Quark coalescence in the mid rapidity region at RHIC

中考英语太空探索的科学意义单选题40题1. The first man-made satellite, Sputnik 1, was launched by the Soviet Union in _.A. 1957B. 1961C. 1969D. 1972答案解析：A。

本题考查太空探索历史中的重要事件时间。

Sputnik 1（ 斯普特尼克1号）是苏联于1957年发射的第一颗人造卫星，这是太空探索历史上的一个里程碑事件。

选项B 1961年是苏联宇航员加加林首次进入太空的时间；选项C 1969年是美国阿波罗11号载人飞船首次登月的时间；选项D 1972年与第一颗人造卫星发射无关。

2. Yuri Gagarin became the first human to journey into outer space in _.A. 1957B. 1961C. 1969D. 1972答案解析：B。

Yuri Gagarin 尤里·加加林）在1961年成为第一个进入外太空的人类，这是太空探索进程中非常关键的事件。

选项A 1957年是第一颗人造卫星发射时间；选项C 1969年是登月时间；选项D 1972年与加加林进入太空的事件无关。

3. Which country first landed on the moon?A. The Soviet UnionB. The United StatesC. ChinaD. The United Kingdom答案解析：B。

美国是第一个实现载人登月的国家，1969年阿波罗11号成功登月。

苏联在太空探索方面有很多成就，但不是第一个登月的国家；中国的太空探索发展较晚，还不是第一个登月的国家；英国在太空探索方面没有率先实现登月。

4. The ancient Chinese made important contributions to astronomy. Which of the following was an early Chinese astronomical observation tool?A. TelescopeB. Armillary sphereC. MicroscopeD. Compass答案解析：B。

