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  1. 核子结构研究与新进展 中国科技大学粒子物理与核物理讨论班 梁作堂 山东大学物理学院 2011年8月25日,合肥,中国科技大学 粒子物理与核物理讨论班

  2. 引言 单举轻子核子深度非弹性散射(DIS)实验,部分子模型与部分子分布函数 --------------- A short overview 半单举轻子核子深度非弹性散射(SIDIS)与部分子关联函数 总结与展望 Contents 粒子物理与核物理讨论班

  3. 引言 核子结构研究的核心问题、特点、意义 Contents Why parton distribution function is defined as 粒子物理与核物理讨论班

  4. 物质结构 原子: 10-10 m=1 核子:1fm=10-15m 电子、夸克:<10-3fm 引言:物质结构图象 质子(p)、中子(n):统称为核子 (Nucleon, N) 夸克(quark) 电子(electron) 原子核 (nucleus, A) 原子(atom) 物质 粒子物理与核物理讨论班

  5. 强子由夸克构成 强子结构的夸克模型 1964年,Gell-Mann, Zweig Nobel prize in 1969. 夸克有三种: flavor(味道) charge(电荷) spin(自旋) u (up) 2/3 1/2 d (down) -1/3 1/2 s (strange) -1/3 1/2 粒子物理与核物理讨论班

  6. 量子场论的基本性质 高速运动的核子的结构? 真空涨落与真空激发 vacuum excitation A dynamical picture for a high energy nucleon that participates in high energy reaction. 核子结构研究的基本问题 粒子物理与核物理讨论班

  7. 核子结构是粒子物理重要前沿 Introduction 粒子物理标准模型 电 弱 强 弱电统一理论 实 验 充分检验 微扰部分 量子色动力学 (QCD) 尚未解决的 重大难题 非微扰部分 Quark has color degree of freedom, strong interaction is color interaction 强相互作用性质、 核子结构、 强子化机制、 … … 高能反应实验 粒子物理与核物理讨论班

  8. 关于核子结构的研究 Introduction 核子结构的研究与 原子分子结构的研究有很大的差别。 非微扰QCD求解困难与色禁闭 目前通常的做法 核子结构 定量描述 与普适性 对高能反应理论描述的需要 高能反应的预言 合适的物理参量 粒子物理与核物理讨论班

  9. Inclusive deep-inelastic lepton-nucleon scattering (DIS) Introduction: DIS and Nucleon Structure The differential cross section: leptonic tensor hadronic tensor 核子结构 理想的探针 电磁相互作用 点结构 电子: 完全确定 的定义式: 电磁流: 质子波函数 一般形式: structure function of nucleon 粒子物理与核物理讨论班

  10. Bjorken Scaling 质子由更小的点粒子构成 Callen-Gross关系 构成质子的点粒子自旋为1/2 Gottfried求和规则 构成质子的点粒子带分数电荷 Jerome I. Friedman Henry W. Kendall Richard E. Taylor Introduction: DIS and Nucleon Structure 几十年实验与理论研究,取得了巨大成就: Nobel Prize 1990 “We see quarks through deeply inelastic lepton-nucleon scattering.” 部分子模型:目前核子结构最成功的描述。 粒子物理与核物理讨论班

  11. 单举轻子核子深度非弹性散射(DIS)实验,部分子模型与部分子分布函数单举轻子核子深度非弹性散射(DIS)实验,部分子模型与部分子分布函数 --------------- A short overview 单举DIS过程与(传统的)部分子模型、 部分子分布函数 Higher twist贡献 Contents 粒子物理与核物理讨论班

  12. Parton model: A fast moving proton A beam of free partons number density of parton q in nucleon. known as parton distribution functions (PDF) (部分子分布函数) DIS and Parton Model(部分子模型) R.P. Feynman, Bjorken and Paschos Lots of virtual processes such as In a fast moving frame, because of time dilatation, they exist for quite long time. In the infinite momentum frame (IMF), they exist forever. E.g.: for electron scatters with free parton scattering amplitude the elementary scattering process 粒子物理与核物理讨论班

