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Resummation of boson-jet correlation at hadron colliders

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  • Published: 06 November 2019
  • volume 2019, Article number: 25 (2019)
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Resummation of boson-jet correlation at hadron colliders
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  • Yang-Ting Chien1,
  • Ding Yu Shao  ORCID: orcid.org/0000-0002-4713-29032 &
  • Bin Wu2 
  • 327 Accesses

  • 27 Citations

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A preprint version of the article is available at arXiv.

Abstract

We perform a precise calculation of the transverse momentum (\( {\overrightarrow{q}}_T \)) distribution of the boson+jet system in boson production events. The boson can be either a photon, W, Z or Higgs boson with mass mV, and \( {\overrightarrow{q}}_T \) is the sum of the transverse momenta of the boson and the leading jet with magnitude qT = |\( {\overrightarrow{q}}_T \)|. Using renormalization group techniques and soft-collinear effective theory, we resum logarithms log (Q/qT) and log R at next-to- leading logarithmic accuracy including the non-global logarithms, where Q and R are respectively the hard scattering energy and the radius of the jet. Specifically, we investigate two scenarios of \( {p}_T^J \) ≲ mV or \( {p}_T^J \) ≳ mV in Z +jet events, and we examine the qT distributions with different jet radii and study the effect of non-global logarithms. In the end we compare our theoretical calculations with Monte Carlo simulations and data from the LHC.

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References

  1. J.C. Collins, D.E. Soper and G.F. Sterman, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys. B 250 (1985) 199 [INSPIRE].

    Article  ADS  Google Scholar 

  2. 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].

  3. 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].

  4. C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [INSPIRE].

  5. M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].

  6. T. Becher, A. Broggio and A. Ferroglia, Introduction to soft-collinear effective theory, Lect. Notes Phys. 896 (2015) 1 [arXiv:1410.1892] [INSPIRE].

    Article  Google Scholar 

  7. Y. Gao, C.S. Li and J.J. Liu, Transverse momentum resummation for Higgs production in soft-collinear effective theory, Phys. Rev. D 72 (2005) 114020 [hep-ph/0501229] [INSPIRE].

  8. S. Mantry and F. Petriello, Factorization and resummation of Higgs boson differential distributions in soft-collinear effective theory, Phys. Rev. D 81 (2010) 093007 [arXiv:0911.4135] [INSPIRE].

  9. T. Becher and M. Neubert, Drell-Yan production at small qT, transverse parton distributions and the collinear anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].

  10. T. Becher, M. Neubert and D. Wilhelm, Electroweak gauge-boson production at small qT: infrared safety from the collinear anomaly, JHEP 02 (2012) 124 [arXiv:1109.6027] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  11. 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].

    ADS  Google Scholar 

  12. M.A. Ebert and F.J. Tackmann, Resummation of transverse momentum distributions in distribution space, JHEP 02 (2017) 110 [arXiv:1611.08610] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. I. Scimemi and A. Vladimirov, Power corrections and renormalons in transverse momentum distributions, JHEP 03 (2017) 002 [arXiv:1609.06047] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. D. Kang, C. Lee and V. Vaidya, A fast and accurate method for perturbative resummation of transverse momentum-dependent observables, JHEP 04 (2018) 149 [arXiv:1710.00078] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  15. M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Subleading power rapidity divergences and power corrections for qT, JHEP 04 (2019) 123 [arXiv:1812.08189] [INSPIRE].

    Article  ADS  Google Scholar 

  16. T. Becher, M. Neubert and D. Wilhelm, Higgs-boson production at small transverse momentum, JHEP 05 (2013) 110 [arXiv:1212.2621] [INSPIRE].

    Article  ADS  Google Scholar 

  17. W. Bizon, P.F. Monni, E. Re, L. Rottoli and P. Torrielli, Momentum-space resummation for transverse observables and the Higgs p⊥ at N LL+N3 NLO, JHEP 02 (2018) 108 [arXiv:1705.09127] [INSPIRE].

    Article  ADS  Google Scholar 

  18. W. Bizoń et al., Fiducial distributions in Higgs and Drell-Yan production at N3 LL+NNLO, JHEP 12 (2018) 132 [arXiv:1805.05916] [INSPIRE].

  19. X. Chen et al., Precise QCD description of the Higgs boson transverse momentum spectrum, Phys. Lett. B 788 (2019) 425 [arXiv:1805.00736] [INSPIRE].

    Article  ADS  Google Scholar 

  20. M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].

  21. M. Dasgupta and G.P. Salam, Accounting for coherence in interjet ET flow: a case study, JHEP 03 (2002) 017 [hep-ph/0203009] [INSPIRE].

  22. P. Sun, C.P. Yuan and F. Yuan, Soft gluon resummations in dijet azimuthal angular correlations in hadronic collisions, Phys. Rev. Lett. 113 (2014) 232001 [arXiv:1405.1105] [INSPIRE].

