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Next-To-Leading-Order QCD Corrections to J/ ψ Production and its polarization At Hadron Collider

Effective Field Theories in Particle and Nuclear Physics KITPC, Beijing, August 6, 2009. Next-To-Leading-Order QCD Corrections to J/ ψ Production and its polarization At Hadron Collider. Jian-Xiong Wang Institute of High Energy Physics, Chinese Academy of Science

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Next-To-Leading-Order QCD Corrections to J/ ψ Production and its polarization At Hadron Collider

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  1. Effective Field Theories in Particle and Nuclear Physics KITPC, Beijing, August 6, 2009 Next-To-Leading-Order QCD Corrections to J/ψ Production and its polarization At Hadron Collider Jian-Xiong Wang Institute of High Energy Physics, Chinese Academy of Science In collabration with Bin Gong, Xue. Qian Li, C. H. Chang, R. Li

  2. Contents • Introduction • NLO QCD corrections to J/ψ polarization via S-wave color singlet state PP collider • NLO QCD corrections to J/ψ production via S-wave color octet states at PP collider • NLO QCD corrections to J/ψ photo-production at HERA • Summary and conclusion • Brief Introduction to FDC package

  3. 1. Introduction QCD, Hadronization, NRQCD, Color-singlet, Color-Octet C quark heavy, clear signal to detect J/ψ P_t distribution of J/ψ production at Tevatron P_t distribution of J/ψ polarization at Tevatron J/ψ production at DESY ep collider HERA J/ψ production at Fix Target Experiments NLO QCD Correction to J/ψ production at B factories will be presented by Dr. Bin Gong Next To Leading Order QCD Correctioins are very large.

  4. Recently NLO QCD corrections to J/ψ hadronproduction have • been calculated and the results show that the total cross section • is boosted by a factor of about 2 while the J/ψtransverse • momentum pt distribution is enhanced more and more as pt • becomes larger. • J. Campbell, F. Maltoni and F. Tramontano, Phys. Rev. Lett. 98, 252002 (2007) • Real correction process was calculated . It gives • sizable contribution to pt distribution of J/ψ at high pt region, • and it alone gives almost unpolarized result. • P. Artoisenet, J. P. Lansberg and F. Maltoni, Phys. Lett. B653, 60 (2007). • C. F. Qiao and J. X. Wang, Phys. Rev. D69, 014015 (2004). So how about the J/ψpolarization status when NLO QCD corrections are included?

  5. 2. NLO QCD corrections to J/ψ polarization via S-wave color singlet state at PP collider LO Cross Section

  6. MV is UV and Coulomb finite, but still contains the IR divergences: VIRTUAL CORRECTIONS 129 diagrams in total only light quarks are included in the renormalization of gluon field and QCD gauge coupling constant

  7. REAL CORRECTIONS Two-cutoff phase space slicing method is applied B. W. Harris and J. F. Owens, Phys. Rev. D65, 094032 (2002). • Soft: (a) • Final Collinear: • (a) and (b) • Initial Collinear: • (a) and (c)

  8. Soft singularities caused by emitting soft gluons from the charm quark-antiquark pair in the s-wave color singlet J/ψ are canceled with each other. Only the process (a) where there could be a soft gluon emitted from the external gluons contains soft singularities. SOFT

  9. Final Hard Collinear Initial

  10. Cross Section at NLO REAL Hard Noncollinear Finite

  11. is applied to obtain transverse momentum distribution are differential cross section of transverse polarization and longitudinal one respectively polarization parameterαis defined as: α=＋1:fully transverse polarization α=－1:fully longitudinal polarization

  12. The NLO QCD corrections • boost the total cross section • by a factor of about 2 • The scale dependence at • NLO is not improved Total cross section of J/ψ production as function of the renormalization scale μrand factorization scale μf

  13. LHC Upper: LHC Lower: Tevatron contribution of NLO correction becomes larger as pt increases Tevatron 2-3 order larger in magnitude at pt=50 GeV Transverse momentum distribution of J/ψproduction

  14. Transverse momentum distribution of J/ψpolarization parameter α J/ψ polarization status drastically changes from transverse polarization dominant at LO into longitudinal polarization dominant at NLO This work is published in Phys. Rev. Lett. 100, 232001 (2008)

  15. NLO QCD Correction to Production and Polarization Upper: LHC Lower: Tevatron Transverse momentum distribution of Υ production

  16. Transverse momentum distribution of the polarization parameterα Polarization also changes greatly with NLO QCD corrections included This work is published in Physical Review D 78, 074011 (2008)

  17. 2. Summary for color singlet • The J/ψ polarization is dramatically changed from transverse polarization dominant at LO into longitudinal polarization dominant at NLO. Even though our results are in a more longitudinal polarization state than the recent experimental result at Tevatron, it raises a hope to solve the large discrepancy between theoretical prediction and experimental measurement on J/ψ polarization. • Next important step is to calculate the NLO corrections to J/ψ hadronproduction via color octet state.

