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Journal of High Energy Physics

, 2016:144 | Cite as

Transverse momentum dependent fragmenting jet functions with applications to quarkonium production

  • Reggie Bain
  • Yiannis Makris
  • Thomas Mehen
Open Access
Regular Article - Theoretical Physics

Abstract

We introduce the transverse momentum dependent fragmenting jet function (TMDFJF), which appears in factorization theorems for cross sections for jets with an identified hadron. These are functions of z, the hadron’s longitudinal momentum fraction, and transverse momentum, p , relative to the jet axis. In the framework of Soft-Collinear Effective Theory (SCET) we derive the TMDFJF from both a factorized SCET cross section and the TMD fragmentation function defined in the literature. The TMDFJFs are factorized into distinct collinear and soft-collinear modes by matching onto SCET+. As TMD calculations contain rapidity divergences, both the renormalization group (RG) and rapidity renormalization group (RRG) must be used to provide resummed calculations with next-to-leading-logarithm prime (NLL’) accuracy. We apply our formalism to the production of J/ψ within jets initiated by gluons. In this case the TMDFJF can be calculated in terms of NRQCD (Non-relativistic quantum chromodynamics) fragmentation functions. We find that when the J/ψ carries a significant fraction of the jet energy, the p T and z distributions differ for different NRQCD production mechanisms. Another observable with discriminating power is the average angle that the J/ψ makes with the jet axis.

