【作者】 李辉；

【导师】 吕准；

【作者基本信息】 东南大学 ， 粒子物理与原子核物理， 2022， 博士

【摘要】 研究强子自旋结构以及量子色动力学(QCD)非微扰区域的动力学是当前QCD自旋物理的重要课题。进行此类研究的重要途径是定量考察高能散射过程中与自旋相关的物理可观测量,其中用到的重要理论工具是因子化定理。在因子化定理中,散射截面可以因子化为短距离的硬过程与长距离的软过程,前者可用微扰QCD计算得到,后者借助实验测量确定的唯像函数来表示。本文采用的唯像函数是部分子分布函数和碎裂函数。本篇学位论文在横动量依赖(TMD)因子化定理中包含TMD演化效应,由以上唯像函数出发探讨这些物理可观测量的来源,以及它们蕴含的强子自旋结构和夸克横动量结构,主要做了以下几个方面的工作:1.利用TMD因子化定理,我们在π介子入射的Drell-Yan过程中,研究了 sin(2φ-φS)方位角依赖的单横向自旋不对称度。该不对称度的主要贡献来自于Boer-Mulders部分子分布函数h1⊥和横向性部分子分布函数h1的卷积,因此可以将h1作为“自旋探针”对包含非极化核子中的横向极化夸克分布信息的Boer-Mulders部分子分布函数h1⊥进行探测。利用已有的h1⊥模型计算结果和h1参数化结果,以及考虑相应的演化效应,在COMPASS运动学范围下数值计算sin(2φ-φs)方位角不对称度。在计算中,作为输入量非微扰TMD演化公式和π介子部分子分布函数,我们分别提供了两种不同的参数化结果和两种不同的光锥模型计算结果进行对比。我们发现,不同的π介子部分子分布函数对该不对称度的影响比较大,而不同的非微扰TMD演化公式只影响了q⊥-不对称度的形状。研究还表明,我们计算得到的xp、xπ、xF和q⊥依赖的不对称度是可观测的,并且在符号和数量级上与目前COMPASS实验组测量结果一致。因此,在TMD因子化框架下,利用横向极化的π-p数据,我们可以获取π介子的部分子分布函数的信息以及其相应的非微扰TMD演化公式的信息。2.利用TMD因子化定理,我们在e+e-→Λ↑π±X和e+e-→Λ↑K±X湮灭过程中,研究了 Λ超子的横向极化度。该横向极化度的主要贡献来自于Λ超子的横向极化碎裂函数(PFF)D1T⊥和π介子或K介子的非极化碎裂函数的卷积。我们采用D1T⊥旁观双夸克模型的计算结果,以及考虑相应的演化效应,在Belle运动学范围下数值计算Λ超子的横向极化度。对于D1T⊥的非微扰TMD演化公式,我们采用两种不同的参数化结果作为输入。研究结果表明,Λπ+和Λπ-产生过程的计算结果与目前Belle实验组的测量值在符号和形状上是一致的,但是Λπ-和ΛK±产生过程的计算值与Belle数据严重不一致。进一步将模型计算得到的PFF与可用的参数化结果对照发现,模型计算得到的D1T⊥Λ/u应该为正值,D1T⊥Λ/d应该为负值且海夸克贡献较大。这些模型结果应该具备的特点与我们的模型输入不一致,所以在未来的模型计算中,我们需要考虑SU(6)对称性破缺以及考虑海夸克的贡献。另外,未来的计算中考虑加入Y项的贡献,从而改变在大动量区域极化度的大小。3.利用TMD因子化定理,我们在横向极化Λ超子产生的半单举深度非弹性散射过程中,研究了sin(φΛ-φS)方位角依赖的单自旋不对称度。该不对称度的主要贡献来自于Λ超子PFFD1T⊥和质子靶非极化部分子分布函数f1的卷积。利用已有的D1T⊥旁观双夸克模型的计算结果(Set Ⅰ)和D1T⊥参数化结果(set Ⅱ)作为不同输入,以及考虑相应的演化效应,对未来电子-离子对撞机(EIC)中的sin(φΛ-φS)单自旋不对称度进行预言。对于输入量D1T⊥的非微扰TMD演化公式,我们采用两种不同的参数化结果进行对比。研究发现,D1T⊥碎裂函数的不同输入导致了该不对称度具有不同的符号。我们详细讨论了计算中用到的假设和近似可能会对EIC中的计算结果带来大的不确定范围,并讨论了 SetI的计算未来需要改进的地方。未来EIC实验组关于sin(φΛ-φS)高精度的测量值可以对PFFD1T⊥提供重要的交叉验证,并对该函数做出更严格的限制。更多还原