  18. 3. NLO QCD corrections to J/ψ production via S-wave color octet states at PP collider 3 tree processes at LO At NLO (267, 413) (49, 111) (49, 111) Real Correction (8 processes at NLO)

  19. The renormalization constant of light quark field is also needed in color-octet case. The renormalization constants

  20. Upper curves: LHC Lower curves: Tevatron The NLO QCD corrections don’t change the total cross section very much. Total cross section of J/ψproduction as function of the renormalization and factorization scale via S-wave color octet states

  21. Upper: LHC Lower: Tevatron Only slight change appears when the NLO QCD corrections are included. Transverse momentum distribution of J/ψproduction via S-wave color octet states

  22. Experimental data with pt <6 GeV • has been abandoned • Feed down fromψ’ has been • included by multiplying a factor of Notes in fitting Our fitted matrix elements: • Contribution via P-wave has not • been included Prediction for LHC Transverse momentum distribution of prompt J/ψproduction

  23. Transverse momentum distribution of polarization parameterαfor prompt J/ψ • Dash and solid lines are • LO and NLO results for • J/psi polarization via • color octet state 3S1. It • has changed little when • NLO QCD corrections • are included. • 1S0 gives contribution to • α=0. • Obvious gap is shown • between our prediction • and experimental data • at Tevatron. Upper: Tevatron Lower: LHC This work is published in Phys. Lett. B673 (2008)

  24. 3. Conclusion and Summary • Comparing the theoretical results calculated up to NLO with the experimental measurements at Tevatron, obvious gap is shown, even though both color singlet and octet are included. • NLO corrections to J/ψ production via P-wave color octet state 3PJand J/ψ production by feed-down from χcJhaven’t been calculated yet. • If we assume that the NLO QCD corrections to the two P-wave states are just as those for the S-wave color octet states, it is reasonable for us to reach the conclusion that the large discrepancy of J/ψ polarization between theoretical prediction and the experimental measurement cannot be solved by just including NLO corrections within NRQCD framework and new solutions should be considered.

  25. 4. NLO QCD corrections to J/ψ photo-production at HERA Chekanov et~al.(ZEUS), Eur. Phys. J. C27, Adloff et~al.(H1), Eur. Phys. J., C25. T. Ahmed et al. (H1), Phys. Lett. 338B (1994) M. Kramer, Nucl. Phys. B459,1996. P. Artoisenet , John M. Campbell , F. Maltoni F. Tramontano,Phys.Rev.Lett.102:142001,2009. e-Print: arXiv:0901.4352 [hep-ph] Chao-Hsi Chang , Rong Li, Jian-Xiong Wang . e-Print: arXiv:0901.4749 [hep-ph]

  26. Scale dependence of J/psi polarization parameters

  27. 4. Summary and Conclusion • The results show: • that the transverse momentum p_t and energy fraction z • distributions of $J/\psi$ production do not agree with the • observedones very well. • the theoretical uncertainties for the z distributions of J/\psi • polarization parameters in respect to various choices of the • renormalization and factorization scales are too large to give • a definite predications. • the uncertainties for the p_t distributions of these parameters • are small when p_t>3GeV and the obtained p_t distributions • can not describe the experimental data even just in this region.

  28. 5. Summary and Conclusion • The J/ψ polarization is dramatically changed from transverse • polarization dominant at LO into longitudinal polarization dominant • at NLO. • Comparing the theoretical results calculated up to NLO with the • experimental measurements at Tevatron, obvious gap is shown, • even though both color singlet and octet are included. • the large discrepancy of J/ψ polarization between theoretical prediction • and the experimental measurement cannot be solved by just including • NLO corrections within NRQCD framework and new solutions should • be considered.