    Article  ADS  Google Scholar 

  23. P. Sun, C.P. Yuan and F. Yuan, Transverse momentum resummation for dijet correlation in hadronic collisions, Phys. Rev. D 92 (2015) 094007 [arXiv:1506.06170] [INSPIRE].

  24. L. Chen et al., Study of isolated-photon and jet momentum imbalance in pp and PbPb collisions, Nucl. Phys. B 933 (2018) 306 [arXiv:1803.10533] [INSPIRE].

    Article  ADS  Google Scholar 

  25. P. Sun, B. Yan, C.P. Yuan and F. Yuan, Resummation of high order corrections in Z boson plus jet production at the LHC, Phys. Rev. D 100 (2019) 054032 [arXiv:1810.03804] [INSPIRE].

  26. P. Sun, B. Yan and C.P. Yuan, Transverse momentum resummation for s-channel single top quark production at the LHC, Phys. Rev. D 99 (2019) 034008 [arXiv:1811.01428] [INSPIRE].

  27. Q.-H. Cao, P. Sun, B. Yan, C.P. Yuan and F. Yuan, Transverse momentum resummation for t-channel single top quark production at the LHC, Phys. Rev. D 98 (2018) 054032 [arXiv:1801.09656] [INSPIRE].

  28. Q.-H. Cao, P. Sun, B. Yan, C.P. Yuan and F. Yuan, Soft gluon resummation in t-channel single top quark production at the LHC, arXiv:1902.09336 [INSPIRE].

  29. M.G.A. Buffing, Z.-B. Kang, K. Lee and X. Liu, A transverse momentum dependent framework for back-to-back photon+jet production, arXiv:1812.07549 [INSPIRE].

  30. Y. Hatta and T. Ueda, Resummation of non-global logarithms at finite Nc , Nucl. Phys. B 874 (2013) 808 [arXiv:1304.6930] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  31. S. Caron-Huot, Resummation of non-global logarithms and the BFKL equation, JHEP 03 (2018) 036 [arXiv:1501.03754] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. A.J. Larkoski, I. Moult and D. Neill, Non-global logarithms, factorization and the soft substructure of jets, JHEP 09 (2015) 143 [arXiv:1501.04596] [INSPIRE].

    Article  ADS  Google Scholar 

  33. T. Becher, M. Neubert, L. Rothen and D.Y. Shao, Effective field theory for jet processes, Phys. Rev. Lett. 116 (2016) 192001 [arXiv:1508.06645] [INSPIRE].

    Article  ADS  Google Scholar 

  34. D. Neill, The edge of jets and subleading non-global logs, arXiv:1508.07568 [INSPIRE].

  35. T. Becher, M. Neubert, L. Rothen and D.Y. Shao, Factorization and resummation for jet processes, JHEP 11 (2016) 019 [Erratum ibid. 05 (2017) 154] [arXiv:1605.02737] [INSPIRE].

  36. T. Becher, B.D. Pecjak and D.Y. Shao, Factorization for the light-jet mass and hemisphere soft function, JHEP 12 (2016) 018 [arXiv:1610.01608] [INSPIRE].

    Article  ADS  Google Scholar 

  37. A.J. Larkoski, I. Moult and D. Neill, The analytic structure of non-global logarithms: convergence of the dressed gluon expansion, JHEP 11 (2016) 089 [arXiv:1609.04011] [INSPIRE].

    Article  ADS  Google Scholar 

  38. D. Neill, The asymptotic form of non-global logarithms, black disc saturation and gluonic deserts, JHEP 01 (2017) 109 [arXiv:1610.02031] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  39. T. Becher, R. Rahn and D.Y. Shao, Non-global and rapidity logarithms in narrow jet broadening, JHEP 10 (2017) 030 [arXiv:1708.04516] [INSPIRE].

    Article  ADS  Google Scholar 

  40. Y. Hatta, E. Iancu, A.H. Mueller and D.N. Triantafyllopoulos, Resumming double non-global logarithms in the evolution of a jet, JHEP 02 (2018) 075 [arXiv:1710.06722] [INSPIRE].

    Article  ADS  Google Scholar 

  41. R. Ángeles Martínez, M. De Angelis, J.R. Forshaw, S. Plätzer and M.H. Seymour, Soft gluon evolution and non-global logarithms, JHEP 05 (2018) 044 [arXiv:1802.08531] [INSPIRE].

  42. M. Balsiger, T. Becher and D.Y. Shao, Non-global logarithms in jet and isolation cone cross sections, JHEP 08 (2018) 104 [arXiv:1803.07045] [INSPIRE].

