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Journal of High Energy Physics

, 2019:210 | Cite as

Relativistic effect of J/๐œ“ hadroproduction in large pT region

  • Rongย Li
  • An-Pingย Chen
  • Jing-Kaiย Huang
  • Yan-Qingย MaEmail author
Open Access
Regular Article - Theoretical Physics
First Online:
  • 31 Downloads

Abstract

By combining NRQCD factorization and collinear factorization, we compute a series of relativistic corrections for J/๐œ“ hadroproduction to all orders in ๐œ2 at large pT limit. The ๐œ2 expansion converges well for all channels. We find that the ratio of relativistic correction term to the corresponding leading term is independent of kinematic variables for any channel, which generalizes the proportional relations found in previous works to all orders.

Keywords

Perturbative QCDย Resummationย 
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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

References

  1. [1]
    G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev.D 51 (1995) 1125 [Erratum ibid.D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
  2. [2]
    E. Braaten, B.A. Kniehl and J. Lee, Polarization of prompt J/๐œ“ at the Tevatron, Phys. Rev.D 62 (2000) 094005 [hep-ph/9911436] [INSPIRE].
  3. [3]
    CDF collaboration, Measurement of J/๐œ“ and ๐œ“ (2S) polarization in p \( \overline{p} \)collisions at \( \sqrt{s} \) = 1.8 TeV, Phys. Rev. Lett.85 (2000) 2886 [hep-ex/0004027] [INSPIRE].
  4. [4]
    CDF collaboration, Polarization of J/๐œ“ and ๐œ“ 2SMesons Produced in p \( \overline{p} \)Collisions at \( \sqrt{s} \) = 1.96 TeV, Phys. Rev. Lett.99 (2007) 132001 [arXiv:0704.0638] [INSPIRE].
  5. [5]
    J.M. Campbell, F. Maltoni and F. Tramontano, QCD corrections to J/๐œ“ and ฯ’ production at hadron colliders, Phys. Rev. Lett.98 (2007) 252002 [hep-ph/0703113] [INSPIRE].
  6. [6]
    P. Artoisenet, J.P. Lansberg and F. Maltoni, Hadroproduction of J/๐œ“ and ฮฅ in association with a heavy-quark pair, Phys. Lett.B 653 (2007) 60 [hep-ph/0703129] [INSPIRE].
  7. [7]
    B. Gong and J.-X. Wang, Next-to-leading-order QCD corrections to J/๐œ“ polarization at Tevatron and Large-Hadron-Collider energies, Phys. Rev. Lett.100 (2008) 232001 [arXiv:0802.3727] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    B. Gong and J.-X. Wang, QCD corrections to polarization of J/๐œ“ and ฮฅ at Tevatron and LHC, Phys. Rev.D 78 (2008) 074011 [arXiv:0805.2469] [INSPIRE].
  9. [9]
    Y.-Q. Ma, K. Wang and K.-T. Chao, QCD radiative corrections to ฯ‡ cJproduction at hadron colliders, Phys. Rev.D 83 (2011) 111503 [arXiv:1002.3987] [INSPIRE].ADSGoogle Scholar
  10. [10]
    Y.-Q. Ma, K. Wang and K.-T. Chao, J/๐œ“ (๐œ“ โ€ฒ) production at the Tevatron and LHC at ๐’ช (\( {\alpha}_s^4{\upsilon}^4 \)) in nonrelativistic QCD, Phys. Rev. Lett.106 (2011) 042002 [arXiv:1009.3655] [INSPIRE].
  11. [11]