Keywords

Jets 

Notes

Open Access

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]
    A. Altheimer et al., Boosted objects and jet substructure at the LHC. Report of BOOST2012, held at IFIC Valencia, 23rd-27th of July 2012, Eur. Phys. J. C 74 (2014) 2792 [arXiv:1311.2708] [INSPIRE].
  2. [2]
    S. Sapeta, QCD and Jets at Hadron Colliders, Prog. Part. Nucl. Phys. 89 (2016) 1 [arXiv:1511.09336] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Procura and I.W. Stewart, Quark Fragmentation within an Identified Jet, Phys. Rev. D 81 (2010)074009 [Erratum ibid. D 83 (2011) 039902] [arXiv:0911.4980] [INSPIRE].
  4. [4]
    C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
  5. [5]
    C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in BX s γ in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].
  6. [6]
    C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
  7. [7]
    C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
  8. [8]
    A. Jain, M. Procura and W.J. Waalewijn, Parton Fragmentation within an Identified Jet at NNLL, JHEP 05 (2011) 035 [arXiv:1101.4953] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  9. [9]
    X. Liu, SCET approach to top quark decay, Phys. Lett. B 699 (2011) 87 [arXiv:1011.3872] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    C.F. Berger, T. Kucs and G.F. Sterman, Event shape/energy flow correlations, Phys. Rev. D 68 (2003) 014012 [hep-ph/0303051] [INSPIRE].
  11. [11]
    R. Bain, L. Dai, A. Hornig, A.K. Leibovich, Y. Makris and T. Mehen, Analytic and Monte Carlo Studies of Jets with Heavy Mesons and Quarkonia, JHEP 06 (2016) 121 [arXiv:1603.06981] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Procura and W.J. Waalewijn, Fragmentation in Jets: Cone and Threshold Effects, Phys. Rev. D 85 (2012) 114041 [arXiv:1111.6605] [INSPIRE].ADSGoogle Scholar
  13. [13]
    M. Baumgart, A.K. Leibovich, T. Mehen and I.Z. Rothstein, Probing Quarkonium Production Mechanisms with Jet Substructure, JHEP 11 (2014) 003 [arXiv:1406.2295] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    Y.-T. Chien, Z.-B. Kang, F. Ringer, I. Vitev and H. Xing, Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory, JHEP 05 (2016) 125 [arXiv:1512.06851] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Jain, M. Procura and W.J. Waalewijn, Fully-Unintegrated Parton Distribution and Fragmentation Functions at Perturbative k T , JHEP 04 (2012) 132 [arXiv:1110.0839] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    A. Jain, M. Procura, B. Shotwell and W.J. Waalewijn, Fragmentation with a Cut on Thrust: Predictions for B-factories, Phys. Rev. D 87 (2013) 074013 [arXiv:1207.4788] [INSPIRE].ADSGoogle Scholar
  17. [17]
    C.W. Bauer and E. Mereghetti, Heavy Quark Fragmenting Jet Functions, JHEP 04 (2014) 051 [arXiv:1312.5605] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    L. Dai, C. Kim and A.K. Leibovich, Fragmentation of a Jet with Small Radius, arXiv:1606.07411 [INSPIRE].
  19. [19]
    Z.-B. Kang, F. Ringer and I. Vitev, Jet substructure using semi-inclusive jet functions within SCET, arXiv:1606.07063 [INSPIRE].
  20. [20]
    M. Ritzmann and W.J. Waalewijn, Fragmentation in Jets at NNLO, Phys. Rev. D 90 (2014) 054029 [arXiv:1407.3272] [INSPIRE].ADSGoogle Scholar
  21. [21]
    Z.-B. Kang, F. Ringer and I. Vitev, Semi-inclusive jet cross sections within SCET, arXiv:1609.07112 [INSPIRE].
  22. [22]
    A. Metz and A. Vossen, Parton Fragmentation Functions, Prog. Part. Nucl. Phys. 91 (2016) 136 [arXiv:1607.02521] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M.G. Echevarria, A. Idilbi and I. Scimemi, Factorization Theorem For Drell-Yan At Low q T And Transverse Momentum Distributions On-The-Light-Cone, JHEP 07 (2012) 002 [arXiv:1111.4996] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    M.G. Echevarria, A. Idilbi, A. Schäfer and I. Scimemi, Model-Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL, Eur. Phys. J. C 73 (2013) 2636 [arXiv:1208.1281] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    M.G. Echevarria, A. Idilbi and I. Scimemi, Unified treatment of the QCD evolution of all (un-)polarized transverse momentum dependent functions: Collins function as a study case, Phys. Rev. D 90 (2014) 014003 [arXiv:1402.0869] [INSPIRE].ADSGoogle Scholar
  26. [26]
    M.G. Echevarria, I. Scimemi and A. Vladimirov, Transverse momentum dependent fragmentation function at next-to-next-to-eading order, Phys. Rev. D 93 (2016) 011502 [arXiv:1509.06392] [INSPIRE].ADSGoogle Scholar
  27. [27]
    M.G. Echevarria, I. Scimemi and A. Vladimirov, Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order, arXiv:1604.07869 [INSPIRE].