  29. Brief Introduction to FDC package Feynman Diagram Calculation(FDC). This first version of FDC was presented at AIHENP93 workshp,1993. FDC Homepage:： http://www.ihep.ac.cn/lunwen/wjx/public_html/index.html FDC-LOOP FDC-PWA FDC-EMT Written in REDUCE, RLISP,C++. To generate Fortran FDC-SM-and-Many-Extensions FDC-NRQCD FDC-MSSM Event Generator

  30. Thanks！

  31. FDC-LOOP • 发展FDC单圈修正计算的意义 • 单圈修正计算的基本方法简介 • FDC单圈修正计算的检验 • 有些计算只能借助计算机才能完成 • 现有程序如LoopTools等，仍然有各自的缺陷 • 遇到问题后需要等待开发者来处理 • 作为FDC系统的一部分，需要有独立的处理能力

  32. Real Correction Next leading Order Correction Virtual Correction One loop diagram Counter term diagram Next to Leading Order Correction

  33. Counter term

  34. Renormalization Constants

  35. 标准函数 圈图

  36. FDC系统计算标准函数的流程图 • 张量降阶采用Passarino和Veltman的方法 • G. Passarino and M. J. G. Veltman, Nucl. Phys. B160, 151 (1979). • Gram为时需要采用改进后的方法

  37. 外动量线性相关 注意：有可能方程组矛盾最后无解！ + Less than N-1 Equations 2 Equations

  38. “D”表示维数正规化 “ε”表示用传播子中自带的小量进行正规化 Calculation of Scalar Integral • 主要基于: • ‘t Hooft和Veltman计算标量函数的方法 • (用于在四维内计算标量函数) • G. ‘t Hooft and M. J. G. Veltman, Nucl. Phys. B153, 365 (1979). • Stefan Dittmaier的分离标准函数发散部分的方法 • (用于不同正规化方案之间的转换) • S. Dittmaier, Nucl. Phys. B675, 447 (2003). 分离的发散部分用包含发散的三点来表示

  39. 一点和两点函数 (直接在D维内积分) • 三点标量函数 • 包含发散的在D维内积分 • 不包含发散的在四维内积分 • 四点标量函数 （包括不能向下化简的更高点标量函数） • 不包含发散的在四维内积分 • 包含发散的, 用前面的式子将发散分离后, 分别在D维 • 和四维内积分. 四维内的积分采用小ε的正规化方案 D维内的积分手动积好，由程序对号调用 四维内的积分由程序完成

  40. 计算实修正采用“相空间二分法” B. W. Harris and J. F. Owens, Phys. Rev. D65, 094032 (2002). FDC系统计算实修正的流程

  41. LO的结果 软区域中的部分可以通过因子化方法, 将其表示为LO结果与一个因子的乘积. 例如, 对于一个LO是2到2的过程, 相应的软区域部分可以表示成(假设粒子5是软胶子):

  42. 共线部分也有相应的因子化方法, 末态粒子共线的结果是(仍以前面的过程为例, 假设共线的粒子是4和5):

  43. G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977). 要对所有可能的c’求和，同样，PDF中也要对所有可能的b’求和 初态粒子共线的情况稍微复杂一点, 需要重新定义PDF将发散吸收进去. 我们选用的是下面这个重定义的PDF: 这部分可以表成为(假设共线的粒子是2和5):

  44. 小 结 各部分所包含的发散都是解析分 离的, 因此看发散的抵消比较容易 各部分有限项在相空间内作数值 积分得到最后的数值结果 实修正对截断的不依赖通过数值 方式验证

  45. 三种不同的计算矩阵元平方的 方法互相比较 检查结果是否具有规范不变性 不包含发散的标量积分的结果 与LoopTools进行比较 计算矩阵元的前后分别将某个 极化矢量换成相应的动量 内部检查适用于任何过程 • FDC单圈修正计算的校验

  46. R. Barbieri, E. d’Emilio, G. Curci, and E. Remiddi, • Nucl. Phys. B154, 535 (1979). • K. Hagiwara, C. B. Kim and T. Yoshino, • Nucl. Phys. B177, 461 (1981). • P. B. Mackenzie and G. P. Lepage, Phys. Rev. Lett. 47, 1244 (1981). • G. T. Bodwin, E. Braaten and G. P. Lepage, Phys. Rev. D51 1125 (1995). 更容易得到认可的验证方式: 计算某些具体过程的QCD修正与已知的结果进行比较. 为此, 我们计算了下列过程的QCD修正:

  47. 用下面的例子来说明: FDC的指标求和全部选用路线A1

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