    M. Butenschoen and B.A. Kniehl, Reconciling J/๐œ“ production at HERA, RHIC, Tevatron and LHC with NRQCD factorization at next-to-leading order, Phys. Rev. Lett.106 (2011) 022003 [arXiv:1009.5662] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    D. Li, Y.-Q. Ma and K.-T. Chao, ฯ‡ cJproduction associated with a c \( \overline{c} \)pair at hadron colliders, Phys. Rev.D 83 (2011) 114037 [arXiv:1106.4262] [INSPIRE].
  13. [13]
    M. Butenschoen and B.A. Kniehl, J/๐œ“ polarization at Tevatron and LHC: Nonrelativistic-QCD factorization at the crossroads, Phys. Rev. Lett.108 (2012) 172002 [arXiv:1201.1872] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    K.-T. Chao, Y.-Q. Ma, H.-S. Shao, K. Wang and Y.-J. Zhang, J/๐œ“ Polarization at Hadron Colliders in Nonrelativistic QCD, Phys. Rev. Lett.108 (2012) 242004 [arXiv:1201.2675] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    B. Gong, L.-P. Wan, J.-X. Wang and H.-F. Zhang, Polarization for Prompt J/๐œ“, ๐œ“ (2S) Production at the Tevatron and LHC, Phys. Rev. Lett.110 (2013) 042002 [arXiv:1205.6682] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    K. Wang, Y.-Q. Ma and K.-T. Chao, ฮฅ (1S) prompt production at the Tevatron and LHC in nonrelativistic QCD, Phys. Rev.D 85 (2012) 114003 [arXiv:1202.6012] [INSPIRE].ADSGoogle Scholar
  17. [17]
    B. Gong, L.-P. Wan, J.-X. Wang and H.-F. Zhang, Complete next-to-leading-order study on the yield and polarization of ฮฅ (1S, 2S, 3S) at the Tevatron and LHC, Phys. Rev. Lett.112 (2014) 032001 [arXiv:1305.0748] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    H. Han, Y.-Q. Ma, C. Meng, H.-S. Shao, Y.-J. Zhang and K.-T. Chao, ฮฅ (nS) and ฯ‡ b (nP) production at hadron colliders in nonrelativistic QCD, Phys. Rev.D 94 (2016) 014028 [arXiv:1410.8537] [INSPIRE].ADSGoogle Scholar
  19. [19]
    M. Butenschoen, Z.-G. He and B.A. Kniehl, ฮท cproduction at the LHC challenges nonrelativistic-QCD factorization, Phys. Rev. Lett.114 (2015) 092004 [arXiv:1411.5287] [INSPIRE].
  20. [20]
    H. Han, Y.-Q. Ma, C. Meng, H.-S. Shao and K.-T. Chao, ฮท cproduction at LHC and indications on the understanding of J/๐œ“ production, Phys. Rev. Lett.114 (2015) 092005 [arXiv:1411.7350] [INSPIRE].
  21. [21]
    H.-F. Zhang, Z. Sun, W.-L. Sang and R. Li, Impact of ฮทc hadroproduction data on charmonium production and polarization within NRQCD framework, Phys. Rev. Lett.114 (2015) 092006 [arXiv:1412.0508] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    G.T. Bodwin, K.-T. Chao, H.S. Chung, U.-R. Kim, J. Lee and Y.-Q. Ma, Fragmentation contributions to hadroproduction of prompt J/๐œ“, ฯ‡ cJand ๐œ“ (2S) states, Phys. Rev.D 93 (2016) 034041 [arXiv:1509.07904] [INSPIRE].ADSGoogle Scholar
  23. [23]
    Y. Feng, B. Gong, C.-H. Chang and J.-X. Wang, Remaining parts of the long-standing J/๐œ“ polarization puzzle, Phys. Rev.D 99 (2019) 014044 [arXiv:1810.08989] [INSPIRE].
  24. [24]
