation,both beta-III-Tubulin and alpha-Tubulin were used as a loading marker for SNAP-25quantitation.Notably,SNAP-25levels in heterozy-gous mice tended to progressively increase relatively to SNAP-25+/+mice,indicating a partial compensation of protein expression during postnatal development(*P<0.05; **P<0.01;***P<0.001,t-test)(Fig.1A,C).A comparable trend was observed when SNAP-25levels were normalized to alpha-tubulin(*P<0.05;**P<0.01;***P<0.001,t-test)(Fig.1D).The protein increase was not accompanied by a parallel in-crease in SNAP-25mRNA levels,as assessed by qRT-PCR analysis(Fig.1B).No significant difference in syntaxin (Fig.1E)or GAP-43(Fig.1F)expression was found between SNAP-25+/+and SNAP-25+/−mice during development.In the adult SNAP-25+/−brain,a reduced level of SNAP-25was de-tected,in the absence of changes in SNAP-47,SNAP-29, SNAP-23,the calcium-binding protein CB,and the vesicular glutamate transporter vGlut1(Fig.1G).Lack of Anatomical Alterations in SNAP-25+/−BrainWe analyzed whether anatomical alterations occur in brains of SNAP-25+/−when compared with SNAP-25+/+mice.The main brain structures,cortex,hippocampus,and thalamus were comparable in SNAP-25+/+and SNAP-25+/−P2mice,as indi-cated by thionin staining(Fig.2A,B).Normal cortical plate and layers V and VI(Fig.2D,F)and similar hippocampal CB expression(Fig.2C,E)were observed.Consistently,no major differences in the main brain structures were detected between SNAP-25+/+and SNAP-25+/−adult animals(Fig.2G,H). The thickness of the cortices and the cortical lamination was comparable,as indicated by thionin staining(Fig.2I,J)and immunostaining for SMI311,which labels a subpopulation of pyramidal cells mainly located in layers II–III and V(Fig.2N, O).The expression pattern of the calcium-binding proteins CB and CR,identifying the subfields of hippocampus(Fig.2L, M,R,S)and of CCK and NPY(Fig.2P,Q,U,V)was identical in SNAP-25+/+and SNAP-25+/−mice.Also,DCX staining in the subgranular zone,labeling migrating neuronal precursor cells that eventually integrate into hippocampal circuitry(Parent et al.1997;van Praag et al.2002),was comparable in amount and distribution(Fig.2W,X).Also,the distribution of excit-atory and inhibitory terminals in CA1hippocampal region was not different between SNAP-25+/+and SNAP-25+/−mice (Fig.2K,T).Finally,no major alterations were observed in the barrel cortex of SNAP-25+/−mice when compared with wild type,although further analysis may unveil slight segregation differences(Fig.2Y,Z).A quantitation of vGAT and vGlut1-positive puncta,expressed as either a fraction of V AMP2-positive puncta or a reciprocal ratio,revealed no significant differences between SNAP-25+/+and SNAP-25+/−mice,at366Altered EEG and memory in SNAP-25+/−mice•Corradini et al. at Lanzhou University on April 14, 2015 / Downloaded fromleast in the CA1region of the hippocampus (vGAT/V AMP2ratio:SNAP-25+/+1±0.080;SNAP-25+/−0.972±0.096;P =0.83;vGlut1/VAMP2ratio:SNAP-25+/+1±0.129;SNAP-25+/−0.975±0.137;P =0.89;vGAT/vGlut1ratio:SNAP-25+/+1±0.085;SNAP-25+/−1.024±0.122;P =0.88).Also,no major difference was observed in vGlut2distribution in the dentate gyrus of SNAP-25+/+and SNAP-25+/−mice (not shown).SNAP-25+/−Mice,at the age of 7Weeks,Show Motor Hyperactivity due to Lack of HabituationAs a hyperactive phenotype has been described in coloboma mice,which is reduced by the expression of the SNAP-25transgene (Hess et al.1996),we monitored spontaneous motor activity in SNAP-25+/−mice at 7weeks of age (Fig.3)and in the adult (Supplementary Table S1).The time course of horizontal and vertical activity recorded every 10min is given in Figure 3A ,B .During the first 2-h recording,both gen-otypes showed a similar horizontal and vertical activity.However,during the following 2h (120–240min)SNAP-25+/−mice failed to habituate,thus resulting more active than wild-type littermates.S.c.injection of d -amphetamine (4mg/kg)increased horizontal activity in SNAP-25+/+mice during the first hour after treatment (240–300min),whereas in the fol-lowing hour (300–360min),the stimulant effect decreased (Fig.3A ).Conversely,d -amphetamine appears not to exertany effect on SNAP-25+/−mice in the first hour after treat-ment,whereas it signi ficantly reduced motor activity in the following hour (Fig.3A ).However,it has to be noted that removal of animals from the cage to perform injection,induced an increase in motor activity.Indeed,a parallel group of SNAP-25+/+and SNAP-25+/−mice,subjected to the same protocol,but treated with saline instead that amphetamine,showed an increase in motor activity of 250%and 680%,respectively.A recovery of motor function was obtained during the last period.Vertical activity (Fig.3B )was reduced by treatment with d -amphetamine in both genotypes starting from the first hour and a partial recovery was reached at 360min.The observed reduction of vertical movements was prob-ably due to the intense horizontal activity.When the time course was statistically evaluated in terms of 1-h each blocks,signi ficant differences were obtained for horizontal (Fig.3C )and vertical activity (Fig.3D )(see legend of Fig.3C ,D ).A normal locomotor activity was found in SNAP-25+/−adult mice (Supplementary Table S1).SNAP-25+/−Mice Display an Altered EEG Pro file and are More Susceptible to Kainate-Induced SeizuresAs SNAP-25controls neurotransmitter release and VGCC activity,we recorded the EEG pro file of SNAP-25+/−mice.24-h cortical EEG recordings on freely movinganimalsFigure 1.SNAP-25levels in SNAP-25+/−cortices progressively increase during postnatal development.(A ,C ,and D )Western blotting analysis (A )and relative quantitation (C and D )of SNAP-25+/+and SNAP-25+/−cortices from E18,P7,P14,P30and adult (3months old)mice reveals a progressively higher expression ratio in SNAP-25+/−mice during postnatal development (normalized SNAP-25levels:(C )E18,SNAP-25+/+(n =6)1±0.056,SNAP-25+/−(n =7)0.38±0.089;P7,SNAP-25+/+(n =9)1±0.091,SNAP-25+/−(n =5)0.63±0.049;P14-30,SNAP-25+/+(n =8)1±0.054,SNAP-25+/−(n =8)0.71±0.092;adult,SNAP-25+/+(n =6)1±0.068,SNAP-25+/−(n =7)0.75±0.042.*P <0.05;**P <0.01;***P <0.001,unpaired Student ’s t -test.(D )E18,SNAP-25+/+(n =5)1±0.025,SNAP-25+/−(n =6)0.511±0.061,P <0.0001;P7,SNAP-25+/+(n =5)1±0.095,SNAP-25+/−(n =5)0.763±0.0312,P <0.05;P14-30,SNAP-25+/+(n =9)1±0.077,SNAP-25+/−(n =8)0.777±0.065,P <0.05;adult,SNAP-25+/+(n =3)1±0.012,SNAP-25+/−(n =3)0.85±0.022,P <0.01.(B )RT-qPCR analysis reveals that SNAP-25mRNA is about half in SNAP-25+/−mice at all developmental stages (normalized fold expression:P7,SNAP-25+/+(n =2)1±0.044,SNAP-25+/−(n =2)0.551±0.094;P14-30,SNAP-25+/+(n =4)1±0.089,SNAP-25+/−(n =5)0.441±0.056;adult,SNAP-25+/+(n =3)1±0.034,SNAP-25+/−(n =3)0.470±0.046.*P <0.05;***P <0.001,unpaired Student ’s t -test).(E )Quantitation of syntaxin expression at different developmental stages shows no differences in the protein expression between SNAP-25+/+and SNAP-25+/−animals (E18,SNAP-25+/+(n =2)1±0.160,SNAP-25+/−(n =2)0.997±0.095;P7,SNAP-25+/+(n =3)1±0.023,SNAP-25+/−(n =3)0.978±0.051;P14-30,SNAP-25+/+(n =6)1±0.087,SNAP-25+/−(n =6)1.081±0.115;adult,SNAP-25+/+(n =2)1±0.227,SNAP-25+/−(n =2)0.909±0.090)(F )Western blotting analysis of GAP43expression in mice cortices at early developmental stages (E18,P7)reveals the absence of differences between SNAP-25+/+and SNAP-25+/−mice (E18,SNAP-25+/+(n =5)1±0.099,SNAP-25+/−(n =5)1.183±0.169;P7,SNAP-25+/+(n =4)1±0.085,SNAP-25+/−(n =4)1.093±0.102).(G )Western blotting analysis of SNAP-25+/+and SNAP-25+/−adult cortices shows absence of major alterations in the expression of different brain markers.Cerebral Cortex February 2014,V 24N 2367at Lanzhou University on April 14, 2015/Downloaded fromrevealed that heterozygous mice displayed frequent spikes of high amplitude (Fig.4A –C ),which,however,did not lead to spontaneous seizures.In only one case (a het mouse display-ing 365spikes/24h),we could observe occurrence of general-ized seizures following handling.Abnormal EEG pattern was observed in all tested SNAP-25+/−mice.The percentage of SNAP-25+/−mice showing abnormal discharges was signi fi-cantly larger than of SNAP-25+/+mice (Fig.4C ).Epileptiform discharges were also detected by EEG electrodes positioned at hippocampal level (not shown).Furthermore,SNAP-25+/−mice were more susceptible to seizures induced by kainate(KA).Figure 4D shows the time-course of the behavioral response of SNAP-25+/+and SNAP-25+/−mice to 35mg/kg KA over a 3-h period after i.p.administration.In all mice,this dose of KA resulted within the first 10min in immobility and staring,followed by head bobbing and isolated limbic motor (Stage 4)seizures,characterized by forelimb clonus and rearing.Overall,latency to the first Stage 4seizure did not differ between SNAP-25+/+(18.5±5.5min)and SNAP-25+/−mice (18.2±3.6min;P >0.05,unpaired t -test).However,while SNAP-25+/+animals only displayed isolated limbic motor seizures,SNAP-25+/−mice rapidly progressed toStageFigure 2.Cytoarchitectural analysis of SNAP-25+/+and SNAP-25+/−mice brain.(A –F )Analysis of P2brain.Photomicrographs of Thionin-stained coronal sections of brain from SNAP-25+/+(A )and SNAP-25+/−(B )mice show no difference in size and cytoarchitecture of the main brain structures.High magni fication of developing cortices reveal comparable cortical lamination (D and F ).CB expression in hippocampus shows the same pattern of distribution (C and E ).(G –Z )Analysis of adult brain.Photomicrographs of Thionin-stained coronal sections of brain reveal comparable main brain structures,cortex,hippocampus and thalamus,in SNAP-25+/+(G )and SNAP-25+/−(H )mice.The thickness and layering of the cortices are not altered in SNAP-25+/−mice (I and J )as con firmed by immunostaining for the anti-nonphosphorylated neuro filaments SMI311(N and O ).Similar pattern of CB immunoreactivity is evident in SNAP-25+/+(L )and SNAP-25+/−(M ):note CA1and CA2pyramidal layers,mossy fibers and dentate gyrus intensely stained.The labeling for CCK (P and Q )and CR (R and S ),mainly localized in the molecular layer of dentate gyrus,is identical in SNAP-25+/+and SNAP-25+/−mice.High magni fication images of dentate gyrus,show NPY (U and V )and DCX (Y and X )immunoreactivity in the polymorphic layer and in the subgranular zone respectively.No gross difference in synaptic excitatory (vGlut1,red)and inhibitory (vGAT ,green)pattern is detectable in CA1hippocampal regions (K and T ).vGlut2staining of the barrel cortex in SNAP-25+/+and SNAP-25+/−mice (Y and Z ).Scale bar =3mm for A and B ;300µm for C ,E ;400µm for D ,F ;2,4mm for G ,H ;330µm for I ,J ,N ,O ;20µm for K ,T ;450µm for L ,M ;510µm for P ,Q ;490µm for R ,S ;230µm for U-X ;250µm for Y ,Z .368Altered EEG and memory in SNAP-25+/−mice•Corradini et al.at Lanzhou University on April 14, 2015/Downloaded from。