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a r X i v :h e p -p h /9411412v 2 26 A p r 1995UTPT-94-35hep-ph/9411412November 1994Momentum dependent quark mass in two-point correlatorsB.Holdom and Randy Lewis Department of Physics University of Toronto Toronto,Ontario CANADA M5S 1A7ABSTRACTA momentum dependent quark mass may be incorporated into a quark model in a manner consistent with dynamically broken chiral symmetry.We use this to study the high Q 2be-havior of the vector,axialvector,scalar and pseudoscalar two-point correlation functions.Expanding the results to order 1/Q 6,we show the correspondence between the dynamical quark mass and the vacuum condensates which appear in the operator product expansion of QCD.We recover the correct leading logarithmic Q 2dependence of the various terms in the OPE,but we also find substantial subleading corrections which are numerically huge in a specific case.We conclude by using the vector minus axialvector correlator to estimate the π+−π0electromagnetic mass difference.IntroductionFor large momenta,the QCD running coupling is small and calculations may be carried out systematically by a perturbative expansion in the coupling.As the momentum scale is lowered,nonperturbative effects become significant and the coupling expansion is no longer useful.Consider specifically the physics of light quark flavors in the context of a two-point correlation function,Π(q 2),which we define to be dimensionless.From a purely phenomenological standpoint,the onset of nonperturbative effects can be parameterized by a series of correction terms.[1]˜Π(q2)=Π(q 2)−Πpert (q 2)=Nn =1C nqq ,and it (when multiplied by a current quark mass)will contribute to C 2in (1).There is one other condensate in C 2,αs G r µνGr µν,but it does not break chiral symmetry and will not be of direct interest in what follows.Since there are no condensates with mass dimension two,C 1=0in QCD.The existence of a nonzeroqq term of C 2.We obtain expressions for C 3in the vector and axialvector cases which have the known1leading logarithmic running,and we point out the possibility of substantial corrections in C3due to terms that are formally suppressed by logarithms.The same diagram(Fig.1)also represents the scalar and pseudoscalar two-point cor-relators in QCD,although there are no WT identities to constrain the corresponding vertices.If the full scalar or pseudoscalar vertex is approximated by a bare one,C2is not generated in its correct form.Improved scalar and pseudoscalar vertices can be found by appealing to the gauged nonlocal constituent(GNC)quark model.[3]The GNC Lagrangian contains constituent quarks with momentum dependent masses and pseudoscalar mesons,constructed to model dynamically broken chiral symmetry. The couplings of vector and axialvectorfields to quarks are precisely the“minimal”WT vertices mentioned above.Although the GNC Lagrangian originally included the scalar and pseudoscalarfields in a trivial way[3],the Lagrangian allows for a natural extension of these couplings in a manner analogous to its vector and axialvector couplings.For the case of the scalar correlator we verify that this produces the correct expressions for the chiral symmetry breaking pieces of C2.C3also has the correct leading logarithmic running,but here wefind enormous subleading correction terms as well.It is important to stress that we will use the GNC model only to determine the form of the nonperturbative propagators and vertices appearing in the general correlator of QCD in Fig.1.Our main goal is to study the relation between the1/Q2expansion of these correlators and the momentum dependent mass function.We will need to consider the low energy behavior of these correlators only when we treat the pion mass difference. At low energies we may apply the GNC model directly,since it has been shown to model low energy phenomenology rather well[3][4].Thus at low energy the correlators will be described by the GNC model diagrams of Fig.2,and at high energies they will be described by Fig.1.The GNC model includes the pseudo-Goldstone bosons of QCD,and virtual effects of these mesons are accounted for in the low energy contribution according to the standard chiral Lagrangian approach.Meson loops are naturally cutoffin the model at the point where these particles lose their particle-like nature.The vector minus axialvector two-point correlator is of special interest in our study since it would vanish if chiral symmetry was not broken.We will choose an explicit form for the effective quark mass which becomes the known form[2]at large momentum scales and which resembles the successful[3][4]GNC ansatz at small scales.We can then calculate the vector minus axialvector correlator numerically at any momentum scale by2matching the low energy GNC model(Fig.2plus meson loops)to our high energy model (Fig.1)at an intermediate scale.An integral over all momenta produces theπ+−π0 electromagnetic mass difference[5].The general1/Q2expansionIt is convenient to express the vector,axialvector,scalar and pseudoscalar two-point correlators in terms of dimensionless functions of Q2,i d4x e iq·x 0|T{V aµ(x)V bν(0)}|0 =(qµqν−q2gµν)VΠab(Q2)(2) i d4x e iq·x 0|T{A aµ(x)A bν(0)}|0 =(qµqν−q2gµν)A,1Πab(Q2)−qµqνA,0Πab(Q2)(3) i d4x e iq·x 0|T{S a(x)S b(0)}|0 =Q2SΠab(Q2)(4) i d4x e iq·x 0|T{P a(x)P b(0)}|0 =Q2PΠab(Q2)(5) where a,b are SU(N f)flavor indices.Throughout this work we will restrict the discussion to light quarks.According to Fig.1we must determine the full quark propagator and the full vertex for each correlator.The most general quark propagator isiZ(Q2)i S(q)=qq and αs G rµνG rµν .In the limit of vanishing current quark masses,we see on purely dimensional grounds that Z(Q2)cannot contain3Q2qq Q= αs (µ)−d(8)αs(Q)→dπ ln Q2qq represents a single quarkflavor summed over three colors and summed over Dirac indices.The vector and axialvector vertices V,AΓaµ(p,q)are constrained to satisfy the Ward-Takahashi identities.qµVΓaµ(p,p+q)=S−1(p+q)λa2S−1(p)(10)qµAΓaµ(p,p+q)=S−1(p+q)γ5λa2S−1(p)(11)Theλa areflavor generators normalized by Tr(λaλb)=2δab.These identities,plus the requirement that the vertices contain no unphysical singularities,uniquely define the longitudinal part of the vector and axialvector vertices.We will choose the minimal vertices by ignoring any extra transverse pieces that may exist.[6]The resulting vertices, for incoming(outgoing)quark momentum p(p′=p+q),areVΓaµ(p,p′)=λaP′2−P2(12)AΓaµ(p,p′)=λaq2 Σ(P′2)+Σ(P2)γ5(13)Again,P2(P′2)=−p2(−p′2).Notice that the vector vertex is completely free of sin-gularities(assuming none are contained withinΣ(Q2))but that the axialvector vertex is required to have a singular point.This massless state is the Goldstone boson of the dynamically broken symmetry—the pion for N f=2.There are no analogous identities to constrain the forms of the scalar and pseudoscalar vertices.One might be tempted to adopt the bare verticesSΓa(p,p+q)=−λa2γ5(15)4but this will lead to a disagreement with the OPE.One must also decide how to include current quark mass effects.Our approach will be to appeal to the GNC quark model which is the minimal Lagrangian that contains constituent quarks with mass Σ(Q 2)and which respects the dynamically broken chiral symmetry.The original GNC model[3]was used at low energy scales,and the external fields were coupled to quarks according to (12-15),but as stated above,the scalar and pseudoscalar couplings contradict the OPE at larger scales.We therefore propose the following “GNC ′”model,which is identical to the original version except that the S and P fields now appear in the path-ordered exponential as well as in the local term.In Euclidean spacetime,L GNC ′(x,y )=4γµS (y )+iψ(x )Σ(x −y )ξ(x )X (x,y )ξ(y )ψ(y )(16)X (x,y )=P exp−iy xΓµ(z )dz µ(17)Γµ(z )=i2γµS (z )−i2ξ†(z )[∂µ−iV µ(z )+iγ5A µ(z )−12γµγ5P (z )]ξ(z )(18)ξ(x )=exp−iγ52πa (x )(19)πa contains the N 2f -1pseudoscalar mesons with decay constant f ,and ψis the N f -plet of quark fields with mass Σ(Q 2),the Fourier transform of Σ(x −y ).V µ,A µ,S ,P are the external fields.X (x,y )is a path-ordered exponential.Notice that we have assumed the same mass function Σ(Q 2)for all quark flavors,which means thatFor our purposes,we will only require terms linear in M .With Feynman rules in hand,the expressions for the two-point correlators of Fig.1are easily written down in the form of 4-momentum integrals.The integrands are largest when the momentum-squared flowing through one quark propagator is of order Σ2(0)so that the other propagator has a momentum-squared of order Q 2.When the results are expanded in powers of M and 1/Q 2,we obtain a series of the form (1).The simple procedure of expanding the integrand in 1/Q 2generates integral expressions for the various C n ,and these integrals become more divergent for increasing n .We stress that the fullexpression for each ˜Π(Q 2)is finite and it is only the simple expansion technique which creates apparent divergences.Our results areV˜Πab (Q 2)=M abQ 6Υ1Q 2Σ(Q 2)+Υ2Q 8(21)A,1˜Πab(Q 2)=M ab Q 6Υ1Q 2Σ(Q 2)+Υ2Q 8(22)A,0˜Πab(Q 2)=M abQ 8(23)S˜Πab (Q 2)=M abQ 63Υ1Q 8(24)P˜Πab (Q 2)=O14π2Q 2Λ2dxx Σ(x )qq (27)6Υ2≡3x +Σ2(x )=−4d2qq2lnQ 24Q 4 24πQ 4αs G r µνGr µν−A ab (γµγ5)18Q 6+O14Q 424πQ 4αs G r µνGr µν−A ab(γµ)18Q 6+O12Q 4Q 8(31)S˜Πab (Q 2)=3M abqq +δab4παsqσµντr qG r µν+A ab(σµν)12Q 6+O18Q 416πQ 4αs G r µνGr µν+A ab (σµνγ5)12Q 6+O1ψΓµ...τr λa ψψγµτrλa ,λbψq =u,d,s,...masses also agree with the OPE if we can neglect the ellipses in (21-24).(We will jus-tify the neglect of these terms below.)The successful result for the scalar correlator in particular is a reflection of the scalar vertex present in the GNC ′Lagrangian.At dimension six,we neglect M corrections and find expressions for the 4-quark condensates that appear in each of three correlators.9A ab (γµ)+B ab =−18Υ1Q 2Σ(Q 2)δab −3Υ2δab +...=−4d6−dqq2lnQ 2(1−2d )π2δabΛ2−1+ (37)3A ab (σµν)+B ab =−18Υ1Q 2Σ(Q 2)δab +12Υ2δab +...=−4d6+4dqq2ln Q 2qq given in (8)reveals that these functions ex-hibit the known (ln Q 2)2d −1dependence on Q 2.[1]However,the presence of undetermined contributions at the same order in 1/Q 2prevents us from using this approach to obtain complete expressions for these condensates.To proceed,we examine a specific example in detail.Rigorous 1/Q 2expansion for a specific mass functionThe loop integrations from Fig.1can be performed rigorously for the simple mass function which has typically been used in low energy GNC calculations.