    G.T. Bodwin, H.S. Chung, U.-R. Kim and J. Lee, Fragmentation contributions to J/๐œ“ production at the Tevatron and the LHC, Phys. Rev. Lett.113 (2014) 022001 [arXiv:1403.3612] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    Y.-Q. Ma, Y.-J. Zhang and K.-T. Chao, QCD correction to e +e โˆ’โ†’ J/๐œ“ + gg at B Factories, Phys. Rev. Lett.102 (2009) 162002 [arXiv:0812.5106] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    B. Gong and J.-X. Wang, Next-to-Leading-Order QCD Corrections to e +e โˆ’โ†’ J/๐œ“ gg at the B Factories, Phys. Rev. Lett.102 (2009) 162003 [arXiv:0901.0117] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    Y.-J. Zhang, Y.-Q. Ma, K. Wang and K.-T. Chao, QCD radiative correction to color-octet J/๐œ“ inclusive production at B Factories, Phys. Rev.D 81 (2010) 034015 [arXiv:0911.2166] [INSPIRE].
  28. [28]
    Y.-Q. Ma and K.-T. Chao, A new factorization theory for heavy quarkonium production and decay, arXiv:1703.08402 [INSPIRE].
  29. [29]
    Y. Fan, Y.-Q. Ma and K.-T. Chao, Relativistic Correction to J/๐œ“ Production at Hadron Colliders, Phys. Rev.D 79 (2009) 114009 [arXiv:0904.4025] [INSPIRE].ADSGoogle Scholar
  30. [30]
    G.-Z. Xu, Y.-J. Li, K.-Y. Liu and Y.-J. Zhang, Relativistic Correction to Color Octet J/๐œ“ Production at Hadron Colliders, Phys. Rev.D 86 (2012) 094017 [arXiv:1203.0207] [INSPIRE].
  31. [31]
    Z.-G. He and B.A. Kniehl, Relativistic corrections to prompt J/๐œ“ photo- and hadroproduction, Phys. Rev.D 90 (2014) 014045 [Erratum ibid.D 94 (2016) 079903] [arXiv:1507.03882] [INSPIRE].
  32. [32]
    Z.-G. He and B.A. Kniehl, Relativistic corrections to J/๐œ“ polarization in photo- and hadroproduction, Phys. Rev.D 92 (2015) 014009 [arXiv:1507.03883] [INSPIRE].
  33. [33]
    Y.-Q. Ma, General form of s, t and u symmetric polynomials and heavy quarkonium physics, Phys. Rev.D 87 (2013) 034001 [arXiv:1207.3073] [INSPIRE].
  34. [34]
    G.C. Nayak, J.-W. Qiu and G.F. Sterman, Fragmentation, NRQCD and NNLO factorization analysis in heavy quarkonium production, Phys. Rev.D 72 (2005) 114012 [hep-ph/0509021] [INSPIRE].
  35. [35]
    G.C. Nayak, J.-W. Qiu and G.F. Sterman, Fragmentation, factorization and infrared poles in heavy quarkonium production, Phys. Lett.B 613 (2005) 45 [hep-ph/0501235] [INSPIRE].
  36. [36]
    Z.-B. Kang, J.-W. Qiu and G. Sterman, Heavy quarkonium production and polarization, Phys. Rev. Lett.108 (2012) 102002 [arXiv:1109.1520] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    S. Fleming, A.K. Leibovich, T. Mehen and I.Z. Rothstein, The Systematics of Quarkonium Production at the LHC and Double Parton Fragmentation, Phys. Rev.D 86 (2012) 094012 [arXiv:1207.2578] [INSPIRE].
  38. [38]
    S. Fleming, A.K. Leibovich, T. Mehen and I.Z. Rothstein, Anomalous dimensions of the double parton fragmentation functions, Phys. Rev.D 87 (2013) 074022 [arXiv:1301.3822] [INSPIRE].
  39. [39]
    Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu and G. Sterman, Heavy Quarkonium Production at Collider Energies: Factorization and Evolution, Phys. Rev.D 90 (2014) 034006 [arXiv:1401.0923] [INSPIRE].
  40. [40]
    Z.-B. Kang, Y.-Q. Ma, J.-W. Qiu and G. Sterman, Heavy Quarkonium Production at Collider Energies: Partonic Cross Section and Polarization, Phys. Rev.D 91 (2015) 014030 [arXiv:1411.2456] [INSPIRE].
  41. [41]