英语联合国有组织的核心磋商环节发言稿全文共3篇示例，供读者参考篇1Honored Representatives, Distinguished Delegates, Ladies and Gentlemen,It is with profound humility and sincere gratitude that I stand before you today, a student granted the extraordinary privilege of addressing this august assembly. In a world grappling with unprecedented challenges, it is imperative that the voices of the youth are not merely heard but actively engaged, for we are the architects of tomorrow's reality.Our planet is at a crossroads, facing a multitude of crises that transcend national boundaries and generational divides. The climate emergency looms large, threatening the very existence of countless species, including our own. Ecological degradation, resource depletion, and the loss of biodiversity have reached alarming levels, jeopardizing the delicate balance upon which all life depends.Yet, amidst this turmoil, we must not succumb to despair, for it is through collective action and unwavering resolve that wecan forge a path towards a sustainable and equitable future. The United Nations, a beacon of hope and a symbol of international cooperation, must lead the charge in this endeavor, ensuring that no one is left behind.It is imperative that we prioritize the implementation of the Paris Agreement and the Sustainable Development Goals, not merely as abstract ideals but as tangible, measurable objectives. We must hold nations accountable for their commitments, fostering transparency and mutual support in the pursuit of a carbon-neutral global economy. Failure to do so would be a betrayal of the trust placed in us by future generations.Furthermore, we must acknowledge the inextricable link between environmental degradation and socioeconomic disparities. Poverty, conflict, and human rights abuses often serve as catalysts for ecological destruction, while simultaneously being exacerbated by its consequences. It is a vicious cycle that must be broken through a holistic approach that addresses the root causes of these interconnected challenges.Education, my esteemed colleagues, is the cornerstone upon which we can build a more sustainable and equitable world. By empowering individuals with knowledge, critical thinking skills,and a deep appreciation for the intricate web of life, we can cultivate a generation of responsible global citizens. It is incumbent upon us to ensure that quality education is accessible to all, regardless of socioeconomic status, gender, or geographic location.Moreover, we must foster an environment that encourages innovation and entrepreneurship, particularly in the realm of clean technologies and sustainable solutions. By harnessing the power of human ingenuity and the boundless potential of the digital age, we can unlock new avenues for economic growth that are in harmony with the natural world.Yet, our efforts must extend beyond the confines ofnation-states and embrace a truly global perspective. We live in an interconnected world, where the actions of one nation can have profound implications for all. It is therefore imperative that we strengthen international cooperation, fostering open dialogue, sharing knowledge and best practices, and forging partnerships that transcend political ideologies and cultural divides.To the esteemed representatives gathered here today, I implore you to act with urgency and conviction. The weight of history rests upon your shoulders, and the fate of generationsyet unborn hangs in the balance. Let us not be paralyzed by the enormity of the challenges we face, but rather be emboldened by the knowledge that through collective action, we can overcome any obstacle.To my fellow youth, I call upon you to raise your voices, to demand action, and to be the catalysts for change. We are the torchbearers of hope, the inheritors of this planet, and the custodians of its future. Let us embrace our roles with unwavering determination, for it is only through our collective efforts that we can create a world where sustainability and equity are not mere aspirations, but living realities.In the words of the great Nelson Mandela, "It always seems impossible until it's done." Let us, together, make the impossible a reality, for the sake of our planet, for the sake of humanity, and for the sake of generations yet to come.Thank you, and may our collective efforts be guided by wisdom, compassion, and an unwavering commitment to a better world.篇2Distinguished Delegates, Ladies and Gentlemen,It is with great honor and humility that I stand before you today to address this esteemed body on the core consultations surrounding the vital work of our United Nations. As a student representative, I carry the voices and aspirations of millions of young people around the world who look to this institution as a beacon of hope for a more just, peaceful, and sustainable future.The United Nations was founded on the ashes of two world wars, born from the collective desire to prevent such atrocities from ever happening again. It was a bold and audacious vision, one that recognized the inherent dignity and worth of every human being, and the interconnectedness of our fates as a global community.Over the past seven decades, the UN has played a pivotal role in shaping the course of human history. From mediating conflicts and promoting disarmament, to advancing human rights and fostering economic and social development, the UN's impact has been far-reaching and profound.However, as we gather here today, we must acknowledge that our world is facing unprecedented challenges that test the very foundations of our global order. Climate change, armed conflicts, rising inequalities, and the erosion of democratic normsthreaten to unravel the hard-won gains of the past and imperil the future we wish to build.It is in this context that the core consultations at the United Nations take on even greater significance. For it is through these deliberations that we can forge a collective vision, a shared blueprint for action that transcends national boundaries and speaks to our common humanity.The core consultations must be a space for open and honest dialogue, where diverse perspectives are not only heard but embraced. We must resist the temptation to retreat into silos of self-interest, for the challenges we face demand a truly global response.As we engage in these consultations, we must be guided by the principles enshrined in the UN Charter – principles of sovereignty, territorial integrity, and non-interference, but also of human rights, sustainable development, and the peaceful resolution of disputes.We must also recognize that the world has changed dramatically since the UN's inception, and our institution must adapt to remain relevant and effective. The rise of non-state actors, the growing influence of technology, and the changingdynamics of geopolitical power all necessitate a reimagining of the UN's role and structure.At the same time, we must not lose sight of the fundamental values that underpin our work – values of justice, equality, and human dignity. These are not mere abstractions but the bedrock upon which a stable and prosperous world order must be built.As a student representative, I am acutely aware of the profound impact that the decisions made within these halls will have on the lives of young people around the world. It is our generation that will inherit the consequences of the actions taken today, both the triumphs and the failures.We, the youth, are not mere spectators in this process, but active participants and stakeholders. We bring a unique perspective, a sense of urgency, and a willingness to embrace bold and innovative solutions.It is our duty, our moral imperative, to ensure that the voices of young people are amplified and their concerns are given due consideration. For it is the youth who will bear the brunt of the challenges we face, from climate change to the erosion of economic opportunities.We must also acknowledge that the youth are not a monolithic bloc, but a diverse tapestry of experiences, cultures, and aspirations. Our consultations must be inclusive, embracing the perspectives of young people from all corners of the globe, regardless of their backgrounds or circumstances.As we engage in these core consultations, let us be guided by a spirit of collaboration, a recognition that our fates are inextricably linked, and that the challenges we face can only be overcome through collective action.Let us draw inspiration from the words of the UN Charter, which affirms our "faith in fundamental human rights, in the dignity and worth of the human person, in the equal rights of men and women and of nations large and small."Let us renew our commitment to the ideals of peace, justice, and human solidarity, and work tirelessly to build a world where every individual, regardless of their circumstances, has the opportunity to live a life of dignity, freedom, and fulfillment.The task before us is daunting, but our collective resolve is unshakable. For it is in the crucible of adversity that the true strength of our global community is forged.Let us seize this moment, this opportunity to shape the course of history, and leave a legacy that future generations will look back upon with pride and gratitude.Thank you.