Σ(Q 2)=(A +1)m 30For any A>1.44,the Euclidean propagator can be expanded in a convergent geometric series.1Q2+Am20∞k=0 Am20−Σ2(Q2)l!(k−l)!(Am20)k−l(−(A+1)2m60)l(4π)2M ab tu2ln 1A2m0→Σ2(0)Q2→Σ(Q2)A3→Σ3(0)2−0.45v0.44(46) The value of Y V(0)is exact,and all derivatives at v=0are infinite in the true(series) expression as well as in this approximation.If we assume(incorrectly)that this result remains valid when(39)is modified to be consistent with the correct asymptotic form of(7),then we getV˜Πab(Q2)=dqq ln Q2Σ2(0) −Y V(˜v) +O(u3)(47)˜v≡Σ3(0)4dπ2 Λ2(48)9A comparison with (29)shows thatwe haveobtainedthe correctleading logarithm except for a missing factor of 1/d .This is to be expected.If we had put the true form of the mass function (7)into the integral of Fig.1,there would have been an extra factor of 1/d which arises from the integration.This is easily demonstrated by computing the large Q 2behavior of Υ1,as defined in (27),with a cutoff.Q 2Λ2dx x Σ(x )x ln xd lnQ 2(4π)2u 3v ln1(4π)2u 3v ln1(4π)2u 3v ln 151+0.24√42+0.40√5+1.20v ln(1+v )(55)10The values of Z X(0)are exact,and all derivatives at v=0are infinite in the true(series) expressions as well as in these approximations.If we consider a modification of(39)to make it consistent with the correct asymp-totic form of(7),then we see that each correlator regains the known leading logarithmic behavior of(36-38).Moreover,we can now estimate the size of these condensates.9A ab(γµ)+B ab=28d2π2δab Λ2 −2 ln ˜v Q2qq 2 ln Q2Σ2(0) −Z V(˜v) (57) 3A ab(σµν)+B ab=−20d2π2δab Λ2 −2 ln ˜v Q2dπ2δab Λ2 −1(59)99A ab(γµγ5)+B ab=−352qq 2 ln Q2dπ2δab Λ2 −1(61)9The two expressions have the same leading logarithmic dependence on Q2,but the numer-ical factors in front differ.We could make similar remarks here as made in the discussion surrounding(47-49).Of greater interest are the terms which are subleading to the leading logarithm,and which correspond to terms which are often neglected in approximations to QCD such as vacuum saturation.We may compare the terms in brackets in(47)and(56-58)to the leading logarithm,ln(Q2/Λ2).By making reasonable estimates of the various quantities involved,100MeV<∼Λ<∼300MeV(62)400MeV<∼Σ(0)<∼500MeV(63)−(230MeV)3<∼ Λ2 −d<∼−(180MeV)3(64)11and by setting d =4/9and Q =1GeV we obtain2.4<∼lnQ 2Σ2(0) −Y V (˜v )<∼4.2(66)1.7<∼ln˜v Q 2Σ2(0)−Z V (˜v )<∼1.5(68)−12.1<∼ln ˜v Q 24πf 2π∞0dQ 2 Q 2LR ˜Π(Q 2)(71)where αis the electromagnetic coupling.We will neglect the tiny effects of nonzero current quark masses.As discussed earlier,the large(small)Q 2portion of the correlator will be obtained from Fig.1(Fig.2plus meson loops).In fact,it will become evident as we proceed that we can get an upper bound on the mass difference by simply using Fig.1for all Q 2.We must also decide how to extend the asymptotic form of Σ(Q 2)given in (7)tosmaller Q 2.The following simple ansatz contains four parameters:Am 20,Bm 30,C and12M2.(As in[3],m0represents the scale of the constituent quark mass.Since it is not an independent parameter here,we are free to choose it to be numerically identical to its value in[3].)Σ(Q2)=Bm30M2 1−d (72)The motivation for this functional form comes from the M→∞limit,whereΣ(Q2) becomes the mass function used originally in the low energy GNC model.We wish to include the correct logarithmic behavior of the mass function at high energies without making significant changes to the original low energy form.The ten dimensionless quan-tities L i(µ)which appear in the standard chiral Lagrangian[8]have been obtained from the GNC model(i.e.Fig.2)in the M→∞limit.[3][4]They are sensitive to the shape of the mass function,but not to the overall scale,so from this we can determine the value of Am20.(470MeV)2<∼Am20<∼(550MeV)2(73)One constraint on the three remaining parameters in(72)comes from demanding that Σ(Q2)satisfies the high energy behavior of(7),where the numerical value ofC≈−4dπ2qqµ lnµ26(4π)2 5µ2+O(Q4)(75)N f is the number of quarkflavors.The dependence of L10on the renormalization scaleµis canceled by the logarithm(which comes from internal meson loops),so that LR˜Π(Q2)is independent ofµ.We will eliminate the parameters Bm30and C by using the phenomeno-logical values forBefore proceeding,we point out an interesting relation between the high and low energy calculations.From the evaluation of Fig.2,we obtainF20=3[s+Σ2(s)]2(76)and a more lengthy expression for L10.It turns out that exactly the same expression for F0happens to come from Fig.1.The two expressions for L10are not the same;Fig.1 correctly predicts that L10is negative,but the magnitude is only about half of the correct GNC result.This means that if Fig.1is used for all momenta,the slope of the LR correlator at Q2=0is too shallow(see Fig.5),and an upper bound is obtained for∆m2π. We choose the strongest upper bound by using the smallest value of M which keeps L10 (of Fig.2)within25%of the original(M→∞)GNC result.For definiteness,we use d=4/9with the following inputs,F0≈88MeV(77)Λ2 −d≈−(220MeV)3(78) Note that this last expression is independent ofµ.With these values,the parameters B and C of(72)are of order unity,and the scale M is about3GeV.Fig.1then gives an upper bound on the electromagnetic pion mass difference.mπ+−mπ0,<∼5.1MeV(79) To obtain a direct estimate we will calculate the high energy expression for the LR correlator from Fig.1down to some intermediate scale Q2high and use Fig.2plus meson loops below the scale Q2low such thatQ2LR˜Π(Q2low)=Q2LR˜Π(Q2high)≡R2(80) Between Q2low and Q2high,this function will be approximated by the constant R2.The LR correlator is plotted versus Q2in Fig.5,and our result for the pion mass difference is shown in Fig.6as a function of R.The experimental value(after subtracting m d−m u effects)is[8][mπ+−mπ0]expt=4.43±0.03MeV(81)14and corresponds to50MeV<∼R<∼55MeV.This implies that for this calculation,our low energy model is good up to a scale of order Q2low∼400−450MeV and our high energy model is good down to a scale of order Q2high∼750−850MeV.Both of these scales are very reasonable.ConclusionsOne consequence of the dynamical breakdown of chiral symmetry in QCD is the gener-ation of a momentum dependent light quark mass.In the context of the vector,axialvector and scalar two-point correlators we have shown how this effective mass can be included systematically in calculations.The Ward-Takahashi identities and chiral symmetry are respected,as are thefirst few terms(at least)of the operator product expansion(OPE). An interesting result is the existence of terms at order1/Q6which do not contain the leading logarithm but which are not insignificant,especially in the case of the scalar correlator.It appears that for the scalar two-point function a naive application of the OPE in con-junction with the vacuum saturation approximation does not adequately describe some expected physics of QCD,namely the physics associated with the dynamical quark mass. This is perhaps not surprising.Practitioners of sum rules have long claimed[9]that there is something deficient in the usual application of the OPE in the case of the scalar and pseudoscalar two-point functions.This is particularly clear in the pseudoscalar case,for which the conventional OPE does not adequately account for the pion appearing in the sum rule.This has led to speculations of additional contributions to these OPEs,includ-ing instantons[9],renormalons[10],and effective four-fermion interactions[11].Our work indicates that the additional contributions will also have to reflect effects associated with chiral symmetry breaking,and in particular the momentum dependence of the dynamical quark mass.On the other hand in the case of the vector and axialvector two-point func-tions,the subleading terms in our analysis are not substantial enough to say that there is a serious conflict with standard treatments.We have described in this work a minimal model.It could be extended for example by including an effective wavefunction renormalization parameter in the quark propagator,or by adding extra terms to the vertices which maintain the Ward-Takahashi identities and15the OPE.Interestingly enough,wefind that the minimal model is sufficient to account for theπ+−π0electromagnetic mass difference.AcknowledgementsWe thank Michael Luke for useful discussions.This research was supported in part by the Natural Sciences and Engineering Research Council of Canada.References[1]M.A.Shifman,A.I.Vainshtein and V.I.Zakharov,Nucl.Phys.B147(1979)385.[2]H.D.Politzer,Nucl.Phys.B117(1976)397.See also ne,Phys.Rev.D10(1974)2605;H.Pagels,Phys.Rev.D19(1979)3080.[3]B.Holdom,Phys.Rev.D45(1992)2534.[4]B.Holdom,J.Terning,and K.Verbeek,Phys.Lett.245B(1990)612and273B(1991)549E;B.Holdom,Phys.Lett.292B(1992)150;B.Holdom,R.Lewis,and R.R.Mendel,Z.Phys.C63(1994)71.[5]T.Das,G.Guralnik,V.Mathur,F.Low and J.Young,Phys.Rev.Lett.18(1967)759.[6]J.S.Ball and T.-W.Chiu,Phys.Rev.D22(1980)2542.[7]J.Terning,Phys.Rev.D44(1991)887.[8]J.Gasser and H.Leutwyler,Nucl.Phys.B250(1985)465.[9]V.A.Novikov et.al.,Nucl.Phys.B191(1981)301,and references therein.[10]V.I.Zakharov,Nucl.Phys.B385(1992)452.[11]K.Yamawaki and V.I.Zakharov,University of Michigan preprints UM-TH-94-19,hep-ph/9406373and UM-TH-94-20,hep-ph/9406399.16Figure1:The complete QCD contribution to a two-point correlator.Both propagatorsγµ[γ5]. are full propagators;one vertex is full and the other vertex is a bareλa2Figure2:The quark contribution to a two-point correlator in the GNC′model.Meson contributions are not shown.Figure3:The two distinct components of the full axialvector and pseudoscalar vertices as derived from the GNC′model.The dashed line represents a pseudoscalar meson prop-agator which is generated from the diagrams of Fig.4.Figure4:The GNC′Lagrangian does not contain an explicit meson propagator,but a propagator is generated by the quark loop diagrams shown here.Figure5:The vector minus axialvector two-point correlator obtained from the GNC′model at low energies and from Fig.1at high energies for a typical choice of parameters. The two pieces are matched to a constant,R2,in the intermediate region.Figure6:The electromagnetic mass difference of the pion as a function of R,defined by (80),for a typical choice of parameters.17This figure "fig1-1.png" is available in "png" format from: /ps/hep-ph/9411412v2This figure "fig2-1.png" is available in "png" format from: /ps/hep-ph/9411412v212345020406080Figure 6m + - m o [M e V ]R [MeV]ππ00.0010.0020.0030.0040.0050.0060.0070.00800.51 1.52Figure 5 Q 2 L R (Q 2) [G e V 2]Q [GeV]Π~Figure 1Figure 2Figure 3Figure 4。