【Abstract】 The spin of hadrons and the non-perturbative Quantum Chromodynamics(QCD)are the important topics in current QCD spin physics,in which the investigation on the spin-related physical observables in high energy scattering processes can serve as the precious approach,within the factorization theorem as an important theoretical tool.Based on the factorization theorem,the physical observables can be separated into two parts:the short distance part,which can be calculated by perturbative QCD,and the long distance part,which is usually obtained by phenomenological extraction from experimental data.In this paper,the later one corresponds to the distribution functions and fragmentation functions.And in this thesis,we explore the origin of the spin-related physical observables from those phenomenological functions,and their implication to the spin structure of hadrons and quark transverse momentum,within the transverse momentum dependent(TMD)factorization including evolution effects.The main content of the thesis are organized as follows:1.We investigate the single transverse-spin asymmetry with a sin(2φ-φS)modulation in the pion induced Drell-Yan process within the theoretical framework of the TMD factorization.Since the asymmetry is contributed by the convolution of the Boer-Mulders function h1⊥ and the transversity h1,the transversity h1 can serve as a " spin analyzer" to access the Boer-Mulders function h1⊥ which represents the transversely polarization of quarks inside an unpolarized hadron.Using the model results for h1⊥ and the available parametrization for h1,and considering the TMD evolution effect of the parton distribution functions by including the Sudakov form factors,we numerically estimate the sin(2φ-φS)asymmetry at the kinematics of COMPASS.For comparison,we apply two different nonperturbative TMD evolution formalism associated with the distribution functions of the proton and the pion and two different model result associated with the distribution functions of the pion.we find that the asymmetry is sensitive to the choice of the pion distribution function,while different choice of the TMD evolution formalism will only on the nonperturbative TMD evolution only affect the shape of the q⊥-dependent of the asymmetry.We also find that the sin(2φ-φS)asymmetry as functions of xp,xπ,xF and q⊥ is sizable and qualitatively consistent with the recent COMPASS measurement in both sign and magnitude.Furthermore,our study may provide a framework to access the Boer-Mulders function of the pion and the corresponding nonperturbative TMD evolution formalism through transversely polarized πp data.2.We investigate the transverse polarization of the 1 hyperon in the processes e+e-→Λ↑π±X and e+e-→Λ↑K±X within the framework of the TMD factorization.The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function(PFF)D1T⊥ of the lambda hyperon and the unpolarized fragmentation function D1 of pion/kaon.We adopt the spectator diquark model result for D1T⊥,and considering the TMD evolution effect of the fragmentation functions by including the Sudakov form factors,to numerically estimate the transverse polarization in e+e-→Λ↑hX process at the kinematical region of Belle Collaboration.For comparison,we apply two different nonperturbative TMD evolution formalism associated with the fragmentation functions of the Λ,pion and kaon.It is found that our prediction on the polarization in the Λπ+ production and Λπ-is consistent with the recent Belle measurement in size and sign,while the model predictions on the polarizations in Λπ-and ΛK+ productions show strong disagreement with the Belle data.A comparison with our model input for the PFF with the available parameterizations indicates that a positive D1T⊥Λ/u,negative D1T⊥Λ/d and sizable sea PFF are essential to describe the many aspects of the Belle data.Possible improvements of the model calculation include allocating substantial SU(6)breaking effect to lead to a opposite sign of the u quark PFF compared with the d quark PFF,incorporating the sea quarks in the model,and taking into the Y-term in the large momentum region.3.We investigate the sin(φΛ-φS)single-spin asymmetry in the transversely polarized Λproduction in semi-inclusive deeply inelastic scattering process within the framework of the transverse momentum dependent(TMD)factorization.The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function D1T⊥ of the Λ hyperon and the unpolarized TMD distribution function f1 of the proton target.We adopt the spectator diquark model result(Set Ⅰ)and the available parametrization(set Ⅱ)for,D1T⊥,Λ↑/q,and considering the TMD evolution effect of the parton distribution functions and the fragmentation functions by including the Sudakov form factors,to numerically estimate the sin(φΛ-φS)asymmetry at the kinematical region of electron ion collider(EIC).For comparison,we apply two different nonperturbative TMD evolution formalism associated with the distribution function of the proton and the fragmentation function of the Λ.It is found that the spectator di quark model result(Set Ⅰ)and the parameterized result(set Ⅱ)of D1T⊥,Λ↑/q lead to different sink(φΛ-φS)asymmetry,particularly in sign.We also discuss the impact of the assumptions and approximations applied in the calculations,which may bring large uncertainties to the results in EIC.Future measurements on the sin(φΛ-φS)asymmetry with high precision at EIC can provide important cross check on the availableΛ polarizing fragmentation functions as well as constrain them more stringently.更多还原