篇3Honorable Chairs, Distinguished Delegates,It is with great honor that I stand before you today as the representative for the Republic of Nauru. Our small island nation in the Pacific may be diminutive in land area, but the issues we face loom as large as any confronting the international community.The topic of today's consultation - achieving the Sustainable Development Goals related to climate action, life below water, and affordable and clean energy by 2030 - strikes at the very heart of threats to my country's existence. The harsh reality is that the Republic of Nauru is on the front lines of climate change impacts driven by the unabated emissions of greenhouse gases from large industrialized nations.As an island nation with a mean elevation of only 4 meters above sea level, we face the terrifying prospect of complete inundation and loss of total sovereignty if dramatic action is nottaken immediately to curb global temperature rise. The latest reports from climate scientists make it clear - if emissions continue at the current rate, most of the land mass of my country will be swallowed by the rising Pacific waters within the next few decades, rendering Nauru uninhabitable.This looming catastrophe is not due to any actions by my people. We are among the lowest emitters of greenhouse gases on the planet. Rather, it is the direct result of the heavy reliance on dirty fossil fuels and environmentally destructive policies prioritized by the largest, wealthiest nations who have been the primary drivers of climate change since the start of the industrial age over 200 years ago.The injustice we face is appalling. Why should the Nauruan people have to surrender our ancestral homeland, our cultural identity, and our way of life, all because of the negligent actions of others on the other side of the world? It defies all principles of equity and ethical behavior between nations. We did not choose this path, yet we are condemned to a harsh sentence of extreme suffering, displacement, and potential extinction if comprehensive action is not taken globally with the utmost urgency.I implore this assembly - we cannot allow the Republic of Nauru to be rendered the first indelible loss of an entire nation state due to climate change. Such a historic tragedy would be an unacceptable stain on the collective conscience of the world, and would permanently undermine the credibility of the international institutions tasked with resolving issues of global peace and security.The time for hollow gestures and insincere rhetoric has passed. We require firm, binding commitments from all nations, particularly those with high per capita emissions and those that possess the technological and economic capacity for rapid transformation, to take dramatic steps to curb emissions and invest in renewable energy infrastructure and carbon capture. Words alone are meaningless without measurable action and accountability.The global commitments made thus far through mechanisms like the Paris Climate Accords, while positive initial steps, fall drastically short of the scale of action required based on the latest data. We cannot afford the world to miss the 2030 targets for SDGs related to climate action, ocean health, and clean energy, as that will likely constitute a point of no return,spelling catastrophe for my nation and several others in a similar precarious situation.Beyond the direct climate threats, Nauru faces immense challenges in relation to the SDGs on ocean conservation and sustainable ocean-based economies. As a nation almost entirely reliant on the bounty of the Pacific Ocean, we have witnessed firsthand the rapid depletion of marine stocks due to unsustainable industrial fishing practices by external commercial fleets. Overfishing and bycatch have decimated our coral reefs and pelagic fish populations that our traditional way of life has depended on for countless generations.The loss of our marine ecosystems, coupled with the warming, acidification, and pollution of our surrounding ocean environment due to carbon emissions, plastics, and other human factors, poses an existential risk not just to our sovereignty, but our basic ability to source adequate nutrition and develop a sustainable economic foundation.We call on the international community to take stronger stances against illegal, unreported, and unregulated fishing that is rapidly stripping the global ocean environment of its abundance. There must be enhanced cooperation through binding international frameworks, aggressive enforcementthrough monitoring and identification of bad actors, and significant financial consequences for nations that turn a blind eye to these practices within their jurisdictions.Additionally, we urge wealthier nations to contribute significant financial and technological resources to assist small island states like Nauru in developing sustainable marine conservation, aquaculture, and renewable energy programs that can serve as economic foundations after our fossil fuel reserves have been depleted.The Republic of Nauru understands that the path ahead will be challenging and complex, but we have an unshakable ethical obligation to our people and to humanity as a whole to pursue the most ambitious possible agenda to rapidly reduce emissions, protect our oceans, and transition to clean energy in order achieve the Sustainable Development Goals in these critical areas. The fate of countless communities like ours depends on the willingness of all nations in this assembly to take on this great challenge with courage and resolve.Talk, my friends, is cheap in the face of this crisis. We demand true leadership and true commitment through binding actions and accountability for the wealthiest polluters. Too many innocent lives across the Pacific, the Arctic, and all coastalregions hang in the balance to accept anything less. The course we set at this consultation and beyond will quite literally determine if the Republic of Nauru and several other nations survive as coherent societies and cultures in the decades ahead. I implore this assembly not to be the authors of such a historic and ethically indefensible tragedy.I yield the floor, but the world is watching and countless futures hang on the courage of our collective actions. Thank you.。

CHIN.PHYS.LETT.Vol.25,No.2(2008)517Truncated States Obtained by Iteration∗W.B.Cardoso 1∗∗,N.G.de Almeida 21Instituto de F´ısica,Universidade Federal de Goi´a s,74.001-970,Goiˆa nia (GO),Brazil2N´u cleo de Pesquisas em F´ısica,Universidade Cat´o lica de Goi´a s,74.605-220,Goiˆa nia (GO),Brazil.We introduce the concept of truncated states obtained via iterative processes (TSI)and study its statisticalfeatures,making an analogy with dynamical systems theory (DST).As a specific example,we have studied TSI for the doubling and the logistic functions,which are standard functions in studying chaos.TSI for both the doubling and logistic functions exhibit certain similar patterns when their statistical features are compared from the point of view of DST.PACS:42.50.−p,42.65.SfQuantum state engineering is an area of grow-ing importance in quantum optics,its relevance ly-ing mainly in the potential applications in other areas of physics,such as quantum teleportation,[1]quantum computation,[2]quantum communication,[3]quantum cryptography,[4]quantum lithography,[5]decoherence of states,[6]and so on.To give a few examples of their usefulness and relevance,quantum states arise in the study of quantum decoherence effects in mesoscopic fields;[7]entangled states and quantum correlations;[8]interference in phase space;[9]collapses and revivals of atomic inversion;[10]engineering of (quantum state)reservoirs;[11]etc.Also,it is worth mentioning the importance of the statistical properties of one state in determining some relevant properties of another,[12]as well as the use of specific quantum states as input to engineer a desired state.[13]The dynamical systems theory (DST)is an area whose interest lies mainly in nonlinear phenomena,the source of chaotic phenomena.DST groups of several approaches to the study of chaos,involving Lyapunov exponent,fractal dimension,bifurcation,and sym-bolic dynamics among other elements.[14]Recently,other approaches have been considered,such as in-formation dynamics and entropic chaos degree.[15]In this Letter,we propose a truncated state with coefficients obtained via iterative process (TSI)and we study its statistical properties.We note that un-like previous states studied in the literature,[16]each coefficient of the TSI is obtained from the previous one by iteration of a function.Features of this state are studied by analysing several of its statistical prop-erties in different regimes (chaotic versus nonchaotic)according to DST,and for some iterating functions,we find properties of TSI very sensitive (resembling chaos)to the first coefficient C 0,which is used as a seed to obtain the remaining C n .We define TSI as |T SI =∑Nn =0C n |n ,where C n is the normalized complex coefficient obtained as then th iteration of a previously given generating func-tion.For example,given C 0,C n can be the n th iterateof the quadratic functions:C n (µ)=C 2n −1+µ;sine functions:C n (µ)=µsin(C n −1);logistic functions C n (µ)=µC n −1(1−C n −1);exponential functions:C n =µexp(C n −1);doubling function defined on the interval [0,1):C n =2C n −1mod 1,and so on,µbeing a parameter.It is worth recalling that all the functions in the above list are familiar to researchers in the field of dynamical systems theory (DST).For example,for some values of µ,it is known that some of these func-tions can behave in quite a chaotic manner.