Quantum Computers in the CloudWith the rapid advancements in technology, quantum computing has emerged as a revolutionary concept that has the potential to transform various industries. Traditional computers rely on bits for processing information, which are represented as 0s and 1s. In contrast, quantum computers utilize quantum bits or qubits, which can exist in multiple states simultaneously. This unique property of qubits allows quantum computers to perform complex calculations at an unprecedented speed, revolutionizing the world of computing.One of the recent trends in the field of quantum computing is the development of cloud-based quantum computers. The concept of cloud computing has already gained traction in the tech industry, enabling users to access computational resources through the internet without the need for physical infrastructure. The combination of quantum computing and cloud technology has the potential to democratize quantum computing and make it accessible to a wider audience.One of the main advantages of quantum computers in the cloud is the scalability it offers. Quantum computers are notoriously challenging to build and maintain due to the delicate nature of qubits. By providing quantum computing resources through the cloud, organizations can bypass the need for investing in expensive hardware and infrastructure. They can simply access the quantum computing power they require, on-demand, without worrying about the complexities of maintenance and upgrades.Furthermore, cloud-based quantum computers have the potential to accelerate the pace of research and development in various fields. Industries such as pharmaceuticals, materials science, and cryptography can benefit greatly from the immense computational power offered by quantum computers. These industries often require extensive simulations and calculations, which can be time-consuming on traditional computers. With the availability of quantum computers in the cloud, researchers and scientists can now leverage this power to unravel complex problems and drive innovation.Security is another aspect where cloud-based quantum computers can play a significant role. Quantum cryptography, a field that utilizes the principles of quantum mechanics for secure communication, can be further enhanced with the advent of cloud-based quantum computers. Quantum key distribution protocols, which ensure secure transmission of encryption keys, can be bolstered by the use of powerful quantum computers. This has the potential to revolutionize the field of cybersecurity and protect sensitive data from malicious attacks.However, it is important to note that there are still challenges to overcome before cloud-based quantum computers become mainstream. Quantum computers are highly sensitive and require specialized environments with extremely low temperatures and minimal noise. Ensuring these conditions in a cloud-based infrastructure presents a significant technical challenge.In conclusion, quantum computers in the cloud hold immense potential to transform various industries by providing scalable and high-performance computing resources. The combination of quantum computing and cloud technology can democratize access to quantum computing and accelerate research and development in fields such as pharmaceuticals and cryptography. While there are challenges to overcome, the future of quantum computers in the cloud looks promising and could pave the way for groundbreaking innovations in the years to come.。