  28. [28]
    M. Anselmino, M. Boglione, J.O. Gonzalez Hernandez, S. Melis and A. Prokudin, Unpolarised Transverse Momentum Dependent Distribution and Fragmentation Functions from SIDIS Multiplicities, JHEP 04 (2014) 005 [arXiv:1312.6261] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    M. Procura, W.J. Waalewijn and L. Zeune, Resummation of Double-Differential Cross sections and Fully-Unintegrated Parton Distribution Functions, JHEP 02 (2015) 117 [arXiv:1410.6483] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    B.U. Musch, P. Hägler, J.W. Negele and A. Schäfer, Exploring quark transverse momentum distributions with lattice QCD, Phys. Rev. D 83 (2011) 094507 [arXiv:1011.1213] [INSPIRE].ADSGoogle Scholar
  31. [31]
    J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    D. Neill, I.Z. Rothstein and V. Vaidya, The Higgs Transverse Momentum Distribution at NNLL and its Theoretical Errors, JHEP 12 (2015) 097 [arXiv:1503.00005] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    T. Lübbert, J. Oredsson and M. Stahlhofen, Rapidity renormalized TMD soft and beam functions at two loops, JHEP 03 (2016) 168 [arXiv:1602.01829] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    T. Becher, M. Neubert and D. Wilhelm, Higgs-Boson Production at Small Transverse Momentum, JHEP 05 (2013) 110 [arXiv:1212.2621] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    T. Becher, M. Neubert and D. Wilhelm, Electroweak gauge-boson and Higgs production at Small q T : Infrared safety from the collinear anomaly, in Proceedings, 20th International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS 2012), Bonn, Germany, 26-30 March 2012, pg. 721-724, DESY-PROC-2012-02/314.Google Scholar
  36. [36]
    V. Ahrens, T. Becher, M. Neubert and L.L. Yang, Renormalization-Group Improved Prediction for Higgs Production at Hadron Colliders, Eur. Phys. J. C 62 (2009) 333 [arXiv:0809.4283] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    C.W. Bauer, F.J. Tackmann, J.R. Walsh and S. Zuberi, Factorization and Resummation for Dijet Invariant Mass Spectra, Phys. Rev. D 85 (2012) 074006 [arXiv:1106.6047] [INSPIRE].ADSGoogle Scholar
  38. [38]
    Y.-T. Chien, A. Hornig and C. Lee, Soft-collinear mode for jet cross sections in soft collinear effective theory, Phys. Rev. D 93 (2016) 014033 [arXiv:1509.04287] [INSPIRE].ADSGoogle Scholar
  39. [39]
    P. Pietrulewicz, F.J. Tackmann and W.J. Waalewijn, Factorization and Resummation for Generic Hierarchies between Jets, JHEP 08 (2016) 002 [arXiv:1601.05088] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    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].
  41. [41]
    E. Braaten, K.-m. Cheung and T.C. Yuan, Z 0 decay into charmonium via charm quark fragmentation, Phys. Rev. D 48 (1993) 4230 [hep-ph/9302307] [INSPIRE].
  42. [42]
    E. Braaten and T.C. Yuan, Gluon fragmentation into heavy quarkonium, Phys. Rev. Lett. 71 (1993) 1673 [hep-ph/9303205] [INSPIRE].
  43. [43]
    E. Braaten and S. Fleming, Color octet fragmentation and the psi-prime surplus at the Tevatron, Phys. Rev. Lett. 74 (1995) 3327 [hep-ph/9411365] [INSPIRE].
  44. [44]
    E. Braaten and Y.-Q. Chen, Helicity decomposition for inclusive J/ψ production, Phys. Rev. D 54 (1996) 3216 [hep-ph/9604237] [INSPIRE].
  45. [45]
    J.C. Collins and D.E. Soper, Parton Distribution and Decay Functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].ADSGoogle Scholar
  46. [46]
    S.M. Aybat and T.C. Rogers, TMD Parton Distribution and Fragmentation Functions with QCD Evolution, Phys. Rev. D 83 (2011) 114042 [arXiv:1101.5057] [INSPIRE].ADSGoogle Scholar
  47. [47]
    J.-y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, The Rapidity Renormalization Group, Phys. Rev. Lett. 108 (2012) 151601 [arXiv:1104.0881] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    S.D. Ellis, C.K. Vermilion, J.R. Walsh, A. Hornig and C. Lee, Jet Shapes and Jet Algorithms in SCET, JHEP 11 (2010) 101 [arXiv:1001.0014] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    M. Butenschoen and B.A. Kniehl, World data of J/ψ production consolidate NRQCD factorization at NLO, Phys. Rev. D 84 (2011) 051501 [arXiv:1105.0820] [INSPIRE].ADSGoogle Scholar
  50. [50]
    M. Butenschoen and B.A. Kniehl, Next-to-leading-order tests of NRQCD factorization with J/ψ yield and polarization, Mod. Phys. Lett. A 28 (2013) 1350027 [arXiv:1212.2037] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of PhysicsDuke UniversityDurhamU.S.A.

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