    Y.-Q. Ma, J.-W. Qiu, G. Sterman and H. Zhang, Factorized power expansion for high-pT heavy quarkonium production, Phys. Rev. Lett.113 (2014) 142002 [arXiv:1407.0383] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    G.P. Lepage and B.A. Thacker, Effective Lagrangians for Simulating Heavy Quark Systems, Nucl. Phys. Proc. Suppl.4 (1988) 199 [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    E. Braaten and T.C. Yuan, Gluon fragmentation into heavy quarkonium, Phys. Rev. Lett.71 (1993) 1673 [hep-ph/9303205] [INSPIRE].
  44. [44]
    E. Braaten, K.-m. Cheung and T.C. Yuan, Z0 decay into charmonium via charm quark fragmentation, Phys. Rev.D 48 (1993) 4230 [hep-ph/9302307] [INSPIRE].
  45. [45]
    E. Braaten and T.C. Yuan, Gluon fragmentation into P wave heavy quarkonium, Phys. Rev.D 50 (1994) 3176 [hep-ph/9403401] [INSPIRE].
  46. [46]
    E. Braaten and T.C. Yuan, Gluon fragmentation into spin triplet S wave quarkonium, Phys. Rev.D 52 (1995) 6627 [hep-ph/9507398] [INSPIRE].
  47. [47]
    J.P. Ma, Quark fragmentation into p wave triplet quarkonium, Phys. Rev.D 53 (1996) 1185 [hep-ph/9504263] [INSPIRE].
  48. [48]
    W. Qi, C.F. Qiao and J.X. Wang, On the Application of Gluon to Heavy Quarkonium Fragmentation Functions, Phys. Rev.D 75 (2007) 074012 [hep-ph/0701264] [INSPIRE].
  49. [49]
    G. Hao, Y. Zuo and C.-F. Qiao, The Fragmentation Function of Gluon Splitting into P-wave Spin-singlet Heavy Quarkonium, arXiv:0911.5539 [INSPIRE].
  50. [50]
    G.T. Bodwin, H.S. Chung, U.-R. Kim and J. Lee, Quark fragmentation into spin-triplet S-wave quarkonium, Phys. Rev.D 91 (2015) 074013 [arXiv:1412.7106] [INSPIRE].
  51. [51]
    S.M. Moosavi Nejad and D. Mahdi, Gluon fragmentation into S-wave heavy quarkonium, arXiv:1401.5223 [INSPIRE].
  52. [52]
    S.M. Moosavi Nejad, Fragmentation functions of g โ†’ ฮทc (1S 0 ) and g โ†’ J/๐œ“ (3S 1 ) considering the role of heavy quarkonium spin, Eur. Phys. J. Plus130 (2015) 136 [arXiv:1506.08861] [INSPIRE].
  53. [53]
    S.M. Moosavi Nejad and M. Delpasand, Spin-dependent fragmentation functions of Gluon splitting into heavy quarkonia considering three different scenarios, Int. J. Mod. Phys.A 30 (2015) 1550179 [arXiv:1512.01342] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  54. [54]
    P. Zhang, Y.-Q. Ma, Q. Chen and K.-T. Chao, Analytical calculation for the gluon fragmentation into spin-triplet S-wave quarkonium, Phys. Rev.D 96 (2017) 094016 [arXiv:1708.01129] [INSPIRE].
  55. [55]
    F. Feng, S. Ishaq, Y. Jia and J.-Y. Zhang, Fragmentation function of gluon into spin-singlet P -wave quarkonium, arXiv:1712.09986 [INSPIRE].
  56. [56]
    S.M. Moosavi Nejad, The impact of Fermi motion on the heavy quarkonia fragmentation using the light-cone wave function, Eur. Phys. J. Plus133 (2018) 25 [INSPIRE].CrossRefGoogle Scholar
  57. [57]
    E. Braaten and J. Lee, Next-to-leading order calculation of the color octet 3S 1gluon fragmentation function for heavy quarkonium, Nucl. Phys.B 586 (2000) 427 [hep-ph/0004228] [INSPIRE].
  58. [58]