[14]Also,note that by computing all C n we are in fact determin-ing the orbit of a given function,and because the C n and P n ,the photon number distribution,are related by P n =|C n |2,fixed or periodic points of a function will correspond to fixed or periodic P n .Rather than studying all the functions listed in this section,we focus on the doubling function and the logistic func-tion.These two functions have been widely used to understand chaos in nature.As we will see in the fol-lowing,although very different from each other,these functions give rise to different TSI having similar pat-terns.Since the expansion of TSI is known in the number state |n ,we haveP n =|C n |2.(1)Figures 1(a)and 1(b)show the plots of the photon-number distribution P n versus n for TSI using the doubling function.The Hilbert space dimension is N =50.In order to illuminate the behaviour of TSI for different values of C 0,we take C 0as 0.3and 0.29711,respectively,shown in Figs.1(a)and 1(b).Note the regular behaviour for C 0=0.3and rather an irregular,or chaotic,behaviour for C 0=0.29711.Figures 2(a)and 2(b)show P n for the logistic func-tion.For C 0=0.2and µ=3.49the logistic func-tion behaves regularly (Fig.2(a)),showing clearly (as∗Supportedby the CNPq,Brazilian Agency,and VPG-Vice-Reitoria de P´o s Gradua¸c ˜a o e Pesquisa da Universidade Cat´o lica deGoi´a s.∗∗Email:wesleybcardoso@c2008Chinese Physical Society and IOP Publishing Ltd518W.B.Cardoso et al.Vol.25 in the case of the doubling-function)four values forP n;by contrast,forµ=4and C0=0.2,P n oscil-lates quite irregularly(Fig.2(b)).This is because thephoton number distribution is equivalent to the orbitof the TSI dynamics.[14]Thus,once afixed-attractingor periodic-point is attained,the subsequent coeffi-cients,and hence the subsequent P n,will behave in aregular manner.Conversely,when nofixed point ex-ists,P n will oscillate in a chaotic manner.Therefore,by choosing suitable C0and/orµ,we can comparethe properties of TSI when different regimes(chaoticversus nonchaotic)in the DST sense are encountered.Note the similarity between the properties of the logis-tic and the doubling functions when the DST regimesare the same.Interestingly,these similarities are ob-served when other properties are analysed,as we will see in the following.Fig.1.Photon number distribution for the doubling func-tion with(a)C0=0.3and(b)C0=0.29711.Fig.2.Photon number distribution for the logistic func-tion with(a)C0=0.2andµ=3.49and(b)C0=0.2and µ=4.The functions P odd and P even represent the pho-ton number distribution for n odd and even,respec-tively,given by Eq.(1).It is well established in quantum optics[17]that if P odd>0.5the Glauber–Sudarshan P-function assumes negative values,pro-hibited in the usual probability distribution func-tion,and the quantum state has no classical ana-logue.Since P odd+P even=1,the same is true when P even<0.5.Figure3(a)and3(b)show the behaviour ofP odd for C0=0.3and C0=0.29711for the dou-bling function the Hilbert space N is increased.Fig-ure4(a)and4(b)refer to the logistic function for µ=3.49andµ=4.In Figs.3(a)and4(a)(corre-sponding to a nonchaotic regime in DST),note that TSI has a classicalanalogue as N increases.From Figs.3(a)and3(b)(corresponding to a chaotic regime in DST),TSI can behave as a nonclassical state,de-pending on N.More interestingly,note the following pattern:whenever the coefficients of TSI correspond to the nonchaotic regime in DST,P odd(and so P even) will remain above or below0.5on a nearly monotonic curve,as seen in Figs.3(a)and4(a);whenever the co-efficients of TSI correspond to the chaotic regime in DST,P odd(and so P even)will tend to oscillate around 0.5(Figs.3(b)and4(b)).Fig.3.(a)Even(solid)and odd(dots)photon number distributions for the doubling function for C0=0.3to co-incide with the nonchaotic behaviour in the DST sense.(b)Even(solid)and odd(dots)photon number distribu-tions for the doubling function for C0=0.29711is chosen to coincide with chaotic behaviour in the DST sense.Fig.4.(a)Even(solid)and odd(dots)photon number distributions for the logistic function for C0=0.2and µ=3.49to coincide with nonchaotic behaviour in the DST sense.(b)Even(solid)and odd(dots)photon num-ber distributions for the logistic function for C0=0.2and µ=4to coincide with chaotic behaviour in the DST sense.The average number ˆn and the variance ∆ˆn in TSI are obtained straightforwardly from ˆn =∑Nn=0P(n)n,and ∆ˆn =√ˆn2 − ˆn 2.Figure5(a) shows the plot of ˆn and Fig.5(b)the plot of ∆ˆn as functions of the dimension N of Hilbert space,for the doubling function.Note the near linear behaviour of the average photon number and its variance as N increases for C0=0.3(nonchaotic regime in DST); this is not seen when C0=0.29711(chaotic regime in DST).Figures6(a)and6(b)for the logistic function show essentially the same behaviour when these two DST regimes are shown together.The Mandel Q parameter is defined as Q=(∆ˆn2−No.2W.B.Cardoso et al.519 ˆn )/ ˆn ,while the second order correlation function isg(2)(0)=( ˆn2 − ˆn )/ ˆn 2,and for Q<0(Q>0)thestate is said to be sub-Poissonian(super-Poissonian).Also,the Q parameter and the second order correla-tion function g(2)are related by[18]Q=[g(2)(0)−1]ˆn .(2)Fig.5.(a)Average photon number for the doubling func-tion for C0=0.3(dots)and C0=0.29711(solid).(b) Variance of the photon number for the doubling function for C0=0.3(dots)as well as C0=0.29711(solid).Fig.6.(a)Average photon number for the logistic func-tion for C0=0.2withµ=3.49(dots)orµ=4(solid).(b)Variance of the photon number for the logistic functionfor C0=0.2withµ=3.49(dots)orµ=4(solid).If g(2)(0)<0,then the Glauber–Sudarshan P-function assumes negative values,outside the range of the usual probability distribution function.More-over,by Eq.(2)it is readily seen that g(2)(0)<1 implies Q<0.As for a coherent state Q=0,a given state is said to be a“classical”one if Q>0.Fig-ures7(a)–8(b)show the plots of the Q parameter and the correlation function g(2)(0)versus N,for both the doubling and the logistic functions.Note that TSI is predominantly super-Poissonian for these two func-tions(Q>0and g(2)(˙0)>1),thus being a“classical”state in this sense for N 12,while for small values of N(N<12),the Q parameter is less than0,showing sub-Poissonian statistics and is thus associated with a “quantum state”.From Figs.7(a)and8(a),note that using C0=0.3for the doubling function,C0=0.2and µ=3.49for the logistic function(nonchaotic regime in DST),Q shows a linear dependence on N.How-ever,using C0=0.29711for the doubling function, C0=0.2andµ=4for the logistic function(chaotic regime in DST),Q oscillates irregularly.Similarly,from Figs.7(b)and8(b),using C0=0.3for the dou-bling function,C0=0.2andµ=3.49for the logis-tic function,we see that g(2)(0)increases smoothly, while using C0=0.29711for the doubling function, C0=0.2andµ=4for the logistic function,the rise of g(2)(0)is rather irregular.This pattern is observed for other C0as input as well as for other values of the parameterµ,and whenever the dynamics is chaotic (regular),the Q parameter and the g(2)(0)correlation function oscillate irregularly(regularly).The same can be said about the transition from sub-Poissonian to super-Poissonian statistics around N=12.TSI can be generated in various contexts,as for example trapped ions,[19]cavity QED,[13,20]and trav-elling wave-fields.[21]A similar example for generation of TSI in travelling waves can be found in Ref.[22], where we proposed the truncated state with random coefficients(TSRC)and a scheme for its generation, including the possible imperfections in the beam split-ters and detectors.Fig.7.(a)Q parameter for the doubling function for C0=0.3(dots)and C0=0.29711(solid);(b)second order correlation function for the doubling function for C0=0.3(dots)and C0=0.29711(solid).Fig.8.(a)Q parameter for the logistic function for C0=0.2withµ=3.49(dots)andµ=4(solid);(b) second order correlation function for the logistic function for C0=0.2,withµ=3.49(dots)andµ=4(solid).In conclusion,to characterize the TSI for the dou-bling and logistic functions we have studied various of its features,including some statistical properties, as well as the behaviour of these features when the dimension N of Hilbert space is increased.Interest-ing,we have found a transition from sub-Poissonian statistics to super-Poissonian statistics when N is rel-atively small(N∼12).A similar behaviour is found in Ref.[22].This opens a new perspective for future520W.B.Cardoso et al.Vol.25studies related to the transition from quantum to clas-sical behaviour depending on the size of the Hilbert parison between the properties of the states with coefficients generated through the logistic and double functions shows the similar behaviour.As afinal remark,we leave the following questions:Does every truncated state present the same transition be-haviour in N∼12?Can the statistical properties of TSI be significantly different so that they can be used in communication protocols?References[1]Bennett C H et al1993Phys.Rev.Lett.701895[2]Kane B E1998Nature393143[3]Pellizzari T1997Phys.Rev.Lett.795242[4]Gisin N et al.2002Rev.Mod.Phys.74145[5]Bj¨o rk G and Sanchez-Soto L L2001Phys.Rev.Lett.864516M¨u tzel M et al2002Phys.Rev.Lett.88083601[6]Zurek W H1991Phys.Today4436Gerry C C and Knight P L1997Am.J.Phys.65964Varcoe B T H et al2000Nature403743[7]Raimond J M et al1996Phys.Rev.Lett.791964;Osnaghi S et al2001Phys.Rev.Lett.8737902[8]Brune M et al1996Phys.Rev.Lett.774887[9]Bennett C H and Vicenzo D P2000Nature404247Ekert A K1991Phys.Rev.Lett.67661[10]Narozhny N B et al1981Phys.Rev.A23236Rempe G et al1987Phys.Rev.Lett.58353[11]Poyatos J F et al1996Phys.Rev.Lett.774728[12]Barnett S M and Pegg D T1996Phys.Rev.Lett.764148[13]Serra R M et al2000Phys.Rev.A6243810[14]Devaney R L1989An Introduction to Chaotic DynamicalSystems2nd edn(Redwood City,CA:Addison-Wesley)[15]Ohya M1998Int.J.Theor.Phys.37495[16]Dodonov V V2002J.Opt.B4R1[17]Mandel L and Wolf E1995Optical Coherence and Quan-tum Optics(Cambridge:Cambridge University Press) [18]Walls D F and Milburn G J1994Quantum Optics(Berlin:Springer)[19]Serra R M et al2001Phys.Rev.A63053803[20]Vogel k1993Phys.Rev.Lett.711816Moussa M H Y and Baseia B1998Phys.Lett.A238223[21]Dakna M et al1999Phys.Rev.A591658[22]Cardoso W B and de Almeida N G2006Phys.Lett.A356104。

