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1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。
X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。
yang baxter方程
Yang-Baxter方程是一个数学方程，涉及到代数和数学物理学领域。
它是由中文数学家杨振宁和美国数学家Baxter于20世纪70年代提出的。
该方程定义了三个线性空间V，W和Z之间的线性映射R。
如果R 满足以下方程：
R12R13R23 = R23R12R13
其中R12 = R I I，R13 = I R I，R23 = I I R，I是恒等映射，表示张量积，则称R为Yang-Baxter映射。
这个方程在代数和数学物理学中都有非常广泛的应用。
在代数学中，它与李群的可积表示理论相关；在数学物理学中，它与量子群、统计物理等领域有紧密联系。
Yang-Baxter方程的研究在数学和物理学中都有重要意义，它不仅是研究李群、量子群和统计物理等领域的重要工具，还对解决其它代数问题有一定的启示作用。
- 1 -。
a rXiv:085.3816v1[he p-ex]25M ay28Commissioning ATLAS and CMS with top quarks B.S.Acharya (1)F.Cavallari (2),G.Corcella (3)(4),R.Di Sipio (5)and G.Petrucciani (4)(1)Abdus Salam International Center for Theoretical Physics and INFN,Sezione di Trieste,Italy (2)INFN,Sezione di Roma,Italy (3)Museo Storico della Fisica e Centro Studi e Ricerche E.Fermi,Roma,Italy (4)Scuola Normale Superiore and INFN,Sezione di Pisa,Italy (5)Universit`a di Bologna and INFN,Sezione di Bologna,Italy Summary.—The large t ¯t production cross-section at the LHC suggests the use of top quark decays to calibrate several critical parts of the detectors,such as the trigger system,the jet energy scale and b -tagging.PACS 14.65.Ha –Top quarks.PACS 13.38.Be –Decays of W bosons.PACS 13.85.Hd –Inelastic scattering:many-particle final states.1.–Introduction Events in which top-quark pairs are produced will be extremely important at the LHC,as they will provide a unique environmentto study physics within the Standard Modeland beyond [1].Final states in t ¯t events are classified in three categories,according tothe W -decay mode in top decay t →bW :fully hadronic,semileptonic or fully leptonic.Semileptonic t ¯t decays produce complex signatures within the detector,involving missing transverse energy,charged leptons,light-particle jets and b -jets.Therefore,in order to study these events accurately at the LHC,the understanding of all the parts of the detectors is mandatory.In particular,the following should be mastered:•Trigger system;•Lepton and jet reconstruction;•Calculation of missing transverse energy;•b -tagging.12 B.S.ACHARYA F.CA V ALLARI,G.CORCELLA,R.DI SIPIO and G.PETRUCCIANI Conversely,the top quark is an excellent instrument,thanks to the large t¯t cross-section at the LHC,σ(t¯t)∼830pb,more than100times larger than at the Tevatron accelerator [2].Semileptonic t¯t events link all these items together and can therefore be used to make what is commonly referred to as an in-situ calibration.2.–TriggersAt the LHC collisions will happen with a frequency of up to40MHz,and this number has to be compared with the capabilities of the ATLAS and CMS mass storage systems of about200Hz.So,the trigger system of ATLAS and CMS has been designed to select one event out of10millions,when running at the highest design luminosity.The ATLAS and CMS trigger systems both have a hardware-based level1and a software-based high-level trigger[3,4].Level1makes use of the muon detectors and calorimeters in order to identify particles,while higher levels perform a more refined reconstruction.In order to choose interesting events and reduce the output rate,the two experiments designed their trigger systems in two different ways.ATLAS makes use of Regions of Interest(RoI),a technique that gives access to high-granularity information only for the regionsflagged as interesting by the Level1Trigger. The CMS High Level Trigger can access the full detector readout,but it performs only the minimal amount of reconstruction needed to determine if an event has to be accepted or dropped.At the end of the process,both ATLAS and CMS trigger systems will write data with a frequency of about100Hz and a latency of fewµs.In thefirst days of data-taking,close attention will be paid to the study of the single-lepton triggers.In fact,a large number of important processes involve the production of at least one isolated charged lepton,and leptonic decays of top quarks are amongst these. Fig.1shows the efficiency of the level-1single-lepton triggers in t¯t events,calculated with respect to the offline reconstruction.Moreover,semileptonic events are triggered from jet triggers,too,giving the possibil-ity to measure directly the efficiency of the leptonic triggers.Thus,the very large cross section of t¯t events can