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

Center for High Energy Physics ， Peking University 2009 年 3 月 30 日. Next-To-Leading-Order QCD Corrections to J/ ψ Production and its polarization. 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

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  1. Center for High Energy Physics，Peking University 2009年3月30日 Next-To-Leading-Order QCD Corrections to J/ψ Production and its polarization Jian-Xiong Wang Institute of High Energy Physics, Chinese Academy of Science In collabration with Bin Gong, Xue. Qian Li

  2. Contents • Introduction • NLO QCD corrections to J/ψ polarization via S-wave color singlet state • NLO QCD corrections to J/ψ production via S-wave color octet states • NLO QCD corrections to J/ψ+ at B-factory • NLO QCD corrections to J/ψ+ J/ψ at B-factory • NLO QCD corrections to J/ψ+gg at B-factory • NLO QCD corrections to J/ψ+cc_bar at B-factory • Brief Introduction to FDC package • Summary and conclusion

  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 B factories J/ψ production at DESY ep collider HERA J/ψ production at Fix Target Experiments 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. NLO QCD corrections to J/ψ polarization via S-wave color singlet state 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. 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. NLO QCD corrections to J/ψ production via S-wave color octet states 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. 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. Experimental Data: • K. Abe et al. (Belle Collaboration), Phys. Rev. Lett. 89, 142001 (2002) • B. Aubert et al. (BABAR Collaboration), Phys. Rev. D72, 031101 (2005). LO NRQCD Prediction: 2.3-5.5 fb NLO QCD Corrections: Gives a K factor of about 2 Y. J. Zhang, Y. J. Gao and K. T. Chao, Phys. Rev. Lett. 96, 092001 (2006). Relativistic Corrections: Gives another K factor of about 2 G. T. Bodwin, D. Kang, T. Kim, J. Lee and C. Yu, AIP Conf. Proc. 892, 315 (2007). Z. G. He, Y. Fan, and K. T. Chao, Phys. Rev. D75, 074011 (2007). Combination of above corrections may resolve the large discrepancy. QCD修正在这个问题中有极为重要的影响, 而这个过程的计算又很复杂. 因此我们用FDC系统重新计算了这个过程的NLO QCD修正. 这是对结果的检验, 同时也是对FDC系统单圈修正计算部分的再次校验.

  26. Phys. Rev. D77, 054028 (2008) LO NLO 80 diagrams in total

  27. NLO QCD correction to at B factory 36 NLO diagrams with up to Six-point diagrams • 结果对重整化标度的依赖很强, 有相当大的不确定性. • 尽管如此, 我们还是能看到, NLO QCD修正使得反应截面大大 • 减小, 如果再考虑相对论修正的影响, 已经能够解释为什么这个 • 过程在B工厂上找不到. This work was published in Phys. Rev. Lett. 100, 181803 (2008).

  28. 0.07 - 0.20 pb 0.15 - 0.3 pb 0.3 - 0.8 pb LO NRQCD Prediction: Experimental Data:

  29. 2. Calculation and results for at NLO LO (a) , 6; NLO (d1—d8), 111 Real (c1,c2), 36 Real (b), 6 Dimensional regularization has been adopted for isolating the ultraviolet (UV) and infrared (IR) singularities. Coulomb Singularity is isolated by v and mapped into the cc wave function. Y. Q. Ma, Y. J. Zhang and K. T. Chao, (2008) 0812.5106 G. Bin and J. X. wang, (2009) 0901.1117

  30. is extracted from the Leptonic decay width at NLO formulation. Where Renormalization Scheme:

  31. The two-cutoff phase space slicing method is adopted by introducing two small cutoffs . For Soft region: For Hard Collinear region: Where

  32. Indicate by the experiment Feed-down Rencent new measurement 043+-0.09+-0.09 pb

  33. The scale dependence of cross section has been improved at NLO. The K factor does not change very much as center-of-mass energy increases. Cross section as function of the renormalization scale and center-of-mass energy.

  34. The differential cross section decreases faster near right bound. The angular distribution changes slightly except a factor of about 1.2. Differential cross section as function of the momentum of J/ψ and the angle between J/ψ and the beam.

  35. Both the polarization factor and the angular distribution coefficient do not change very much at NLO. Polarization and angular distribution parameters as function of the momentum of J/ψ

  36. 0.07 - 0.20 pb LO NRQCD Prediction: Experimental Data: 0.7 pb Y. J. Zhang and K. T. Chao Phys. Rev. Lett. 98,092003, 2007 Rencent new measurement

  37. 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. • The convergence for the NLO QCD correction to • is very good, and to compare the polarization and momentum • disturbution with experimental results should be a good test for • QCD predictions

  38. Thanks！

  39. 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

  40. 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

  41. 实修正 单圈修正 虚修正 圈图 抵消项 单圈修正计算的基本方法简介

  42. 抵消项

  43. 重整化常数

  44. 标准函数 圈图

  45. 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

  46. 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

  47. “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 标量函数的计算 • 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

  48. 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

  49. 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

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