  13. Parton model: A fast moving proton A beam of free partons DIS and Parton Model(部分子模型) Lots of Virtual processes such as In a fast moving frame, because of time dilatation, they exist for quite long time. In the infinite momentum frame, they exist forever. Impulse Approximation(冲量近似): During the interaction of the lepton with the nucleon (1) interaction between the partons can be neglected; (自由的夸克) (2) the lepton interacts only with one single parton; (无多重散射) (3) interaction of the lepton with different partons can be added incoherently. (传统、经典) 粒子物理与核物理讨论班

  14. Parton model: DIS and Parton Model(部分子模型) direct consequences Bjorken Scaling: 不依赖 Q 质子由更小的自由的点粒子构成 Callen-Gross关系 构成质子的自由的点粒子自旋为1/2 Gottfried求和规则 构成质子的自由的点粒子带分数电荷 “We see quarks through deeply inelastic lepton-nucleon scattering.” Nobel prize in 1990 for Friedman, Kendall and Taylor. 粒子物理与核物理讨论班

  15. Parton model: Drell-Yan process: High transverse momentum jet production: parton distribution functions cross sections for elementary scattering process Parton Model and Other High Energy Reactions A fast moving proton A beam of free partons The factorized form for the differential cross section: The parton distribution functions have to rely on parameterizations. 粒子物理与核物理讨论班

  16. Parton model parton distribution functions cross sections for elementary scattering process Global QCD analysis and PDFLIB Experimental data for the cross sections of, e.g.: Empirical forms of the PDF’s parameterizations of the parton distribution functions 粒子物理与核物理讨论班

  17. Parton distribution function library:many different sets Global QCD analysis and PDFLIB E.g.: CTEQ collaboration and CTEQ parameterizations Home page at: http://www.phys.psu.edu/~cteq Early parameterizations: Duke-Owens: D. Duke and J. Owens, Phys. Rev. D30, 49 (1984); Morfin-Tung: J.G. Morfin and W.K. Tung, Z. Phys. C52, 13(1991). The CTEQ Collaboration is founded by Wu-Ki Tung in Michgan State University and colleagues in the early 1990s and now consists of 31 theorists and experimentalists at 18 universities. Different versions of parameterizations: from CTEQ1 to CTEQ10. 粒子物理与核物理讨论班

  18. Global QCD analysis and PDFLIB 粒子物理与核物理讨论班

  19. Parton distribution functions: Global QCD analysis and PDFLIB Some of the salient features: Bjorken scaling violation: QCD evolutions Gluon contribution: Quarks and anti-quarks carry only half of the momentum of proton Symmetry breaking in the sea distributions: Gottfried sum rule violation Brodsky, Ma; NuTev, ... 粒子物理与核物理讨论班

  20. with polarized beams and targets c.m. frame of Polarized DIS and spin structure of nuleon polarized photon make selection of polarization of quark/anti-quark Spin dependent structure function ± means: helicity of qj = ± helicity of p Integrated over x: contribution of spins of quarks to that of proton 粒子物理与核物理讨论班

  21. DIS & Parton Model: Extracting  from Inclusive DIS data Integrated over x: Operator expression: SUf(3) Symmetry in Hyperon Decay Wigner-Eckart Theorem: the 8-dimensional representation of the SUf(3) group. E.g.: 粒子物理与核物理讨论班

  22. Earliest experiments: Extracting  from Inclusive DIS data SLAC E80, E130, in 1970s-80s. 1989: EMC+E130+E80: “proton’s spin crisis” Since then, intensive studies have been performed. 粒子物理与核物理讨论班