be successfully exploited to calibrate the triggers.For example,a sample of events can be collected according to the offline selection defined in Tab.I.Then,a sub-sample is extracted,containing only events thatfired the single-lepton trigger.From this sub-sample,one can easily calculate the fraction of t¯t events thatfired the jet trigger.This technique can be subsequently applied,e.g., to several jet triggers for each lepton trigger,leading to a very good determination of combined trigger efficiencies[4].Top-quark production is also suitable to study other triggers,such as double-lepton (for full-leptonic decays),jet and missing-E T triggers.In fact,two leptons give a very clean signature for triggering,albeit limited in statistics at the very beginning.With early data,the fully hadronic channel is extremely challenging triggerwise,due to the large QCD background.Reasonably,this channel will be studied accurately in a subsequent phase of the experiment.ATLAS and CMS will also estimate the single-lepton trigger efficiency as a function of its momentum from processes which do not involve top quarks,such as Z→ee/µµ.However,since the jet energy scale and underlying event might be different between Z→ee and t¯t processes,it is clearly preferable to calculate efficiencies for t¯t events by using t¯t events themselves.COMMISSIONING ATLAS AND CMS WITH TOP QUARKS3 3.–Jet Energy ScaleThe cone algorithm for jet reconstruction,with a cone radius R=0.4or0.5,is commonly used both in ATLAS and CMS,since it provides a good compromise between energy reconstruction and angular resolution[5].Due to a HCAL resolution lower than ATLAS,CMS found better results using the particleflow,a useful technique when dealing with low-granularity calorimeters.Prelim-inary studies show an overall efficiency similar to that of ATLAS.The(mis)calibration of the Jet Energy Scale(JES)appears as an important source of systematic uncertainty on M W and M t.The a priori knowledge of jet-energy calibration is about10%.The goal of1GeV error on M t requires understanding the JES to1%.The Jet Energy Scale can be evaluated using the method of p T-balance applied to Z/γ+jets events.Here,the well reconstructed Z/γtransverse momentum can be balanced against the jets in the events,allowing a p T-dependent jet calibration.These processes are also useful for the b-jet energy scale,when jets are tagged as b-jets.However,as stated before,it would be better to measure the JES for t¯t events by means of t¯t events themselves,at least for two main reasons:•t¯t selection cuts can lead to JES different from that of Z/γ+jets;•the underlying event(UE)may be different for the two processes.To this end one could exploit the t→W b→jjb decay chain,since it gives an identifiable W→jj sample(in-situ calibration).The jj invariant mass should of course yield the well-known W-boson mass.ATLAS will determine the JES by studying the reconstructed M W after the offline selection(as defined in Tab II).Its impact,after varying the reconstructed jet energies by±1%,has been evaluated.Unfortunately,offline selection introduces a bias caused by the p T-cut which is important near threshold[5].To handle this problem,fitting techniques are applied to determine the jet-energy-scale factors as a function of the jet energy and pseudorapidityη.Starting from the same principles,CMS will calculate M W by combining the two jets.The light-quark jet energy is scaled by a global correction factor∆C,chosen to fit the reconstructed W mass within the world average,as shown in Fig.2.Studies show that the main sources of systematic uncertainty on∆C are the pile-up and b-tag efficiency[6].More refined techniques are under study,based on a kinematicfit of M bjj in t→W b→jjb decays,so that one can also measure the b-JES.4.