a rXiv:077.477v2[he p-ex]21D ec27EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN–PH–EP/2007–02409July 2007revised 25October 2007The Polarised Valence Quark Distribution from Semi-inclusive DIS The COMPASS Collaboration Abstract The semi-inclusive difference asymmetry A h +−h −for hadrons of opposite charge has been measured by the COMPASS experiment at CERN.The data were collected in the years 2002–2004using a 160GeV polarised muon beam scattered offa large polarised 6LiD target in the kinematic range 0.006<x <0.7and 1<Q 2<100(GeV /c )2.In leading order QCD (LO)the deuteron asymmetry A h +−h −measures the valence quark polarisation and provides an evaluation of the first moment of ∆u v +∆d v which is found to be equal to 0.40±0.07(stat .)±0.06(syst .)over the measured range of x at Q 2=10(GeV /c )2.When combined with the first moment of g d 1previously measured on the same data,this result favours a non-symmetric polarisation of light quarks ∆d at a confidence level of two standard deviations,in contrast to the often assumed symmetric scenario ∆d =∆The COMPASS CollaborationM.Alekseev32),V.Yu.Alexakhin8),Yu.Alexandrov18),G.D.Alexeev8),A.Amoroso30), A.Arbuzov8),B.Bade l ek33),F.Balestra30),J.Ball25),J.Barth4),G.Baum1),Y.Bedfer25),C.Bernet25),R.Bertini30),M.Bettinelli19),R.Birsa27),J.Bisplinghoff3),P.Bordalo15,a), F.Bradamante28),A.Bravar16,27),A.Bressan28,11),G.Brona33),E.Burtin25),M.P.Bussa30), A.Chapiro29),M.Chiosso30),A.Cicuttin29),M.Colantoni31),S.Costa30,+),M.L.Crespo29),S.Dalla Torre27),T.Dafni25),S.Das7),S.S.Dasgupta6),R.De Masi20),N.Dedek19),O.Yu.Denisov31,b),L.Dhara7),V.Diaz29),A.M.Dinkelbach20),S.V.Donskov24),V.A.Dorofeev24),N.Doshita21),V.Duic28),W.D¨u nnweber19),P.D.Eversheim3),W.Eyrich9), M.Faessler19),V.Falaleev11),A.Ferrero30,11),L.Ferrero30),M.Finger22),M.Finger jr.8), H.Fischer10),C.Franco15),J.Franz10),J.M.Friedrich20),V.Frolov30,b),R.Garfagnini30),F.Gautheron1),O.P.Gavrichtchouk8),R.Gazda33),S.Gerassimov18,20),R.Geyer19), M.Giorgi28),B.Gobbo27),S.Goertz2,4),A.M.Gorin24),S.Grabm¨u ller20),O.A.Grajek33), A.Grasso30),B.Grube20),R.Gushterski8),A.Guskov8),F.Haas20),J.Hannappel4),D.von Harrach16),T.Hasegawa17),J.Heckmann2),S.Hedicke10),F.H.Heinsius10),R.Hermann16),C.Heß2),F.Hinterberger3),M.von Hodenberg10),N.Horikawa21,c),S.Horikawa21),N.d’Hose25),C.Ilgner19),A.I.Ioukaev8),S.Ishimoto21),O.Ivanov8),Yu.Ivanshin8),T.Iwata21,35),R.Jahn3),A.Janata8),P.Jasinski16),R.Joosten3),N.I.Jouravlev8),E.Kabuß16),D.Kang10),B.Ketzer20),G.V.Khaustov24),Yu.A.Khokhlov24),Yu.Kisselev1,2),F.Klein4),K.Klimaszewski33),S.Koblitz16),J.H.Koivuniemi13,2),V.N.Kolosov24),E.V.Komissarov8),K.Kondo21),K.K¨o nigsmann10),I.Konorov18,20),V.F.Konstantinov24),A.S.Korentchenko8),A.Korzenev16,b),A.M.Kotzinian8,30),N.A.Koutchinski8),O.Kouznetsov8,25),A.Kral23),N.P.Kravchuk8),Z.V.Kroumchtein8),R.Kuhn20),F.Kunne25),K.Kurek33),dygin24),manna11,28),J.M.Le Goff25),A.A.Lednev24),A.Lehmann9),S.Levorato28),J.Lichtenstadt26),T.Liska23),I.Ludwig10), A.Maggiora31),M.Maggiora30),A.Magnon25),G.K.Mallot11),A.Mann20),C.Marchand25),J.Marroncle25),A.Martin28),J.Marzec34),F.Massmann3),T.Matsuda17),A.N.Maximov8,+),W.Meyer2),A.Mielech27,33),Yu.V.Mikhailov24),M.A.Moinester26),A.Mutter10,16),A.Nagaytsev8),T.Nagel20),O.N¨a hle3),J.Nassalski33),S.Neliba23),F.Nerling10),S.Neubert20),D.P.Neyret25),V.I.Nikolaenko24),K.Nikolaev8),A.G.Olshevsky8),M.Ostrick4),A.Padee34),P.Pagano28),S.Panebianco25),R.Panknin4),D.Panzieri32),S.Paul20),B.Pawlukiewicz-Kaminska33),D.V.Peshekhonov8),V.D.Peshekhonov8),G.Piragino30),S.Platchkov25),J.Pochodzalla16),J.Polak14),V.A.Polyakov24),J.Pretz4),S.Procureur25),C.Quintans15),J.-F.Rajotte19),S.Ramos15,a), V.Rapatsky8),G.Reicherz2),D.Reggiani11),A.Richter9),F.Robinet25),E.Rocco27,30), E.Rondio33),A.M.Rozhdestvensky8),D.I.Ryabchikov24),V.D.Samoylenko24),A.Sandacz33),H.Santos15,a),M.G.Sapozhnikov8),S.Sarkar7),I.A.Savin8),P.Schiavon28),C.Schill10),L.Schmitt20,d),P.Sch¨o nmeier9),W.Schr¨o der9),O.Yu.Shevchenko8),H.-W.Siebert12,16), L.Silva15),L.Sinha7),A.N.Sissakian8),M.Slunecka8),G.I.Smirnov8),S.Sosio30),F.Sozzi28),A.Srnka5),F.Stinzing9),M.Stolarski33,10),V.P.Sugonyaev24),M.Sulc14),R.Sulej34),V.V.Tchalishev8),S.Tessaro27),F.Tessarotto27),A.Teufel9),atchev8),G.Venugopal3),M.Virius23),N.V.Vlassov8),A.Vossen10),R.Webb9),E.Weise3,10), Q.Weitzel20),R.Windmolders4),S.Wirth9),W.Wi´s licki33),H.Wollny10),K.Zaremba34), M.Zavertyaev18),E.Zemlyanichkina8),J.Zhao16,27),R.Ziegler3)and A.Zvyagin19)The COMPASS experiment at CERN has recently published an evaluation of the deuteron spin-dependent structure function g d1(x)in the DIS region,based on measurements of the spin asymmetries observed in the scattering of160GeV longitudinally polarised muons on a longi-tudinally polarised6LiD target[1].These measurements provide an accurate evaluation of the first moment of g1for the average nucleon N in an isoscalar target g N1=(g p1+g n1)/2ΓN1(Q2=10(GeV/c)2)= 10g N1(x,Q2=10(GeV/c)2)d x=0.051±0.003(stat.)±0.006(syst.)(1)from which thefirst moment of the strange quark distribution can be extracted if the value of the octet matrix element(a8=3F−D)is taken from semi-leptonic hyperon decays.1)At LO in QCD the strange quark polarisation is given by∆s+∆12a8=−0.09±0.01(stat.)±0.02(syst.)(2) at Q2=10(GeV/c)2.Since quarks and antiquarks of the sameflavour equally contribute to g1,inclusive data do not allow to separate valence and sea contributions to the nucleon spin.We present here additional information on the contribution of the nucleon constituents to its spin based on semi-inclusive spin asymmetries measured on the same data as those used in Ref.[1].The semi-inclusive spin asymmetries for positive and negative hadrons h+and h−are defined byA h+=σh+↑↓−σh+↑↑σh−↑↓+σh−↑↑,(3)where the arrows indicate the relative beam and target spin orientations.The data used in the present analysis were collected by the COMPASS collaboration at CERN during the years2002–2004.The event selection requires a reconstructed interaction vertex defined by the incoming and scattered muons and located inside one of the two target cells [2].The energy of the beam muon is required to be in the interval140GeV<Eµ<180GeV and its extrapolated trajectory is required to cross entirely the two cells in order to equalise thefluxes seen by each of them.DIS events are selected by cuts on the photon virtuality(Q2>1(GeV/c)2) and on the fractional energy of the virtual photon(0.1<y<0.9).Final state muons are identified by signals collected behind the hadron absorbers.The hadrons used in the analysis are required to originate from the interaction vertex and to be produced in the current fragmentation region.The latter requirement is satisfied by selecting hadrons with fractional energy z>0.2. In addition an upper limit z<0.85is imposed in order to suppress hadrons from exclusive diffractive processes and to avoid contamination from muons close to the beam axis which escape identification by the muonfilters.The hadron identification provided by the RICH detector is not used in the present analysis.The resulting sample contains30and25million of positive and negative hadrons,respectively.The target spins are reversed at regular intervals of8hours during the data taking.The spin asymmetries are obtained from the numbers of hadrons collected from each target cell during consecutive periods before and after reversal of the target spins,following the same procedure as for inclusive asymmetries[3].They are listed in Table1and also shown in Fig.1as a function of x,in comparison to the SMC[4,5]and HERMES[6]results.The consistency of the results from the three experiments illustrates the weak Q2dependence of the semi-inclusive asymmetries. The COMPASS results show a large gain in statistical precision with respect to SMC,especially in the low x region(x<0.04),while at larger x the COMPASS errors are comparable to those of HERMES.The systematic errors,shown by the bands at the bottom of thefigure,result fromFigure1:Hadron