2019年9月18日GRE填空真题答案（回忆）填空1. As a historical genre, biography is best when _____, a careful reconstruction of the past in all its unfamiliar particularity.A. introspectiveB. reflectiveC. concreteD. conciseE. meticulousF. thorough2. Despite the occasional (i)_____ of their venues, the culture of corporate conferences is a deeply (ii)_____ conference, each day consisted of nearly nine hours of continuous lectures and panels enlivened by pleasantries or anything that could be construed as a joke. The only(iii)_____ sensory deprivation of the sessions came from the handsome color slides favored by the corporate presenters.A. seclusionD. sycophanticG. allusion toB. opulenceE. asceticH. ramification ofC. enormityF. mercenaryI. respite from3.There are great _____ in countries’ greenhouse gas emissions, especially in per capita terms： while the United States and China are similar in aggregate emissions, United States per capita emissions are a huge multiple of China’s.A. distortionsB. disparitiesC. fluctuationsD. advancesE. variancesF. vacillations4. The building affairs minister rightly recognizes that the current planning system—under which the government controls every aspect of construction—creates disastrous developments, but she is wrong to propose the opposite： the wholesale(i)_____ of the building market. Such a complete (ii)_____ of responsibility on the part of the state can hardly be in the public’s interest.A. liberalizationD. abnegationE. recapitulationC. regulationF. accretion5. Motivation is the hardest of all managerial tasks, and it is _____ to expect a single memo, no matter how well crafted, to have much effect on the staff’s attitude.A. ingeniousB. reasonableC. fancifulD. scrupulousE. radical6. The notion of film producers as the ogres of the movie business has proved an (i)_____ one, but according to The Producers by Tim Adler, it is not always grounded in reality. Attacking what he calls the “auteur myth”—the idea of the director as the single purveyor of art in an industry otherwise peopled with (ii)_____—he places at the heart of his book an image of the producer, not the director, as the primary (iii)_____ force in the development and production of a movie.（此题在考试时已经改成了双空题）A. accurateD. visionariesG. financialE. profitmongersH. inertialC. enduringF. innocentsI. creative7. Since the 1920s, historical fiction writers in China have emancipated the genre from the traditional notion that(i)_____ was the ultimate goal of history writing. Yet the traditional commitment to (ii)_____ was not simply (iii)_____：this new genre was expected to capture the essence ofhistorical truth even as it allowed space for the writer’s imagination.A. comprehensivenessD. veracityG. jettisonedB. factualityE. thoroughnessH. rationalizedC. entertainmentF. pleasureI. acknowledged。

a r X i v :h e p -p h /0303187v 1 21 M a r 2003hep-ph/0303187March,2003Determining γusing B ±→DK ±with multibody D decaysAnjan Giri,1Yuval Grossman,1Abner Soffer,2and Jure Zupan 1,31Department of Physics,Technion–Israel Institute of Technology,Technion City,32000Haifa,Israel2Department of Physics,Colorado State University,Fort Collins,CO 805233J.Stefan Institute,Jamova 39,P.O.Box 3000,1001Ljubljana,Slovenia Abstract We propose a method for determining γusing B ±→DK ±decays followed by a multibody D decay,such as D →K S π−π+,D →K S K −K +and D →K S π−π+π0.The main advantages of the method is that it uses only Cabibbo allowed D decays,and that large strong phases are expected due to the presence of resonances.Since no knowledge about the resonance structure is needed,γcan be extracted without any hadronic uncertainty.I.INTRODUCTIONThe theoretically cleanest way of determining the angleγ=arg(−V ud V∗ub/V cd V∗cb),(1)is to utilize the interference between the b→c¯u s and b→u¯c s decay amplitudes[1–12].Be-cause these transitions involve only distinct quarkflavors,there are no penguin contributions to these decays.In the original idea by Gronau and Wyler(GW)[3]the B±→D CP K±decay modes are used,where D CP represents a D meson which decays into a CP eigen-state.The dependence onγarises from the interference between the B±→D0K±and B±→D0K±decay rates.In practice,however,measuringγin this way is not an easy task.Due to the values of the CKM coefficients and color suppression,the ratio between the two interfering amplitudes, r B[see Eq.(4)],is expected to be small,of order10%−20%.This reduces the sensitivity to γ,which is roughly proportional to the magnitude of the smaller amplitude.In addition,if the strong phases vanish,measuringγmakes use of terms of order r2B.In contrast,if a large strong phase is involved in the interference,there is a sensitivity toγat order r B with most methods.Thus,in general,having large interfering amplitudes with large relative strong phases is a favorable situation.Since the hadronic parameters are not yet known,it is still not clear which of the proposed methods is more sensitive.In addition,all the methods are expected to be statistically limited.It is therefore important to make use of all modes and methods,as well as to try tofind new methods.Any new method that is based on“unused”decay channels increases the total statistics.Moreover,many of the analyses are sensitive to common hadronic parameters,for example,r bining them will increase the sensitivity of the measurement by more than just the increase in statistics.Here we study the possibility to use B±→DK±,followed by a multibody D decay,in order to cleanly determineγ.While this idea was already discussed in[5],most of our results and applications are new.For the sake of concreteness,we concentrate on the D→K Sπ−π+ decay mode.The advantage of using such decay chains is threefold.First,one expects large strong phases due to the presence of resonances.Second,only Cabibbo allowed D decay modes are needed.Third,thefinal state involves only charged particles,which have a higher reconstruction efficiency and lower background than neutrals.The price one has to pay is that a Dalitz plot analysis of the data is needed.We describe how to do the Dalitz plot analysis in a model-independent way,and explore the advantages gained by introducingverifiable model-dependence.Thefinal balance between the advantages and disadvantages depends on yet-to-be-determined hadronic parameters and experimental considerations.II.MODEL INDEPENDENT DETERMINATION OFγAs we shall show in this section,to perform a model independent determination of the angleγone needs to measure the two CP-conjugate decay modes,B±→DK±→(K Sπ−π+)D K±and to perform a Dalitz plot analysis of the K Sπ−π+final state originating from the intermediate D meson.(In the following discussion we neglect D0−¯D0mixing, which is a good approximation in the context of the Standard Model.See appendix A for details.)Let usfirst focus on the following cascade decayB−→DK−→(K Sπ−π+)D K−,(2) and define the amplitudesA(B−→D0K−)≡A B,(3)A(B−→D0K−)is color suppressed and cannot be determined from experiment in this way[4].The color suppression together with the experimental values of the ratio of the relevant CKM elements leads to the theoretical expectation r B∼0.1−0.2(see recent discussion in[11]).For the three-body D meson decay we defineA D(s12,s13)≡A12,13e iδ12,13≡A(D0→K S(p1)π−(p2)π+(p3))=A(equality the CP symmetry of the strong interaction together with the fact that thefinal state is a spin zero state has been used.With the above definitions,the amplitude for the cascade decay isA(B−→(K Sπ−π+)D K−)=A B P D A D(s12,s13)+r B e i(δB−γ)A D(s13,s12) ,(6) where P D is the D meson propagator.Next,we write down the expression for the reduced partial decay widthdˆΓ(B−→(K Sπ−π+)D K−)= A212,13+r2B A213,12+2r B R e A D(s12,s13)A∗D(s13,s12)e−i(δB−γ) dp,(7) where dp denotes the phase space variables,and we used the extremely accurate narrow width approximation for the D meson propagator.In general,there is no symmetry between the two arguments of A D in Eq.(6),and thus in the rates over the Dalitz plot.A symmetry would be present if,for instance,the three-body D decay proceeded only throughρ-like resonances.We emphasize,however,that the product A D(s12,s13)A∗D(s13,s12)in the interference term in Eq.