–b-taggingIdentification of b-jets is crucial in many analyses at the LHC,such as the searches for the Higgs boson,supersymmetry and other New Physics scenarios.Thus,to calibrate b-tagging algorithms,one would like to isolate a sample of b-jets as pure as possible.Again,the large t¯t cross section offers the possibility of an in-situ calibration with several advantages,since almost every t¯t event contains two b-quarks.In fact,semilep-tonic t¯t events are identifiable without b-tagging and hence give a handle on b-tagging mechanisms[7].With an integrated luminosity of100/pb,several hundred events are expected.To gain more statistics,di-jet events could be used but for b-tagging calibra-tion.However the b-tagging efficiency,-like the JES-is sample and analysis dependent. For this reason a measurement of the efficiency from top events themselves is preferable.4 B.S.ACHARYA F.CA V ALLARI,G.CORCELLA,R.DI SIPIO and G.PETRUCCIANIThe default ATLAS b-tagger uses a likelihood algorithm weight w,constructed from the impact parameter and the secondary-vertex taggers.Choosing a threshold on the weight translates into an efficiency to recognize correctly the b-jets(ǫb)and to reject the jets originated from the lighter quarks(R l−jets=1/ǫl−jets).As shown in Fig.3,w is large for b-jets and low for light-jets,proving itself as a good quantity to distinguish b-jets from light-jets.For example,setting the cut w>6,an overall efficiencyǫb=63% and light-jet rejection R l−jets=250can be achieved[7].In a recent CMS study an attempt was made to evaluate the b-tagging efficiency directly from data.In this study,a simple algorithm was used,mainly based on track counting and track probability.One can associate to each track inside the jet an impact parameter and a secondary vertex location.If these values are greater than their thresh-olds,the track is‘counted’.Then,the jet is b-tagged if it contains more‘counted’tracks than a minimum.Tagging one of the b-jets hardly allows to have a rather pure b-jets sample from the other top and evaluate the performance of the b-tagging.However,this study shows that with1fb−1one can reach an uncertainty on the b-tagging efficiency of ∼5%.Other strategies,such as the soft lepton method,are also under study.Assuming that each selected event actually contains two b-jets,ǫb can be measured from the data themselves,counting the number of tagged jets as b-jets.To take into account mistagged events and backgrounds,a more refined likelihood function can be written,withǫb and R l−jets as parameters.Overall,the main sources of systematic uncertainty are light-jet rejection,JES,W+jets background contamination,and the uncertainty on the measurement of the top mass. 5.–ConclusionsTop-quark events and,in particular,those with semileptonic decays,will be a poweful source of data for the measurement of trigger efficiencies,jet energy scale and b-tagging performance.Both ATLAS and CMS are developing methods and algorithms to capi-talise on this opportunity.t¯t events,especially semileptonic,allow one to trigger on both leptons and jets independently,thereby allowing the possibility to measure trigger efficiencies.Moreover,the presence of W-bosons,light jets and b-jets in t¯t events,allows one to measure the JES for both light jets and b-jets.The goal of measuring the top-quark mass with an uncertainty of1GeV requires a1%error on the JES,which can be achieved with at least1/fb of data.Since almost every decaying top quark produces a b quark,t¯t events supply a pure sample of b-jets,which could be used to calibrate the b-taggers.Much work is in progress to develop these techniques in preparation for thefirst data-taking.REFERENCES[1]Beneke M.et al.,Top quark physics hep-ph/0003033.[2]Bonciani R.,Catani S.,Mangano M.L.and Nason P.,Nucl.Phys.B,529(1998)529.[3]The CMS Collaboration,CMS High Level Trigger,CERN/LHCC2007-021(2007)[4]Collins N.,Thomas J.,Watson A.et al.,Triggering top quark events in ATLAS(CSCNote T5)[5]The ATLAS Collaboration,Light jets in t¯t events,ATLAS Note in preparation.COMMISSIONING ATLAS AND CMS WITH TOP QUARKS5 [6]The CMS Collaboration,Measurement of jet energy scale corrections using top quarkevents,CMS-PAS-TOP-07-004[7]Bachacou H.,Gorfine G.,Harrington R.,Hawkings R.and Sandhoff M.,Flavourtagging calibration with t¯t events in ATLAS[8]The CMS Collaboration,CMS Physics Technical Design Report,Volume1,section12.2.8,CERN/LHCC2006-001(2006).CMS TDR8.1Table I.–Offline selection cuts for semileptonic decays.Table II.–Offline selection cuts for selecting a sample suitable for jet energy scale determina-tion.Fig.1.–ATLAS Level-1efficiencies for one-lepton trigger menu e251(left)and mu20i(right). Efficiencies are calculated with respect to the offline reconstruction.6 B.S.ACHARYA F.CA V ALLARI,G.CORCELLA,R.DI SIPIO and G.PETRUCCIANIFig.2.–CMS will calculate JES byfitting the reconstructed M W to the world average.Cor-by a constant term∆C.rections are applied by multiplying M recoWFig.3.–The ATLAS b-tagger weight w(left)is low for light jets and high for b-jets.A generic selection is made applying a cut w>6.CMS will make use of track counting and track probability taggers(right).。