asymmetries A h+d(left)and A h−d(right)measured by COMPASS,SMC[5]and HERMES[6]experiments.The bands at the bottom of thefigures show the systematic errors of the COMPASS measurements.different sources.The uncertainty on the various factors entering in the asymmetry calculation (beam and target polarisation,depolarisation factor and dilution factor)leads to a relative error of8%on the asymmetry when combined in quadrature.The uncertainty due to radiative corrections is smaller than in the inclusive case due to the selection of hadronic events and does not exceed10−3in any x bin.The presence of possible false asymmetries due to time-dependent apparatus effects has been studied in the same way as for the inclusive asymmetries:the data sample has been divided into a large number of subsamples,each of them collected in a small time interval.The observed dispersion of the asymmetries obtained for these subsamples has been found compatible with the value expected from their statistical error.This allows to set an upper limit for this type of false asymmetries at about half of the statistical error.Asymmetries, obtained with different settings of the microwave frequency used for dynamic nuclear polarisation of the target,have also been compared and did not reveal any systematic difference.Under the common assumption that hadrons in the current fragmentation region are pro-duced by independent quark fragmentation,the semi-inclusive asymmetries A h+,A h−can be written in LO approximation asA h(x,z,Q2)= q e2q∆q(x,Q2)D h q(z,Q2)Q2 A h−d(GeV/c)20.0052−0.010±0.012±0.0061.45−0.008±0.008±0.0042.06−0.009±0.007±0.0042.990.014±0.012±0.0064.030.012±0.016±0.0085.560.025±0.016±0.0088.290.033±0.018±0.00912.60.092±0.028±0.01617.70.132±0.045±0.02525.30.109±0.054±0.02842.60.023±0.101±0.05160.20.643±0.150±0.091Table1:Values of A h+d,A h−d and A h+−h−d with their statistical and systematical errors as afunction of x with the corresponding average value of Q2.asymmetry for the difference of the cross sections for positive and negative hadronsA h+−h−=(σh+↑↓−σh−↑↓)−(σh+↑↑−σh−↑↑)s,the difference asymmetries for pions and kaons are both equal to the valence quark polarisationAπ+−π−N =A K+−K−N=∆u v+∆d vpNhas also the same value butunder more restrictive assumptions and is more likely to be affected by target remnants.Since protons and antiprotons account only for about10%of the selected hadron sample,the relationA h+−h−N ≈∆u v+∆d vpN(x)closely followthe trend of Aπ+−π−N(x)with a difference never exceeding0.02.In addition the semi-inclusiveasymmetries A h+−h−N are found to be very close to the expected values(∆u v+∆d v)/(u v+d v)defined by the input parametrisations in the Monte Carlo simulation with the largest difference (≤0.05)appearing in the two highest intervals of x.At higher order in QCD the difference asymmetries still determine the valence quark polarisation without any assumption on the sea and gluon densities[11].Fragmentation functions no longer cancel out but their effect is expected to be small[12].The relation between the difference asymmetries of Eq.(5)and the single hadron asym-metries of Eq.(3)isA h+−h−=1σh+↑↓+σh+↑↑=σh−The ratio of cross sections for negative and positive hadrons r depends on the event kinematics and is obtained as the product of the corresponding ratio of the number of observed hadrons N−/N+by the ratio of the geometrical acceptances a+/a−r=σh−N+·a+from F2’s in which R=σL/σT was different from zero[15],the other one accounting for deuteron D-state contribution(ωD=0.05±0.01[16]):∆u v+∆d v=(u v+d v)MRSTq|≤5g d15(∆s+∆¯s) .(11)The values obtained by taking only thefirst term on the r.h.s.for x>0.3are also shown in Fig.3.They agree very well with the DNS curve,which is based on previous experiments where the same procedure had been applied[5,6].The upper limit of the neglected sea quark contribution,derived from the saturation of the positivity constraint|∆q|≤q is included in the systematic error.Thefirst moment of the polarised valence distribution,truncated to the measured range of x,Γv(x min)= 0.7x min[∆u v(x)+∆d v(x)]d x,(12)derived from the difference asymmetry for x<0.3and from g d1for0.3<x<0.7,is shown in Fig.3(right).Practically no dependence on the lower limit is observed for x min<0.03.We obtain for the full measured range of xΓv(0.006<x<0.7)=0.40±0.07(stat.)±0.06(syst.)(13) at Q2=10(GeV/c)2,with contributions of0.26±0.07and0.14±0.01for x<0.3and x>0.3, respectively.The uncertainty due to the unpolarised valence quark distributions(≈0.04)has been estimated by comparing different LO parametrisations and been included in the systematic error.It should be noted that removing the factor(1+R)in Eq.(10)would increase the value ofΓv to0.42±0.08±0.06.Our value ofΓv confirms the HERMES result obtained at Q2=2.5(GeV/c)2over a smaller range of x and is also consistent with the SMC result which has three times larger errors(Table2).The factor(1+R)was also used in the analyses of the previous experiments.x -range∆¯u +∆¯d (GeV /c )2Exp.Value Exp.Value 100.26±0.21±0.110.02±0.08±0.06HERMES0.023−0.60.363−0.0050.006−0.70.385−0.007COMPASS 0−1––Table 2:Estimates of the first moments ∆u v +∆d v and∆¯u +∆¯d from the SMC [5],HERMES [6],COMPASS data and also from the DNS fit at LO [17]truncated to the range of each experiment (lines 1–3).The SMC results were obtained with the assumption of a SU (3)f symmetric sea:∆¯u =∆¯d =∆¯s .The last line shows the COMPASS results for the full range of x .The difference between our measured value of Γv (0.006<x <0.3)and the integral of g N 1over the same range of x gives a global measurement of the polarised sea.Indeed,re-orderingEq.(11)we obtain0.300.006(∆d )+1s ) d x =−0.02±0.03(stat .)±0.02(syst .),(14)where the correlation between inclusive and semi-inclusive asymmetries has been taken into account in the statistical error.This result is compatible with zero but also consistent with the strange quark contribution of Eq.(2)and a vanishing contribution from the first term.It should be kept in mind that moments of sea quarks evaluated at LO have to be taken with caution because their values are small and thus comparable to the NLO corrections.The unmeasured contribution to Γv for x >0.7estimated from the LO DNS parameterisa-tion of Ref.[17]is 0.004at Q 2=10(GeV /c )2.Its upper limit corresponding to the assumption A h +−h −d =1for x >0.7is 0.007according to the MRST04parameterisation.The unmeasured low x contribution to Γv is expected to be negligible since the integral shows no significant variation when its lower limit is varied between 0.006and 0.02.We thus estimate the first moment asΓv (0<x <1)=0.41±0.07(stat .)±0.06(syst .).(15)The assumption of a fully flavour symmetric sea ∆d =∆s =∆u +∆2Γv +1u +∆s (Eq.(2))and suggests that ∆d ,if differentfrom zero,must be of opposite sign.Previous estimates by SMC and HERMES,also given in Table 2,are compatible with this hypothesis.The DNS parameterisation finds a positive ∆d ,about equal in absolute value.Opposite signs of ∆d are predicted inseveral models,e.g.in Ref.[24](see also [25]and references therein).Forthcoming COMPASSdata on a proton target will provide separate determinations of ∆d .Figure3:Left:Polarised valence quark distribution x(∆u v(x)+∆d v(x))evolved to Q2= 10(GeV/c)2according to the DNSfit at LO[17](line).Three additional points at high x are obtained from g d1[1].The two shaded bands show the systematic errors for the two sets of values.Right:The integral of∆u v(x)+∆d v(x)over the range0.006<x<0.7as the function of the low x limit,evaluated at Q2=10(GeV/c)2.In conclusion,we have determined at LO QCD the polarised valence quark distribution from the difference asymmetry for oppositely charged hadrons in DIS of muons on a polarised isoscalar target.Itsfirst moment at Q2=10(GeV/c)2over the measured range of x(0.006–0.7) is found to be0.40±0.07(stat.)