(7)is symmetric under the exchange s12↔s13followed by complex conjugation.This fact is used to simplify the analysis.The moduli of the D decay amplitude A12,13can be measured from the Dalitz plot of the D0→K Sπ−π+decay.To perform this measurement theflavor of the decaying neutral D meson has to be tagged.This can be best achieved by using the charge of the soft pion in the decay D∗+→D0π+.However,the phaseδ12,13of the D meson decay amplitude is not measurable without further model dependent assumptions.The cosine of the relevant phase difference may be measured at a charm factory(see section III).If the three-body decay D0→K Sπ−π+is assumed to be resonance dominated,the Dalitz plot can befit to a sum of Breit-Wigner functions,determining also the relative phases of the resonant amplitudes.This is further discussed in section IV.Here we assume that no charm factory data is available and develop the formalism without any model dependent assumptions.Using the trigonometric relation cos(a+b)=cos a cos b−sin a sin b,the last term of(7) can be written asR e A D(s12,s13)A∗D(s13,s12)e−i(δB−γ) =(8) A12,13A13,12[cos(δ12,13−δ13,12)cos(δB−γ)+sin(δ12,13−δ13,12)sin(δB−γ)]. Obviously,to compare with the data,an integration over at least some part of the Dalitz0.51 1.52 2.53s120.511.522.53s13FIG.1:The partitions of Dalitz plot as discussed in text.The symmetry axis is the dashed line.On theaxes we have s 12=m 2K s π−and s 13=m 2K s π+in GeV 2.plot has to be performed.We therefore partition the Dalitz plot into n bins and definec i ≡ idp A 12,13A 13,12cos(δ12,13−δ13,12),(9a)s i ≡ idp A 12,13A 13,12sin(δ12,13−δ13,12),(9b)T i ≡ idp A 212,13,(9c)where the integrals are done over the phase space of the i -th bin.The variables c i and s i contain differences of strong phases and are therefore unknowns in the analysis.The variables T i ,on the other hand,can be measured from the flavor tagged D decays as discussed above,and are assumed to be known inputs into the analysis.Due to the symmetry of the interference term,it is convenient to use pairs of bins that are placed symmetrically about the 12↔13line,as shown in Fig. 1.Consider an even,n =2k ,number of bins.The k bins lying below the symmetry axis are denoted by index i ,while the remaining bins are indexed with ¯i .The ¯i -th bin is obtained by mirroring the i -th bin over the axis of symmetry.The variables c i ,s i of the i -th bin are related to the variables of the ¯i -th bin byc ¯i =c i ,s ¯i =−s i ,(10)while there is no relation between T i and T ¯i .Note that had one used 12↔13symmetric bins centered on the symmetry axis,one would have had s i =0.Together with the information available from the B +decay,we arrive at a set of 4kequationsˆΓ−i≡idˆΓ(B−→(K Sπ−π+)D K−)=T i+r2B T¯i+2r B[cos(δB−γ)c i+sin(δB−γ)s i],(11a)ˆΓ−¯i≡ ¯idˆΓ(B−→(K Sπ−π+)D K−)=T¯i+r2B T i+2r B[cos(δB−γ)c i−sin(δB−γ)s i],(11b)ˆΓ+ i≡idˆΓ(B+→(K Sπ−π+)D K+)=T¯i+r2B T i+2r B[cos(δB+γ)c i−sin(δB+γ)s i],(11c)ˆΓ+¯i≡ ¯idˆΓ(B+→(K Sπ−π+)D K+)=T i+r2B T¯i+2r B[cos(δB+γ)c i+sin(δB+γ)s i].(11d)These equations are related to each other through12↔13and/orγ↔−γexchanges.All in all,there are2k+3unknowns in(11),c i,s i,r B,δB,γ,(12)so that the4k relations(11)are solvable for k≥2.In other words,a partition of the D meson Dalitz plot to four or more bins allows for the determination ofγwithout hadronic uncertainties.This is our main result.Alternatively to this binning,one can use a partition of the Dalitz plot into k bins which are symmetric under12↔13.For that case,s i=0and the set of the4k equations(11) reduces to2k relations(thefirst two and the last two equations in(11)are the same in this case).Then,there are just k+3unknowns to be solved for,which is possible for k≥3. While such binning may be needed due to low statistics,it has several disadvantages,which are further discussed below.When c i=0or s i=0for all i,some equations become degenerate andγcannot be extracted.However,due to resonances,we do not expect this to be the case.Degeneracy also occurs ifδB=0.In this case,γcan still be extracted if some of the c i and/or s i are independently measured,as discussed in the following sections.The optimal partition of the Dalitz plot as well as the number of bins is to be determined once the analysis will be done.Some of the considerations that enter this choice are as follows.First,one would like to have as many small bins as possible,in order that c i and s i do not average out to small numbers.Second,the bins have to be large enough that there are significantly more events than bins.Otherwise there will be more unknowns than observables.There are also experimental considerations,such as optimal parameterization of backgrounds and reconstruction efficiency.III.IMPROVED MEASUREMENT OF c i AND s iSo far,we have used the B decay sample to obtain all the unknowns,including c i and s i ,which are parameters of the charm system.We now discuss ways to make use of high-statistics charm decays to improve the measurement of these parameters,or obtain them independently.Doing so will reduce the number of unknowns that need to be determined from the relatively low-statistics B sample,thereby reducing the error in the measurement of γ.The first improvement in the measurement is obtained by making use of the large sample of tagged D decays,identified in the decay D ∗+→D 0π+,at the B factories.So far we only assumed that we use this data to determine T i .In fact,it can also be used to bound theunknowns c i and s i defined in (9):|s i |,|c i |≤ i dp A 12,13A 13,12≤Dpair.If one D meson is detected in a CP eigenstate decay mode,it tags the other D as an eigenstate of the opposite CP eigenvalue.The amplitude and partial decay width for this state to decay into the final state of interest areA (D 0±→K S (p 1)π−(p 2)π+(p 3))=12(A D (s 12,s 13)±A D (s 13,s 12)),(14)d Γ(D 0±→K S (p 1)π−(p 2)π+(p 3))=1D 0)/√2 i d Γ(D 0+→K S (p 1)π−(p 2)π+(p 3))−i d Γ(D 0−→K S (p 1)π−(p 2)π+(p 3)) .(15)As stated above,obtaining this independent measurements reduces the error in the mea-surement of γby removing k of the 2k +3unknowns.We can further improve the measurement if we take each bin i and further divide it into n i sub-bins,such that the quantities A 12,13,cos(δ12,13−δ13,12),and sin(δ12,13−δ13,12)do not change significantly within each sub-bin i ′.Naively,this statement appears to introduce model dependence.In practice,however,the high statistics in the tagged D sample and the charm factory ψ(3770)sample allow its verification up to a statistical error,which can be measured and propagated to the final measurement of γ.Given this condition,Eq.(9a)may be written asc i= i′c i′= i′A i′A i′)∆p i′= i′ i′cos(δi′−δi′-th sub-bin is the12↔13mirror image of the i′-th sub-bin,A i′andδi′are the values of A12,13andδ12,13on sub-bin i′,taken to be constant throughout the sub-bin, and∆p i′is the area of sub-bin i′.Analogously to Eq.(9c),we have defined the quantities T i′=A212,13∆p i′,which are measured using the tagged D sample.The c i′’s are assumed to be measured at the charm factory,applying(15)to the sub-bin i′.Similarly,Eq.(9b) becomess i= i′ i′sin(δi′−δT i′Ttheoretical,it is expected to be much smaller than the statistical error in the measurement ofγ.It will become a problem only when the B sample is large enough to provide a precision measurement ofγ.By then the tagged D sample will have increased as well,allowing even more precise tests of these assumptions,as well as improving the precision of the methods presented in section III.The decay amplitude can then befit to a sum of Breit-Wigner functions and a constant term.Following the notations of Ref.[20]we writeA D(s12,s13)=A(D0→K S(p1)π−(p2)π+(p3))==a0e iδ0+ r a r e iδr A r(s12,s13),(18)where thefirst term corresponds to the non-resonant term and the second to the resonant contributions.The Breit-Wigner function is defined asA r(s12,s13)=J M r×BW r,(19) where r represent a specific resonance in either the K S(p1)π−(p2),K S(p1)π+(p3)or π−(p2)π+(p3)channel.J M r is the term which accounts for the angular dependence.It depends on the spin J of the resonance.For example,0M r=1and1M r=−2 k1· k3.Herek1, k3are,respectively,the three momenta of one of the particles originating from the res-onance and of the remaining particle,as measured in the rest frame of the two resonating particles[20].BW r corresponds to the relativistic Breit-Wigner function and is given byBW r(s)=1s),(20)where M r is the mass of the r-th resonance andΓr(√V.DISCUSSIONSThe observablesˆΓ±i defined in(11)can be used to experimentally look for direct CP violation.Explicitly,a i CP≡ˆΓ−i−ˆΓ+¯i=4r B sinγ[c i sinδB−s i cosδB],a¯i CP≡ˆΓ−¯i−ˆΓ+i=4r B sinγ[c i sinδB+s i cosδB].(21) It is manifest thatfinite a CP requires non vanishing strong and weak phases.Thefirst terms in the parenthesis in(21)depends on sinδB.This is the same dependence as for a two-body D decays into CP eigenstates.In the second terms,which depend on cosδB,the required strong phase arises from the D decay amplitudes.Due to the resonances,we expect this strong phase to be large.Therefore,it may be that direct CP violation can be established in this mode even before the full analysis to measureγis conducted.With more data,γcan be extracted assuming Breit-Wigner resonances(cf.section IV).Eventually,a model independent extraction ofγcan be done(cf.section II and III).The above proposed method for the model independent measurement ofγinvolves a four-fold ambiguity in the extracted value.The set of equations(11)are invariant under each of the two discrete transformationsPπ≡{δB→δB+π,γ→γ+π},P−≡{δB→−δB,γ→−γ,s i→−s i}.(22) We note that if all the bins used are symmetric under12↔13,the absence of the sin(δB−γ) terms in Eq.(11)introduces a new ambiguity transformation,P ex≡γ→δB,δB→γ.The discrete transformation Pπis a symmetry of the amplitude(6)and is thus an irreducible uncertainty of the method.It can be lifted if the sign of either cosδB or sinδB is known. The ambiguity due to P−can be resolved if the sign of sinδB is known or if the sign of s i can be determined in at least some part of the Dalitz plot.The latter can be done byfitting a part of the Dalitz plot to Breit-Wigner functions.We emphasize that only the sign of the phase of the resonance amplitude is required,and thus we can safely use a Breit-Wigner form for this purpose.The r B suppression present in the scheme outlined above can be somewhat lifted if the cascade decay B−→DX−s→(K Sπ−π+)D X−s is used[6,11].Here X−s is a multibody hadronic state with an odd number of kaons(examples of such modes are K−π−π+,K−π0 and K Sπ−π0).Unlike the B−→other describing the D→K Sπ−π+decay.In appendix C the necessary formalism thatapplies to this case is outlined.Note that the above mentioned treatment for multibody Bdecays also applies to quasi two-body B decays involving a resonance,such as B→DK∗.In addition to using different B modes,statistics may be increased by employing variousD decay modes as well.An interesting possibility is the Cabibbo allowed D→K Sπ−π+π0decay.It comes with an even larger branching ratio than the D→K Sπ−π+decay.Inaddition,it has many intermediate resonances contributing to the greatly varying decayamplitude,which is what is needed for the extraction ofγ.The disadvantages of this modeare the low reconstruction efficiency of theπ0,as well as the binning difficulties introducedby the higher dimensionality of the four-body phase space.The formalism of section IIapplies to this mode as well,but now the partition of the four-body phase space is meantin Eq.