第二章夸克与轻子Quarks and leptons2.1 粒子园The particle zoo学习目标Learning objectives：我们怎样发现新粒子？能否预言新粒子？什么是奇异粒子？大纲参考：3.1.1￣太空入侵者宇宙射线是由包括太阳在内的恒星发射而在宇宙空间传播的高能粒子。
如果宇宙射线粒子进入地球大气层，就会产生寿命短暂的新粒子和反粒子以及光子。
所以，就有“太空入侵者”这种戏称。
发现宇宙射线之初，大多数物理学家都认为这种射线不是来自太空，而是来自地球本身的放射性物质。
当时物理学家兼业余气球旅行者维克托·赫斯（Victor Hess）就发现，在5000m高空处宇宙射线的离子效应要比地面显著得多，从而证明这种理论无法成立。
经过进一步研究，表明大多数宇宙射线都是高速运动的质子或较小原子核。
这类粒子与大气中气体原子发生碰撞，产生粒子和反粒子簇射，数量之大在地面都能探测到。
通过云室和其他探测仪，人类发现了寿命短暂的新粒子与其反粒子。
μ介子（muon）或“重电子”（符号μ）。
这是一种带负电的粒子，静止质量是电子的200多倍。
π介子（pion）。
这可以是一种带正电的粒子（π＋）、带负电的粒子（π－）或中性不带电粒子（π0），静止质量大于μ介子但小于质子。
K介子（kaon）。
这可以是一种带正电的粒子（K＋）、带负电的粒子（K－）或中性不带电粒子（K0），静止质量大于π介子但小于质子。
科学探索How Science Works不同寻常的预言An unusual prediction在发现上述三种粒子之前，日本物理学家汤川秀树（Hideki Yukawa）就预言，核子间的强核力存在交换粒子。
他认为交换粒子的作用范围不超过10－15m，并推断其质量在电子与质子之间。
由于这种离子的质量介于电子与质子之间，所以汤川就将这种粒子称为“介子”（mesons）。
一年后，卡尔·安德森拍摄的云室照片显示一条异常轨迹可能就是这类粒子所产生。
a r X i v :h e p -p h /0310317v 1 28 O c t 2003EPJ manuscript No.(will be inserted by the editor)Constraining the Unitarity Triangle with B →K ∗γand B →ργStefan W.BoschInstitute for High-Energy Phenomenology,Newman Laboratory for Elementary-Particle Physics,Cornell University,Ithaca,NY 14853,U.S.A.CLNS 03/1847Received:date /Revised version:dateAbstract.We discuss the exclusive radiative decays B →K ∗γand B →ργin QCD factorization within the Standard Model.The analysis is based on the heavy-quark limit of QCD.Our results for these decays are complete to next-to-leading order in QCD and to leading order in the heavy-quark limit.Phenomenological implications for branching ratios and isospin breaking effects are discussed.Special emphasis is placed on constraining the CKM unitarity triangle from these observables.1IntroductionThe rare radiative B decays belong to the most valu-able probes of the quark flavour sector (see [1]for a re-cent review).The inclusive b →sγmode,showing good agreement of the theoretical next-to-leading-logarithmic (NLL)QCD prediction and experimental measurements,puts stringent bounds on physics beyond the standard model.CP-averaged branching ratios of exclusive radia-tive channels are measured to be B (B 0→K ∗0γ)=(4.18±0.23)·10−5and B (B +→K ∗+γ)=(4.14±0.33)·10−5[2],and bounded with 90%confidence level as B (B 0→ω0γ)<1.0·10−6,B (B 0→ρ0γ)<1.2·10−6and B (B +→ρ+γ)<2.1·10−6[4].Whereas the inclusive decay can be treated perturba-tively,bound state effects are essential for the exclusive modes and have to be described by some nonperturba-tive quantities like hadronic form factors and light-cone distribution amplitudes (LCDAs).However,in the heavy-quark limit m b ≫ΛQCD a systematic treatment of ex-clusive B decays is possible within QCD [5]:Perturba-tively calculable contributions to the matrix elements can be factorized from nonperturbative form factors and uni-versal light-cone distribution amplitudes.We use the QCD factorization technique for the exclusive radiative decays B →K ∗γand B →ργas in [6–8].The ratio of the B →ργand B →K ∗γbranching fractions is,at lead-ing order in αs ,directly proportional to the side R t in the standard unitarity triangle (UT),whereR t ≡λV td √2Stefan W.Bosch:Constraining the Unitarity Triangle with B→K∗γand B→ργFig. 1.O(αs)contribution at leading power to the hard-scattering kernels T II i from four-quark operators Q i(left)andfrom Q8.The crosses indicate the places where the emitted pho-ton can be attached.I hard-scattering kernels.The non-vanishing contributionsto T II i where the spectator participates in the hard scat-tering are shown in Fig.1.We can express both the typeI and type II contributions to the matrix elements Q i interms of the matrix element Q7 ,an explicit factorαs,and hard-scattering functions G i and H i which are givenexplicitely in[7,12].Weak annihilation contributions are suppressed by onepower ofΛQCD/m b but they are nevertheless calculablein QCD factorization because in the heavy-quark limitthe colour-transparency argument applies to the emitted,highly energetic vector meson.Including them we becomesensitive to the charge of the decaying B meson and thusto isospin