    Article  ADS  Google Scholar 

  43. D. Neill and V. Vaidya, Soft evolution after a hard scattering process, arXiv:1803.02372 [INSPIRE].

  44. D. Neill, Non-global and clustering effects for groomed multi-prong jet shapes, JHEP 02 (2019) 114 [arXiv:1808.04897] [INSPIRE].

    Article  ADS  Google Scholar 

  45. M. Balsiger, T. Becher and D.Y. Shao, NLL’ resummation of jet mass, JHEP 04 (2019) 020 [arXiv:1901.09038] [INSPIRE].

    Article  ADS  Google Scholar 

  46. R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss and pT broadening of high-energy partons in nuclei, Nucl. Phys. B 484 (1997) 265 [hep-ph/9608322] [INSPIRE].

  47. A.H. Mueller, B. Wu, B.-W. Xiao and F. Yuan, Probing transverse momentum broadening in heavy ion collisions, Phys. Lett. B 763 (2016) 208 [arXiv:1604.04250] [INSPIRE].

    Article  ADS  Google Scholar 

  48. A.H. Mueller, B. Wu, B.-W. Xiao and F. Yuan, Medium induced transverse momentum broadening in hard processes, Phys. Rev. D 95 (2017) 034007 [arXiv:1608.07339] [INSPIRE].

  49. W. Dai, I. Vitev and B.-W. Zhang, Momentum imbalance of isolated photon-tagged jet production at RHIC and LHC, Phys. Rev. Lett. 110 (2013) 142001 [arXiv:1207.5177] [INSPIRE].

    Article  ADS  Google Scholar 

  50. R.B. Neufeld and I. Vitev, The Z 0 -tagged jet event asymmetry in heavy-ion collisions at the CERN Large Hadron Collider, Phys. Rev. Lett. 108 (2012) 242001 [arXiv:1202.5556] [INSPIRE].

    Article  ADS  Google Scholar 

  51. X.-N. Wang and Y. Zhu, Medium modification of γ-jets in high-energy heavy-ion collisions, Phys. Rev. Lett. 111 (2013) 062301 [arXiv:1302.5874] [INSPIRE].

    Article  ADS  Google Scholar 

  52. J. Casalderrey-Solana, D.C. Gulhan, J.G. Milhano, D. Pablos and K. Rajagopal, Predictions for boson-jet observables and fragmentation function ratios from a hybrid strong/weak coupling model for jet quenching, JHEP 03 (2016) 053 [arXiv:1508.00815] [INSPIRE].

    Article  ADS  Google Scholar 

  53. Y.-T. Chien and I. Vitev, Towards the understanding of jet shapes and cross sections in heavy ion collisions using soft-collinear effective theory, JHEP 05 (2016) 023 [arXiv:1509.07257] [INSPIRE].

    Article  ADS  Google Scholar 

  54. R. Kunnawalkam Elayavalli and K.C. Zapp, Simulating V+jet processes in heavy ion collisions with JEWEL, Eur. Phys. J. C 76 (2016) 695 [arXiv:1608.03099] [INSPIRE].

    Article  ADS  Google Scholar 

  55. Z.-B. Kang, I. Vitev and H. Xing, Vector-boson-tagged jet production in heavy ion collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 96 (2017) 014912 [arXiv:1702.07276] [INSPIRE].

  56. ATLAS collaboration, Study of jets produced in association with a W boson in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Phys. Rev. D 85 (2012) 092002 [arXiv:1201.1276] [INSPIRE].

  57. CMS collaboration, Event shapes and azimuthal correlations in Z +jets events in pp collisions at \( \sqrt{s} \) = 7 TeV, Phys. Lett. B 722 (2013) 238 [arXiv:1301.1646] [INSPIRE].

  58. CMS collaboration, Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at \( \sqrt{s} \) = 8 TeV, JHEP 04 (2017) 022 [arXiv:1611.03844] [INSPIRE].

  59. CMS collaboration, Study of jet quenching with Z +jet correlations in Pb-Pb and pp collisions at \( \sqrt{s_{NN}} \) = 5.02 TeV, Phys. Rev. Lett. 119 (2017) 082301 [arXiv:1702.01060] [INSPIRE].

  60. CMS collaboration, Measurement of differential cross sections for Z boson production in association with jets in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J. C 78 (2018) 965 [arXiv:1804.05252] [INSPIRE].

  61. ATLAS collaboration, Measurement of the cross section for isolated-photon plus jet production in pp collisions at \( \sqrt{s} \) = 13 TeV using the ATLAS detector, Phys. Lett. B 780 (2018) 578 [arXiv:1801.00112] [INSPIRE].

  62. 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].

  63. D.W. Kolodrubetz, P. Pietrulewicz, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Factorization for jet radius logarithms in jet mass spectra at the LHC, JHEP 12 (2016) 054 [arXiv:1605.08038] [INSPIRE].