  23. Collection of data available Extracting  from Inclusive DIS data 粒子物理与核物理讨论班

  24. Results: large contribution from gluon ? Extracting  from Inclusive DIS data Still puzzling situation for the origin of proton spin 1989: EMC+E130+E80: “proton’s spin crisis” 1990s: SLAC, SMC (CERN), HERMES (DESY) 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : probably small? orbital angular momentum important? 粒子物理与核物理讨论班

  25. Parton Model with QCD corrections The “QCD Analysis” and the x-Dependence Inclusive DIS data on g1 Empirical forms of q and g Wilson coefficients, calculable in pQCD Spin-dependent parton distribution functions 粒子物理与核物理讨论班

  26. NLO Results at Q2=4GeV2 Early example of the results of “QCD Analysis” Blümlein & Böttcher, NPB636(2002)225. 粒子物理与核物理讨论班

  27. Flavor tagging in semi-inclusive DIS Other Measurements To the leading order: purity, spin independent, calculable using e.g. LEPTO. 粒子物理与核物理讨论班

  28. RHIC Spin program Other Measurements polarized pp collisions at 200, 500GeV 粒子物理与核物理讨论班

  29. DSSV parameterization well constrained non-zero, with large uncertainties. with a node for sign change very large uncertainties. Global QCD analysis for polarized parton distributions de Florian, Sassot, Stratmann, Vogelsang, Phys.Rev.D(2009). 粒子物理与核物理讨论班

  30. 单举轻子核子深度非弹性散射(DIS)实验,部分子模型与部分子分布函数单举轻子核子深度非弹性散射(DIS)实验,部分子模型与部分子分布函数 --------------- A short overview 单举DIS过程与部分子模型、 部分子分布函数 部分子分布函数的定义与Higher twist贡献 Contents 粒子物理与核物理讨论班

  31. Need for a proper theoretical framework: Collinear approximation & operator expressions of PDF’s Approximations: What is neglected? Are they indeed small so that we can neglect them? Can we improve the accuracy (order by order)? Parton distribution functions: A proper definition (in terms of operators and wave functions) ? Physical interpretations? Universality? Calculable using models, QCD theory? 粒子物理与核物理讨论班

  32. Towards an accurate theoretical framework leptonic tensor hadronic tensor Collinear approximation & operator expressions of PDF’s The differential cross section: The hadronic tensor: 粒子物理与核物理讨论班

  33. Parton model: Collinear approximation & operator expressions of PDF’s The hadronic tensor: 粒子物理与核物理讨论班

  34. Parton model: Collinear approximation & operator expressions of PDF’s The hard part: The matrix element: Collinear approximation: Leading twist (neglecting 1/Q suppressed terms): parton distribution function 粒子物理与核物理讨论班

  35. Parton distribution function: Collinear approximation & operator expressions of PDF’s the number density of quark and anti-quark. However, the expression is not (local color) gauge invariant! 粒子物理与核物理讨论班

  36. Inclusive DIS with QCD interaction We take the “multiple gluon scattering” into account Parton density matrix: Not gauge invariant! 粒子物理与核物理讨论班

  37. Collinear approximation: Inclusive DIS with QCD interaction  Approximate k in the hard parts as k =xp: Keep only the longitudinal component of the gluon field: Using the Ward identities such as, gauge invariant! gauge link the leading twist contributions can be obtained 粒子物理与核物理讨论班

  38. Collinear expansion: Inclusive DIS with QCD interaction Ellis, Furmanski, Petronzio, (82) Qiu, Sterman (90,91)  Expanding the hard parts around k =xp: Decomposition of the gluon field: Using the Ward identities such as, to replace the derivatives etc. 粒子物理与核物理讨论班

  39. Inclusive DIS with QCD interaction Contain QCD interactions. (Color) gauge invariant ! A consistent theoretical framework for inclusive DIS. 粒子物理与核物理讨论班