breaking effects.3ResultsThe total¯B→Vγamplitude then can be written asA(¯B→Vγ)=G F2[λu a u7+λc a c7] Vγ|Q7|¯B (4)where the factorization coefficients a p7(Vγ)consist of theWilson coefficient C7,the contributions from the type Iand type II hard-scattering and annihilation corrections. Onefinds a sizeable enhancement of the leading ordervalue,dominated by the T I-type correction.The net en-hancement of a7at NLO leads to a corresponding enhance-ment of the branching ratios,forfixed value of the form factor.This is illustrated in Fig.2,where we show theresidual scale dependence for B(¯B→¯K∗0γ)and B(B−→ρ−γ)at leading and next-to-leading order.Our central val-ues for the B→K∗γbranching ratios are higher than thequoted experimental measurements.The dominant uncer-tainty in the theoretical values comes from the B→Vγform factors.We used the light-cone sum rule(LCSR)re-sults F K∗=0.38±0.06and Fρ=0.29±0.04from[13].A recent preliminary lattice QCD determination,F K∗=0.25±0.05±0.02[14],would give a better agreement withthe experimental central values.The charge averaged isospin breaking ratio can be de-fined as∆(Vγ)=Γ(B0→V0γ)−vΓ(B±→V±γ)B(B0→K∗0γ)(6)≈1Vts2ξ−2(1+∆(¯ρ,¯η))(7)where CP averaged branching fractions are understood.Here∆(¯ρ,¯η)is a small perturbative correction[10]andξ=F K∗/Fρ,the ratio of the form factors,is essentially theonly source of theoretical uncertainty.We use the LCSRestimateξ=1.33±0.13[13].A preliminary lattice valueisξ=1.1±0.1[14].Experimentally,so far only an up-per limit on R00exists.Because the B→ωγbranchingratio is up to tiny corrections the same as the one forB0→ρ0γ[10]and its experimental limit is tighter,weuse it to get R exp00<0.024.If we use in addition the ex-perimental measurement sin(2β)=0.734±0.054[16]weStefan W.Bosch:Constraining the Unitarity Triangle with B→K∗γand B→ργ3Fig.3.Impact of the experimental upper bound on R00in the (¯ρ,¯η)plane.The width of the dark band reflects the variation of ξ.The intersection with the light-shaded sin(2β)band defines the apex of the unitarity triangle and the length R t.Fig.4.Same as Fig.3including the implication of a measure-ment of∆(ργ)exp=0(curved band on the right).The width of the band reflects the theoretical uncertainties from varying the hadronic parameterλB and the renormalization scaleµ.(The effect of isospin breaking in the form factors is neglected here.) can construct the overlap of the R00and sin(2β)bandsand extract the length R t as shown in Fig.3.The dashedcurve in Fig.3was obtained settingξ=1in(7).Thiscan be viewed as the lowest possible value.If R00were measured at its current experimental bound R00=0.024,the dashed line would correspond to a conservative lowerbound on R t.The value R t<1.24from R00is already becoming comparable with the constraints from∆M Bd and∆M B s.It is possible that the experimental measure-ment of R00may actually be achieved before the measure-ment of∆M B s.Once a measurement of both the charged and neutral B→ργmodes is available,one can also use ∆(ργ)to constrain the unitarity triangle.For illustration purposes we plot in Fig.4in addition to the R00and sin(2β)bands the implication of an assumed measurement of∆(ργ)exp=0,which would correspond to the Standard Model prediction for a CKM angleγ=60◦.5Conclusions and OutlookWe have discussed a systematic and model-independent NLL framework for the rare radiative decays B→Vγbased on the heavy-quark limit m b≫ΛQCD.As observ-ables of primary interest we considered the branching frac-tions,the ratio R00of the neutral B→ργand B→K∗γbranching fractions,and the isospin breaking ratios ∆(K∗γ)and∆(ργ).Our main focus was on the impli-cations of measurements of these quantities on the(¯ρ,¯η) plane of the CKM unitarity triangle.The theoretically cleanest quantities are R00and∆(ργ)which,however, are not yet measured experimentally.We hope that they will become accessible in the near future with new data from the B factories.Acknowledgements:These results were obtained in col-laboration with Gerhard Buchalla to whom I’m very grate-ful.I would like to thank Sebastien Descotes-Genon,Thor-sten Feldmann,Bj¨o rn Lange,and Enrico Lunghi for inter-esting discussions during this conference.This research was supported by the National Science Foundation under Grant PHY-0098631.References1. 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