    Article  ADS  Google Scholar 

  64. J. Collins and J.-W. Qiu, kT factorization is violated in production of high-transverse-momentum particles in hadron-hadron collisions, Phys. Rev. D 75 (2007) 114014 [arXiv:0705.2141] [INSPIRE].

    ADS  Google Scholar 

  65. T.C. Rogers and P.J. Mulders, No generalized TMD-factorization in hadro-production of high transverse momentum hadrons, Phys. Rev. D 81 (2010) 094006 [arXiv:1001.2977] [INSPIRE].

  66. S. Catani, D. de Florian and G. Rodrigo, Space-like (versus time-like) collinear limits in QCD: is factorization violated?, JHEP 07 (2012) 026 [arXiv:1112.4405] [INSPIRE].

    Article  ADS  Google Scholar 

  67. J.R. Forshaw, M.H. Seymour and A. Siodmok, On the breaking of collinear factorization in QCD, JHEP 11 (2012) 066 [arXiv:1206.6363] [INSPIRE].

    Article  ADS  Google Scholar 

  68. I.Z. Rothstein and I.W. Stewart, An effective field theory for forward scattering and factorization violation, JHEP 08 (2016) 025 [arXiv:1601.04695] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  69. R.J. Hill and M. Neubert, Spectator interactions in soft collinear effective theory, Nucl. Phys. B 657 (2003) 229 [hep-ph/0211018] [INSPIRE].

  70. S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [arXiv:1011.3918] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  71. J.C. Collins and D.E. Soper, Back-to-back jets in QCD, Nucl. Phys. B 193 (1981) 381 [Erratum ibid. B 213 (1983) 545] [INSPIRE].

  72. J.C. Collins and D.E. Soper, Parton distribution and decay functions, Nucl. Phys. B 194 (1982) 445 [INSPIRE].

    ADS  Google Scholar 

  73. I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Factorization at the LHC: from PDFs to initial state jets, Phys. Rev. D 81 (2010) 094035 [arXiv:0910.0467] [INSPIRE].

  74. S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].

  75. Y.L. Dokshitzer, V.A. Khoze, S.I. Troian and A.H. Mueller, QCD coherence in high-energy reactions, Rev. Mod. Phys. 60 (1988) 373 [INSPIRE].

    Article  ADS  Google Scholar 

  76. M. Cacciari, G.P. Salam and G. Soyez, The anti-kt jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  77. T. Becher and G. Bell, Analytic regularization in soft-collinear effective theory, Phys. Lett. B 713 (2012) 41 [arXiv:1112.3907] [INSPIRE].

    Article  ADS  Google Scholar 

  78. 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].

    Article  ADS  Google Scholar 

  79. 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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  80. T. Becher and X. Garcia i Tormo, Factorization and resummation for transverse thrust, JHEP 06 (2015) 071 [arXiv:1502.04136] [INSPIRE].

  81. T. Becher, C. Lorentzen and M.D. Schwartz, Resummation for W and Z production at large pT , Phys. Rev. Lett. 108 (2012) 012001 [arXiv:1106.4310] [INSPIRE].

  82. 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].

    Article  ADS  Google Scholar 

  83. M. Dasgupta, K. Khelifa-Kerfa, S. Marzani and M. Spannowsky, On jet mass distributions in Z +jet and dijet processes at the LHC, JHEP 10 (2012) 126 [arXiv:1207.1640] [INSPIRE].

    Article  ADS  Google Scholar 

  84. T. Sj¨ostrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].

  85. S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].

  86. J.M. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2 jet and Z + 2 jet production at hadron colliders, Phys. Rev. D 65 (2002) 113007 [hep-ph/0202176] [INSPIRE].

  87. J.M. Campbell, R.K. Ellis and D.L. Rainwater, Next-to-leading order QCD predictions for W + 2 jet and Z + 2 jet production at the CERN LHC, Phys. Rev. D 68 (2003) 094021 [hep-ph/0308195] [INSPIRE].

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Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Yang-Ting Chien

  2. Theoretical Physics Department, CERN, CH-1211, Geneva 23, Switzerland

    Ding Yu Shao & Bin Wu

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  2. Ding Yu Shao
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Correspondence to Ding Yu Shao.

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ArXiv ePrint: 1905.01335

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Chien, YT., Shao, D.Y. & Wu, B. Resummation of boson-jet correlation at hadron colliders. J. High Energ. Phys. 2019, 25 (2019). https://doi.org/10.1007/JHEP11(2019)025

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  • Received: 10 May 2019

  • Revised: 09 October 2019

  • Accepted: 15 October 2019

  • Published: 06 November 2019

  • DOI: https://doi.org/10.1007/JHEP11(2019)025

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Keywords

  • Effective Field Theories
  • Perturbative QCD
  • Renormalization Group
  • Resummation

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