±0.06(syst.).This value disfavours the assumption of aflavour symmetric polarised sea at a confidence level of two standard deviations and suggests that∆d are of opposite sign.AcknowledgementsWe gratefully acknowledge the support of the CERN management and staffand the skill and effort of the technicians of our collaborating institutes.Special thanks are due to V.Anosov and V.Pesaro for their technical support during the installation and the running of this exper-iment.This work was made possible by thefinancial support of our funding agencies. 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a r X i v :n u c l -e x /0410038v 1 25 O c t 2004Open Charm Production at STARHaibin Zhang †(for the STAR Collaboration)§†Physics Department,Brookhaven National Laboratory,Upton,NY,11953,USA E-mail:haibin@Abstract.We present the open charm spectra at mid-rapidity from directreconstruction of D 0,D ∗and D ±in d+Au collisions at√relativistic heavy ion collisions.Furthermore,the production of open charm hadrons in the same collision system provides a comparison baseline to test the J/ψproduction mechanism in the relativistic heavy ion collisions at RHIC energies since some theories predict a J/ψenhancement due to the charm quark coalescence effect[5,6,7,8,9]while others predict a J/ψsuppression due to the color screening effect[10].2.MeasurementsThe data used for the direct D0,D∗and D±reconstruction and the charm semileptonic decay analysis were taken during the2003RHIC run in d+Au and p+p collisions at √D0candidate to calculate the invariant mass of a D∗candidate M(Kππs).Panel(b)ofFig.1shows the distribution of the invariant mass difference∆M=M(Kππs)−M(Kπ) after background subtractions.A clear signal is seen around the nominal value of M(D∗)−M(D0).This distribution wasfit with a Gaussian function and the mass difference and the width was found to be146.37±0.15MeV/c2(145.42±0.05MeV/c2in the PDG)and0.57±0.16MeV/c2,respectively.)2) (GeV/cπM(K2Counts/1MeV/c)2) (GeV/cπ)-M(KππM(K2Counts/.3MeV/c)2) (GeV/cππM(K2Counts/1MeV/c)2) (GeV/cρπM(K2Counts/1MeV/cFigure 1.The invariant mass distribution after the mixed-event backgroundsubtraction and a further linear background subtraction of M(Kπ)for the low p T(p T<3GeV/c)D0+¯D0in Panel(a),∆M=M(Kππs)−M(Kπ)for the D∗±inPanel(b),M(Kππ)for the D±in Panel(c),M(Kπρ0)for the high p T(8.6<p T<12GeV/c)D0+¯D0in Panel(d),respectively.The D±signal was reconstructed through the decay of D+→K−π+π+(D−→K+π−π−)with a branching ratio of9.1%.The invariant mass distribution of M(Kππ) after background subtractions is shown in Panel(c)of Fig.1with the D±rapidity |y|<0.75and7.5<p T<11GeV/c.A Gaussian function wasfit to this distribution and the mass and width was found to be1880±5MeV/c2(1869.3±0.5MeV/c2in the PDG) and16.2±8MeV/c2,respectively.The high p T(8.6<p T<12GeV/c)D0was independently reconstructed through the decay of D0→K−π+ρ0(¯D0→K+π−ρ0)which has a branching ratio6.2%.The analysis was similar to that for the low p T D0except that an additionalπ+π−pair with its invariant mass0.62<M(π+π−)<0.86was combined with the selected kaon and pion candidates for a D0candidate.The invariant mass distribution for M(Kπρ0) (=M(Kπππ))after background subtractions is shown in Panel(d)of Fig.1.Thisdistribution was fit with a Gaussian function and the mass and the width was found to be 1850±5MeV/c 2and 13.6±4MeV/c 2,respectively.2.2.Single Electron AnalysisA prototype time-of-flight system (TOFr)[16,17]based on the multi-gap resistive plate chamber technology was installed in STAR with an azimuthal angle coverage ∆φ≃π/30and pseudorapidity range -1<η<0.Besides its capability of hadron identification,electrons/positrons could be identified at p T <3GeV/c by the combination of velocity (β)from TOFr and dE/dx from TPC measurements.In addition,electrons can also be identified with 2<p T <4GeV/c in TPC since hadrons have lower dE/dx due to the relativistic rise of the dE/dx of electrons.The inclusive spectra for the low p T electrons/positrons measured from TOFr+TPC are shown in Fig.2as solid symbols and the spectra for higher p T electrons from TPC only are shown as open circles for p+p (left)and d+Au (right),respectively.-2d y ) (Ge V /c )T d p T p πN )/(22(d 101010(GeV/c)T p R a t i o(GeV/c)T p Figure 2.Upper panels:Electron distributions from p+p (left)and d+Au (right)collisions.Bottom panels:Ratios of inclusive electrons over the total backgrounds.The gray bands represent the systematic uncertainties.The dominant sources of the electron background are the photon conversions γ→e +e −(dashed curves in Fig.2)and π0→γe +e −Dalitz decay (dotted curves)and ηDalitz decay (dash-dotted curves).To measure these photonic electron background spectra,the invariant mass of the e +e −pairs were constructed from an electron (positron)in TOFr and every positron (electron)candidate in TPC.The sum of these photonic background is shown as the solid curves in Fig.2.In the bottom panel ofFig.2,the ratio of the inclusive electron/positron spectra and the background is shown and clear signal excesses are visible with p T>1GeV/c.3.Results3.1.Total c¯c Cross SectionFrom the direct low p T D0reconstruction in the d+Au collisions,the invariant yield d2N/2πp T dp T dy as a function of p T after efficiency and acceptance correction was extracted in four p T bins at p T<3GeV/ing an exponentialfit to the invariant yield in transverse mass(m T),the midrapidity yield dN/dy for D0was found to be 0.028±0.004(stat.)±0.008(sys.).We also performed afit with the combined results of D0and electron distributions in d+Au collisions,assuming that the D0spectrum follows a power law in p T and that the remaining electrons after the background subtractions are charm semileptonic decays.The yield difference between the above twofitting methods is much smaller than the statistical uncertainties.Figure3.The total c¯c cross section per nucleon-nucleon collision vs.the collisionenergy.The dotted line is a power-lawfit.The dashed and dash-dotted curvesare PYTHIA calculations with different options.The solid curve is a NLO pQCDcalculation.We used the ratio R=N(D0)/N(c¯c)=0.54±0.05from e+e−collisions[15]to convert the D0yield to total c¯c yield.The d+Au number of binary collisions N bin and the p+p inelastic scattering cross section was used to convert the dN c¯c/dy in d+Au collisions in to dσc¯c/dy in p+p collisions.A factor of4.7±0.7[18,19]was used to convert the dσ/dy at midrapidity to the total cross section.The total charm cross section per nucleon-nucleon interaction for d+Au collisions at 200GeV is 1.3±0.2±0.4mb from D 0alone and 1.4±0.2±0.4mb from the combined fit of D 0and electrons.The beam energy dependence of the charm cross section from this analysis is depicted in Fig.3by the starsymboland compared to PHENIX [20],UA2[21],FNALand SPS [22]measurements.The dotted line is a power law fit,σNNc ¯c ∝(√s =200GeV,both calculations underpredict the total charm cross section by at least a factor of 3.3.2.Open Charm p T SpectrumThe invariant yield distributions as a function of p T for D ∗±,D ±and the high p T D 0were obtained using the same methods as that for the low p T D 0.With all the data points from the direct open charm measurements shown in Fig.4,the p T distribution was fit to a power-law function,A (1+p T /p 0)−n ,with the ratio of D ∗/D 0=D +/D 0as a free parameter,where A ,p 0and n are fit parameters.From the fit,we obtained dN/dy (D 0)=0.027±0.004±0.007which is consistent with the exponential fit results to the low p T D 0data points only, p T =1.32±0.08±0.16GeV/c,and theFigure 4.The measured invariant yield distributions for D 0,D ∗±and D ±and a power-law fit to the data points.The D ∗and D ±data points were scaled by the ratio D ∗/D 0=D +/D 0=0.40±0.09±0.13after the power-law fit.ratio D∗/D0=D+/D0=0.40±0.09±0.13which agrees with the ratios from previous measurements[23]and theoretical predictions[24]within the experimental uncertainties.4.ConclusionThe direct open charm D0,D∗±and D±signals were reconstructed in d+Au collisions at√。