    J. Lee, Next-to-leading order calculation of a fragmentation function in a light-cone gauge, Phys. Rev.D 71 (2005) 094007 [hep-ph/0504285] [INSPIRE].
  59. [59]
    G.T. Bodwin and J. Lee, Relativistic corrections to gluon fragmentation into spin triplet S wave quarkonium, Phys. Rev.D 69 (2004) 054003 [hep-ph/0308016] [INSPIRE].
  60. [60]
    W.-l. Sang, L.-f. Yang and Y.-q. Chen, Relativistic corrections to heavy quark fragmentation to S-wave heavy mesons, Phys. Rev.D 80 (2009) 014013 [INSPIRE].
  61. [61]
    G.T. Bodwin, U.-R. Kim and J. Lee, Higher-order relativistic corrections to gluon fragmentation into spin-triplet S-wave quarkonium, JHEP11 (2012) 020 [arXiv:1208.5301] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    X. Gao, Y. Jia, L. Li and X. Xiong, Relativistic correction to gluon fragmentation function into pseudoscalar quarkonium, Chin. Phys.C 41 (2017) 023103 [arXiv:1606.07455] [INSPIRE].
  63. [63]
    S.M. Moosavi Nejad and P. Sartipi Yarahmadi, Heavy quark fragmentation functions at next-to-leading perturbative QCD, Eur. Phys. J.A 52 (2016) 315 [arXiv:1609.07422] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    R. Sepahvand and S. Dadfar, NLO corrections to c- and b-quark fragmentation into j/๐œ“ and ฮณ, Phys. Rev.D 95 (2017) 034012 [INSPIRE].
  65. [65]
    P. Artoisenet and E. Braaten, Gluon fragmentation into quarkonium at next-to-leading order, JHEP04 (2015) 121 [arXiv:1412.3834] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    P. Artoisenet and E. Braaten, Gluon fragmentation into quarkonium at next-to-leading order using FKS subtraction, JHEP01 (2019) 227 [arXiv:1810.02448] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    F. Feng and Y. Jia, Next-to-leading-order QCD corrections to gluon fragmentation into \( {}^1{S}_0^{\left(1,8\right)} \)quarkonia, arXiv:1810.04138 [INSPIRE].
  68. [68]
    P. Zhang, C.-Y. Wang, X. Liu, Y.-Q. Ma, C. Meng and K.-T. Chao, Semi-analytical calculation of gluon fragmentation into \( {}^1{S}_0^{\left[1,8\right]} \)quarkonia at next-to-leading order, JHEP04 (2019) 116 [arXiv:1810.07656] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    Y.-Q. Ma, J.-W. Qiu and H. Zhang, Heavy quarkonium fragmentation functions from a heavy quark pair. I. S wave, Phys. Rev.D 89 (2014) 094029 [arXiv:1311.7078] [INSPIRE].
  70. [70]
    Y.-Q. Ma, J.-W. Qiu and H. Zhang, Heavy quarkonium fragmentation functions from a heavy quark pair. II. P wave, Phys. Rev.D 89 (2014) 094030 [arXiv:1401.0524] [INSPIRE].
  71. [71]
    Y.-Q. Ma, J.-W. Qiu and H. Zhang, Fragmentation functions of polarized heavy quarkonium, JHEP06 (2015) 021 [arXiv:1501.04556] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

ยฉย The Author(s)ย 2019

Authors and Affiliations

  1. 1.School of ScienceXiโ€™an Jiaotong UniversityXiโ€™anChina
  2. 2.School of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  3. 3.Center for High Energy PhysicsPeking UniversityBeijingChina
  4. 4.Collaborative Innovation Center of Quantum MatterBeijingChina

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