(11).In the equivalent of(5),this mode has an extra minus sign,since we haveintroduced a new CP-odd state,theπ0.Thefinal set of equations is then obtained from(11)by replacing r B→−r B.The Cabibbo allowed mode D→K−K+K S may also be used for the extraction ofγ,as can the Cabibbo suppressed decays to K−K+π0,π−π+π0,andK S K+π−.One can also use(almost)flavor eigenstate decay modes,such as D→K−π+π0and D→K−π+π−π+[5].Here,the important interference is between the Cabibbo allowedD.Specifically,one typically requires one Cabibbo allowed decay and anotherthat is doubly Cabibbo suppressed,or two decays that are singly Cabibbo suppressed.Toovercome this preconception,our method makes use of K0−D0decays.In addition,it is important that thehadronic three-body D meson decays have a widely changing amplitude over the Dalitz plot,which is ensured by the presence of resonances in this energy region.If the strong phasesδ12,13and the moduli A12,13in Eq.(9)were(almost)constant across the available phase space,the extraction ofγfrom Eqs.(11)would not be possible.Before concluding,we mention that quasi two-body D decays where one of the particles is a resonance,such as D→K∗+π−and D→K+ρ−[4],were proposed for use in measuring γ.But in fact,using such decays requires a Dalitz plot analysis(see e.g.[10,12]).What we showed here is that one can actually use the whole Dalitz plot to carry out the analysis and does not need to single out contributions of one particular resonance.Moreover,we showed that the assumption about the shapes of the resonances can be avoided,essentially with currently available data-sets.In conclusion,we have shown that the angleγcan be determined from the cascade decays B±→K±(K Sπ−π+)D.The reason for the applicability of the proposed method lies in the presence of resonances in the three-body D meson decays that provide a necessary variation of both the phase and the magnitude of the decay amplitude across the phase space.The fact that no Cabibbo suppressed D decay amplitudes are used in the analysis is another advantage of the method.However,it does involve a Dalitz plot analysis with possibly only parts of the Dalitz plot being practically useful for the extraction ofγ.In reality, many methods have to be combined in order to achieve the required statistics for a precise determination ofγ[7].AcknowledgmentsWe thank Michael Gronau,Zoltan Ligeti and Marie-Helene Schune for helpful discussions. Y.G.is supported in part by the Israel Science Foundation(ISF)under Grant No.237/01,by the United States–Israel Binational Science Foundation(BSF)through Grant No.2000133 and by the German–Israeli Foundation for Scientific Research(GIF)through Grant No. G-698-22.7/01.The work of A.S.was supported by the U.S.Department of Energy under contract DE-FG03-93ER40788.J.Z.is supported in part by the Ministry of Education, Science and Sport of the Republic of Slovenia.APPENDIX A:THE EFFECT OF D−D0 and the mass eigenstates|D H,L =p D|D0 ±q D|,(A1)1+λD→fξB−→DwhereλD→f=q D D0→fD0K−q D=r B e−i(2θD−δB+γ),(A2)and we use the definitions of Eqs.(3)and(4)and allow for new physics effects in q D/p D= e i2θD.(In the phase convention where the D decay amplitudes are real,the phaseθD is negligible in the Standard Model).In our case,thefinal state f equals K Sπ−π+,which leads toλD→KS(p1)π−(p2)π+(p3)=e i2θDA D(s13,s12)D mixing is taken into account in the analysis,the expression for the partial decay width(7)is multiplied by the correction term[21]1−R e(χ1)y D+I m(χ1)x D,(A4)where we have expanded the correction term tofirst order in the small parametersx D=∆m2Γ,(A5)where∆m and∆Γare the mass and decay width differences in the D−¯D system,andΓis the D0decay width.The values of x D and y D are constrained by present measurements to be in the percent range,y D=(1.0±0.7)%[22]and|x|<2.8%[23](assuming small strong phases).The ratio of magnitudes,R D(s12,,s13),depends on the position in the Dalitz plot,and can vary widely.Our method is useful for the model independent extraction ofγonly in the region where R D is of order one.We therefore distinguish three limiting cases•R D≫1≫r B,for which R e(χ1),I m(χ1)∼O(1/r B)and therefore the corrections in (A4)can be of order10%.However,this is the region of Dalitz plot where our method is mostly not sensitive toγand therefore the induced corrections due to D−¯D mixing do not translate into an error on the extractedγ.•R D∼1≫r B,for which R e(χ1),I m(χ1)∼O(1)and therefore the corrections in(A4) are at the percent level.This is the value of R D for which our method is most sensitive toγ.•1≫r B∼R D,for which R e(χ1),I m(χ1)∼O(r B,R D)and therefore the corrections in(A4)are very small.In conclusion,we expect errors of at most a few percent due to neglecting D−¯D mixing in our method.In principle,even these errors can be taken into account[16,21,24].APPENDIX B:A FIT TO BREIT-WIGNER FUNCTIONS:AN ILLUSTRATION FOR THREE RESONANCESIn this appendix we provide the formulae for thefit of D meson decay amplitude to a sum of three Breit-Wigner functions describing K∗±(892)andρ0resonances.We write Eq.(18)explicitly asA D(s12,s13)=A(D0→K S(p1)π−(p2)π+(p3))=(B1)=aρAρ0(s23)+a K∗e iδF A K∗(s12)+a K∗r D e iδD A K∗(s13),whereδF(δD)is the strong phase of the Cabibbo favored(doubly Cabibbo suppressed) D0→K∗−π+(D0→K∗+π−)decay with respect to the decay D0→K Sρ0.We further introducedaρ∝A(D0→ρ0K S)=A(D0→K∗+π−),a K∗r D e iδD∝A(D0→K∗+π−)=A(reduced differential decay rate is thendˆΓ(B−→(K Sπ−π+)D K−)∝a2ρ|Aρ0(s23)|2 1−2r B cos(δB−γ)+r2B +a2K∗|A K∗(s12)|2 1+2r B r D cos(δF BD−γ)+(r B r D)2 +a2K∗|A K∗(s13)|2 r2D+2r B r D cos(δD BF−γ)+r2B +2aρa K∗|Aρ0(s23)A K∗(s13)|×r D cosδD+0−r2B cosδF+0−r B r D cos(δD+B0−γ)+r B cos(δBF+0+γ) +2aρa K∗|Aρ0(s23)A K∗(s12)|×cosδF−0−r B cos(δF−B0−γ)+r B r D cos(δBD−0+γ)−r2B r D cosδD−0 +2a2K∗|A K∗(s12)A K∗(s13)|×r D cosδD+F−+r B cos(δB+−+γ)+r B r2D cos(δ+B−−γ)+r2B r D cosδF+D− ,(B6)where the notation of the strong phases is such that the lower(upper)indices indicate phasesappearing with a plus(minus)sign.For example,=δD+δ−−δF−δ+.(B7)δF+D−aρ,a K∗and r D are assumed to be known and thus there arefive unknowns tofit,namelyr B,δD,δF,δB,γ.(B8) Using both B−and B+decays,there is enough information to determine them all.This is true even if one neglects terms that scale as r2B and even if r D=0.This indicates that the method does not rely on doubly Cabibbo suppressed decays of the D,and that it is sensitive toγin terms of order r B,rather than r2B(See discussion in[10]).Moreover,even if some or all of the strong phases that arise from two-body decays,namely,δB,δD,andδF,vanish, there is still enough information to determineγ.APPENDIX C:MULTIBODY B DECAYWe consider the cascade decay B−→DX−s→(K Sπ−π+)D X−s.Let us assume that the phase space of thefirst decay,B−→DX−s,is partitioned into m bins that we label by the index j,and the phase space of the D meson decay is partitioned into n=2k bins labeledby i and¯i as in section II.Instead of Eqs.(11)we now have the set of4k×m equationsˆΓ−i,j≡i,jdΓ(B−→(K Sπ−π+)D X−s)=T i+R B j Ti+R B j T i+cosγ(c i c B j−s i s B j)+sinγ(c i s B j+s i c B j),(C1b)ˆΓ+ i,j≡i,jdΓ(B+→(K Sπ−π+)D X+s)=Ti+cosγ(c i c B j+s i s B j)−sinγ(c i s B j−s i c B j),(C1d)where the integration is over the phase space of the j-th bin in the B decay and the phase space of the i-th bin in the D decay.The j-th bin of the B+decay phase space is obtained from the j-th bin of the B−decay by CP conjugation.We also useds B j= j2r B sinδB,c B j= j2r B cosδB,R B j= j r2B,(C2) where r B andδB are functions of the position in the B decay phase space.From the set of4k×m equations(C1),one has to determine2k+3m+1unknowns c i,s i,c B j,s B j,R B j, andγ.With a partition of the D decay phase space into2k≥4bins and with a partition of the B decay phase space into m≥1bins,one has enough relations to determine all the unknowns,including the angleγ.This is true even for constantδB and r B,in which case the above equations fall into4k sets of m equivalent relations,i.e.the set of4k×m equations is reduced to the set of4k independent relations(11).Finally,we note that the above equations can be used to determineγalso for two-body D decays[6].[1]For a review see,for example,G.C.Branco,voura and J.P.Silva,“CP violation”,Clarendon Press(1999).[2]M.Gronau and D.London,Phys.Lett.B253,483(1991).[3]M.Gronau and D.Wyler,Phys.Lett.B265,172(1991).[4] D.Atwood,I.Dunietz and 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a r X i v :h e p -p h /0405225v 2 17 A u g 2004Transversity and intrinsic motion of the constituentsA.V.Efremov 1,O.V.Teryaev 1and P.Z´a vada 21Bogoliubov Laboratory of Theoretical Physics,JINR,141980Dubna,Russia2Institute of Physics,Academy of Sciences of the Czech Republic,Na Slovance 2,CZ-18221Prague 8(August 17,2004)The probabilistic model of parton distributions,previously developed by one of the authors,is generalized to include the transversity distribution.When interference effects are attributed to quark level only,the intrinsic quark motion produces the transversity,which is about twice as large as the usual polarized distribution.The applicability of such a picture is considered and possible corrections,accounting for interference effects at the parton-hadron transition stage are discussed.I.INTRODUCTIONNucleon spin functions represent a sensitive tool for understanding the nucleon internal structure in the language of QCD.Up to this day we have accumulated a very good knowledge of the nucleon spin functions g 1and g 2,which were measured in deep inelastic scattering [1]-[8].A further important and interesting quark spin distribution function is the transversity,the third non-diagonal element of the quark spin density matrix.Transversity is not accessible from the measuring of deep inelastic scattering,since it corresponds to the helicity flip amplitude.Its measuring is more complicated and that is the reason,why some more accurate and complete experimental data on the transversity are still missing.However,the recent and/or future data from the experiments HERMES (DESY-Hamburg),CLAS (JLab),COMPASS (CERN-Geneva)and RHIC (Brookhaven National Laboratory)could be interpreted also in terms of the transversity [9]-[11].For the present status of research in both theory and experiment,see e.g.