Cloud computing has revolutionized the way businesses and individuals handle data and software applications.It is a model for delivering various services over the internet, such as servers,storage,databases,networking,software,analytics,and more.Heres an essay on the topic of cloud computing,exploring its benefits,challenges,and future prospects.Title:The Impact of Cloud Computing on Modern SocietyIn the digital age,the concept of cloud computing has become an integral part of our daily lives,transforming the way we store,access,and process data.The cloud,a metaphor for the internet,offers a scalable and flexible solution to the evergrowing demand for data storage and computational power.This essay delves into the multifaceted nature of cloud computing,discussing its advantages,the challenges it poses, and its potential to shape the future of technology.IntroductionThe advent of cloud computing has been likened to the shift from individual power generators to centralized power plants during the industrial revolution.Just as electricity became a utility that could be accessed on demand,cloud computing has made computing power and data storage a service that can be consumed as needed.This paradigm shift has farreaching implications for businesses,governments,and individuals alike.Benefits of Cloud Computing1.Cost Efficiency:One of the most significant benefits of cloud computing is its costeffectiveness.By eliminating the need for physical hardware and reducing the costs associated with maintenance and upgrades,businesses can save substantial amounts of money.2.Scalability:The cloud allows for easy scalability,enabling businesses to adjust their computing resources according to their needs.This flexibility is particularly beneficial for startups and enterprises that experience fluctuating workloads.3.Accessibility:Data and applications hosted on the cloud can be accessed from anywhere with an internet connection,providing employees with the freedom to work remotely and collaborate more effectively.4.Reliability and Redundancy:Cloud service providers typically offer robust data protection measures,including data redundancy,which ensures that data is backed up and can be recovered in the event of a failure.Challenges of Cloud ComputingDespite its many advantages,cloud computing is not without its challenges.Key concerns include:1.Security:The security of data in the cloud is a major concern for many organizations. Data breaches and cyberattacks are constant threats,and the responsibility for securing data often falls on the service provider.pliance:Organizations must ensure that their cloud computing solutions comply with various regulations and standards,which can be complex and vary by region.3.Vendor LockIn:The risk of becoming dependent on a single cloud provider can be a significant issue,as it may limit flexibility and increase costs if the provider changes its terms or pricing.Future Prospects of Cloud ComputingAs technology continues to evolve,the role of cloud computing is expected to expand. The integration of artificial intelligence,machine learning,and the Internet of Things IoT with cloud services is set to create new opportunities for innovation.Additionally,the rise of edge computing,which brings computation and data storage closer to the source of data generation,is poised to complement cloud computing by reducing latency and bandwidth usage.ConclusionIn conclusion,cloud computing has become a cornerstone of modern technology, offering a range of benefits that have the potential to transform industries and improve the way we live and work.However,it is crucial for organizations to carefully consider the challenges and ensure that they have the necessary strategies in place to mitigate risks. As we look to the future,the continued development and adoption of cloud computing technologies will undoubtedly play a pivotal role in shaping the digital landscape.This essay provides a comprehensive overview of cloud computing,highlighting its significance in the modern world and the considerations that must be taken into account as we move forward.。