  40. … Inclusive DIS: Summary  collinear approximation leading twist contribution, no gauge invariance.  collinear approximation leading twist contribution, with gauge invariance.  collinear expansion consistent framework for leading and higher twist, with gauge invariance. 粒子物理与核物理讨论班

  41. Lesson (I): … Inclusive DIS with QCD interaction Quark distribution is not merely but i.e., it contains “intrinsic motion” and “multiple gluon scattering”. Intrinsic transverse momentum and multiple gluon scattering effects always mix up to give us the finally observed effects. Lesson (II): Multiple gluon scattering effects are contained in the gauge link. Collinear expansion is the necessary procedure to obtain the correct form of gauge invariant parton distributions. 粒子物理与核物理讨论班

  42. 半单举轻子核子深度非弹性散射(SIDIS)与部分子关联函数半单举轻子核子深度非弹性散射(SIDIS)与部分子关联函数 Contents 粒子物理与核物理讨论班

  43. 半单举深度非弹性散射过程 的其它分量   更复杂的矩阵元,如 Inclusive DIS with QCD interaction What can we learn through inclusive DIS about the structure of nucleon? Quark distribution function: Quark helicity distribution: All concentrate on 描述核子结构的矩阵元: 有8个独立的分量(“广义结构函数”),研究了其中的两个。 (semi-inclusive DIS) 目前有大量实验,如HERMES, COMPASS, JLab, FAIR, ........., 未来eRHIC? 粒子物理与核物理讨论班

  44. Semi-inclusive DIS: Semi-inclusive DIS and Parton Correlation Functions Much more to learn! In inclusive DIS, only longitudinal distributions are studied, e.g. In semi-inclusive DIS, longitudinal and transverse (transverse momentum dependent, TMD) distributions are studied, e.g. Furthermore 粒子物理与核物理讨论班

  45. The 8 independent TMD quark distribution/correlation functions at leading twist Quark distribution/correlation functions at leading twist Nucleon Longitudinally polarized Un-polarized Transversely polarized Quark Un-polarized Sivers function momentum distribution Longitudinal polarization helicity distribution Transverse polarization transversity Boer-Mulders function Pretzelocity 粒子物理与核物理讨论班

  46. Sivers function proton spin, up left proton momentum forward right azimuthal angle Quark distribution/correlation functions at leading twist represents the correlation between the transverse momentum of quark and the spin of proton. single-spin left-right asymmetry. 粒子物理与核物理讨论班

  47. Sivers function Quark distribution/correlation functions at leading twist Single-spin left-right asymmetry AN has been clearly observed in pp collision experiments, e.g. by E704 at FNAL in 1990s. up left spin forward right 粒子物理与核物理讨论班

  48. Sivers function Quark distribution/correlation functions at leading twist 1991, Sivers function was first proposed by D. Sivers to account for AN in pp; 1993, Boros, ZTL, Meng: AN can be obtained from quark orbital angular momentum & “surface effect” in pp collisions; 1993, proof by J. Collins that Sivers function = 0; 2001, HERMES: first measurement of single spin asymmetry in Semi-inclusive DIS which shows that Sivers effect is non-zero; 2002, Brodsky, Hwang, Schmidt: explicit calculations show that, if quark orbital angular momentum & “final state interaction” are taken into account, Sivers effect is non-zero; 2002, Collins: 1993’s proof is wrong because forgot gauge link which represents the “final state QCD interactions”. 粒子物理与核物理讨论班

  49. HERMES results on azimuthal asymmetry in SIDIS Quark distribution/correlation functions at leading twist HERMES, PRD (2001) 粒子物理与核物理讨论班

  50. Lessons: … Quark distribution/correlation functions at leading twist (I) Quark distributions are not merely but include 不是孤立的核子内的部分子的动量分布,而是包含了“末态相互作用”的贡献 (II) Azimuthal asymmetries should be studied in Semi-inclusive DIS. • universality • nuclear effects • spin effects • higher twist effects are important issues. 粒子物理与核物理讨论班