[12]and overview [13].In Refs.[14],[15]the probabilistic,covariant quark-parton model (QPM),in which intrinsic quark motion with spheric symmetry is consistently taken into account,was developed by one of us (P.Z.).It was shown that such a model nicely reproduces some well-known sum rules and gives a very reasonable agreement with experimental data on the spin structure functions g 1and g 2.Assuming SU (6)symmetry,a calculation was done from the input on unpolarized valence quark distributions q V .The aim of this paper is to extend this model also for description and calculation of the transversity distribution.II.TRANSVERSITYFirst,let us shortly summarize,how the spin structure functions g 1,g 2were calculated in the paper [14].The antisymmetric part of the tensor related to the photon absorption by a single quark reads:t αβ=mεαβλσq λw σ,(1)where q,m,w are the photon momentum,quark mass and polarization vector;the corresponding handbag diagram is in Fig.1a.Then it was shown that the corresponding tensor related to the target (proton)consisting of quasifree quarks can be written asT (A )αβ=εαβλσq λm M w σδpq p 0;x =Q 2wσ=APσ+BSσ+Cpσ,(4) where S is the proton polarization vector andA=−pSmA.(5)Finally,in the last step the functions g1,g2were extracted from the tensor(2).In the approximationQ2≫4M2x2(6) and identifying the beam direction with coordinate1in the proton rest frame,we obtaing1(x)=1p0+m δp0+p1p,(7)g2(x)=−1p0+m δp0+p1p,(8)which impliesg T(x)=g1(x)+g2(x)=1p0+m δp0+p1p.(9)Sincem+p1+p21p0+m=p0+p1−(p0−m)(p0+m)−p21p0+m=p0+p1−p2T2 H(p0)Mx−p2T M−x d3px=Mx (G+(p0)+G−(p0))δ p0+p1p0.(11)Now,if one assumes the same spheric shape of the distributions G±for both opposite polarizations,then the corresponding probabilities can be parameterized asG+=G(p0)cos2(η/2),G−=G(p0)sin2(η/2),0≤η≤π,(12) so forη=0(π)we have a pure state with the polarization+(−).For example,in the case of SU(6)we have cosη=2/3(−1/3)for u(d)quarks.The last relations implyG+(p0)+G−(p0)=G(p0),G+(p0)−G−(p0)=G(p0)cosη,(13) so the relations(8)-(11)can be rewritten asg1(x)=1p0+m δp0+p1p,(14)g2(x)=−1p0+m δp0+p1p,(15)g T(x)=1p0+m δp0+p1p,(16)f1(x)=Mx G(p0)δ p0+p1p0.(17)Here,in the same approach,we shall try to calculate the transversity.Generally,transversity may be related to the auxiliary polarized process described by the interference of vector and scalar currents[17],[18],so that the respective quark tensor carries only one Lorentz index.The simplest handbag diagram in Fig.1b corresponds to the expressionτα=εαβλσpβqλwσ,(18) which will be used instead of the tensor(1).In the next step we integrate this vector equally as the tensor in(2).Here we assume for the time being,that due to rotational symmetry in the proton rest frame,the transversity distribution is generated by the same function H as that in the case of the longitudinal one:Tα=εαβλσqλ1M pβwσδpq p.(19)Obviously only the terms Sσ,Pσfrom the vector(4)contribute here,i.e.,Tα=εαβλσqλ1MSσ−pS P q−x d3p2Mν H(p0)p0|q|−p1ν−|q|p22Mν−x d3pν=2 H(p0) p0−p1M(p+m) δp0−p1p(26)=1M(p0+m) δp0−p1p=1M(p0+m) δp0+p1p.So now we shall try to identify the transversity with the dimensionless functionδq(x)=cosη G(p0) Mx−p2T/2M−x d3pFurther,using the Wanzura-Wilczek[19]relation,which was proved for our g1,g2in[15],g1(x)+g2(x)= 1x g1(y)ydy.(32) Moreover,in the same paper we suggested the relations between the spin functions and valence quark distributions:g q1(x)=cosηqy3dy ,g q2(x)=cosηq y3dy ;q=u,d,(33)which implyδq(x)=cosηq q V(x)−x2 1x q V(y)3:(−12 49∆d(x).(35)For the valence functions xu V(x)and xd V(x)we use the parametrization obtained by the standard global analysis in[20].All the parameterizations are taken for Q2=4GeV2/c2.The reason why in thisfigure the(dashed)curve based on the experimental input on g1is above the(solid)curve calculated fromfitted q V,can be the same,as it was discussed in[15]directly for the g1.Now we check if the obtained transversities satisfy the Soffer inequality[22]:|δq(x)|≤1p0+m δ p0+p1p(37)≤1p0+m δp0+p1pand after rearranging the r.h.s.one obtainscosηq G(p0) Mx−p2T/2M−x d3p2Mx(1−cosηq) G(p0)δ p0+p1p0+cosηq G(p0) Mx−p2T/2M−x d3pM−x d3pMx−p2T/22(p0+m)=2Mxp0+2Mxm− p20−m2 +M2x2−2Mxp0+p202(p0+m)>0,we have alsoG(p0) Mx−p2T/2M−x d3p2(p0+m)δ p0+p1p0>0,which means that the transversity sign is controlled only by the sign of cosη,which is determined by the sign of G+(p0)−G−(p0).So in our SU(6)approach the inequality(39)is safely satisfied for u−quarks.Now let us consider negativeδq,for d−quarks in the SU(6)approach,when cosη=−1/3and sin2(η/2)=2/3.Then the combination of Eq.(27)and relation(39)givesG(p0) Mx−p2T/2M−x d3p M−x d3pp0+m δ p0+p1p≤0,(41)which contradicts the inequality(40),so in this limit also the transversity(27)contradicts the Soffer inequality.Why? The reason is in the assumption that transversity is generated by the same function H=G cosηas the spin functions g1and g2.The resulting transversity contradicts the Soffer inequality in the case of large negative quark polarization.Indeed,inequality(36)means that|δq(x)|cannot exceed q+(x).At the same time,large negative polarization takes place for cosη→−1;then q+(x)becomes small,whileδq(x)is large(and negative).Below we shall modify the transversity definition as follows.The structure functions are proportional(see e.g.[17])to the combinations of amplitudes:f1∝ X a∗++(X)a++(X)+a∗+−(X)a+−(X) (42)g1∝ X a∗++(X)a++(X)−a∗+−(X)a+−(X) (43)δq∝ X a∗++(X)a−−(X)+a∗−−(X)a++(X) .(44)Now,in our approach we identifyX a∗++(X)a++(X)=G+(p0), X a∗+−(X)a+−(X)=G−(p0),(45)where G+±G−are the distributions in relations(13),from which the structure functions g1,g2,g T and f1are constructed in Eqs.(14)−(17).But what about the remaining interference functionG T(p0)≡ X a∗++(X)a−−(X)+a∗−−(X)a++(X) ,(46)which we are going to insert into Eq.(27)instead of G+−G−=G cosη?The G T is a new function,which has no definite relation to the functions G±.However,as a consequence ofX a++(X)±a−−(X) 2≥0(47) one gets|G T(p0)|≤G+(p0)=G(p0)cos2(η/2).(48) So in thefirst step we check the Soffer inequality for both corresponding extremes±δq max(x);δq max(x)=cos2(ηq/2) G(p0) Mx−p2T/2M−x d3pδ p0+p1p0,(50)p0+mso the inequality is satisfied for any transversityδq(x)in the band±δq max(x)given by Eq.(49)with anyηq.In fact, two inequalities are now satisfied:1|δq(x)|≤δq max(x)≤dy ;κ=cos2(ηq/2)ydy .(54)y3This approach for the transversity is compared with the previous one in Fig.3,again assuming SU(6)approximation for contributions from u and d valence quarks.However,one should point out that curves corresponding to the second approach represent only upper limitsδq max for transversities,in the sense of the relation(51).The left part of the figure shows results for d-quarks.The relations(53)-dashed and(54)-solid curves are compared with those in Fig.2,calculated from Eqs.(32),(34).It follows,that curves of the second approach are enhanced by the factor cos2(ηu/2)/cosηu=5/4with respect to thefirst one.The right part of thefigure demonstrates similar curves for u−quarks,but since cos2(ηd/2)=−cosηd=1/3,both the corresponding pairs of curves are equal up to sign.So only the second pair is displayed.The dotted curves in both parts represent tranversities calculated in Ref.[21]in the LO and evolved from the initial scale0.6GeV2/c2to4GeV2/c2.Obviously,our results are well compatible with them.Further,let us analyze the relation1δq max(x)≤1One can start from relation(38),where on the l.h.s.cosηq is substituted by cos2(ηq/2).Obviously,its saturation is equivalent to the equality in relation(50),which takes place either forη=0(pure state of the quark with polarization+)or for static quarks(p2T=0).On the other hand,in the limit m→0and with the use of Eq.(33)one can writeq+(x)=1y3dy =cos2(ηq/2)·q V(x)−x2cosηq 1x 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P.G.Ratcliffe,Phys.Rep.359,1(2002).[14]P.Zavada,Phys.Rev.D65,054040(2002).[15]P.Zavada,Phys.Rev.D67,014019(2003).[16]P.Zavada,Phys.Rev.D55,4290(1997).[17]G.R.Goldstein,R.L.Jaffe and X.Ji,Phys.Rev.D52,5006(1995).[18]B.L.Ioffe and A.Khodjamirian,Phys.Rev.D51,3373(1995).[19]S.Wanzura and W.Wilczek,Phys.Lett.B72,195(1977).[20]A.D.Martin,W.J.Stirling and R.G.Roberts,Phys.Rev.D50,6734(1994).[21]P.Schweitzer, D.Urbano,M.V.Polyakov, C.Weiss,P.V.Pobylitsa and K.Goeke,Phys.Rev.D64,034013(2001);P.Schweitzer,private communication.[22]J.Soffer,Phys.Rev.Lett.74,1292(1995).αβαp,wqqp,wap,wqs+c.c.bFIG.1.Diagram related to deep-inelastic scattering (a)and the transversity (b),see text.00.20.40.600.51x x δux-x δd0.050.10.1500.51FIG.2.Transversities of the u and d valence quarks calculated from the valence distributions (solid lines)and extracted from the experimental data on proton spin function g 1(dashed lines)−the first approach,see text.00.20.40.600.51x x δuxx δd0.050.10.1500.51FIG.3.Transversities of the u valence quarks (left)calculated from the valence distributions (solid lines)and extracted from the experimental data on the proton spin function g 1(dashed lines).Lower curves correspond to the first approach from Fig.2,upper curves represent the second approach given by δq max calculated from Eqs.(53),(54).The corresponding transversities δq max of the second approach for the d valence quarks (right)coincide,up to sign,with the first approach from Fig. 2.The dotted lines represent the calculation [21],with opposite sign for d quarks.00.20.40.600.51x x δuxx δd0.050.10.1500.51FIG.4.Bounds on the transversities of the u and d valence quarks:δq max (solid lines)and q +(dashed lines).。