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NLL′ resummation of jet mass

Journal of High Energy Physics volume 2019, Article number: 20 (2019) Cite this article

A preprint version of the article is available at arXiv.

Abstract

Starting from a factorization theorem in effective field theory, we present resummed results for two non-global observables: the invariant-mass distribution of jets and the energy distribution outside jets. Our results include the full next-to-leading-order corrections to the hard, jet and soft functions and are implemented in a parton-shower framework which generates the renormalization-group running in the effective theory. The inclusion of these matching corrections leads to an improved description of the data and reduced theoretical uncertainties. They will have to be combined with two-loop running in the future, but our results are an important first step towards the higher-logarithmic resummation of non-global observables.

References

  1. Y. Hatta, Relating e + e − annihilation to high energy scattering at weak and strong coupling, JHEP 11 (2008) 057 [arXiv:0810.0889] [INSPIRE].

    ADS  Article  Google Scholar 

  2. E. Avsar, Y. Hatta and T. Matsuo, Soft gluons away from jets: distribution and correlation, JHEP 06 (2009) 011 [arXiv:0903.4285] [INSPIRE].

    ADS  Article  Google Scholar 

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

    ADS  Article  MATH  Google Scholar 

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. 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].

    ADS  Article  Google Scholar 

  6. 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].

    ADS  Article  Google Scholar 

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

  8. 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].

  9. 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].

    ADS  Article  Google Scholar 

  10. 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].

    ADS  Article  Google Scholar 

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

    ADS  Article  MATH  Google Scholar 

  12. 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].

    ADS  Article  Google Scholar 

  13. 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].

    ADS  Article  Google Scholar 

  14. 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].

  15. 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].

    ADS  Article  Google Scholar 

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

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

    ADS  Article  Google Scholar 

  18. 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].

    ADS  Article  Google Scholar 

  19. Y.-T. Chien, R. Kelley, M.D. Schwartz and H.X. Zhu, Resummation of jet mass at hadron colliders, Phys. Rev. D 87 (2013) 014010 [arXiv:1208.0010] [INSPIRE].

    ADS  Google Scholar 

  20. Z.L. Liu, C.S. Li, J. Wang and Y. Wang, Resummation prediction on the jet mass spectrum in one-jet inclusive production at the LHC, JHEP 04 (2015) 005 [arXiv:1412.1337] [INSPIRE].

    Article  Google Scholar 

  21. A. Idilbi and C. Kim, Factorization of the jet mass distribution in the small R limit, J. Korean Phys. Soc. 73 (2018) 1230 [arXiv:1606.05429] [INSPIRE].

    ADS  Article  Google Scholar 

  22. Z.-B. Kang, K. Lee, X. Liu and F. Ringer, The groomed and ungroomed jet mass distribution for inclusive jet production at the LHC, JHEP 10 (2018) 137 [arXiv:1803.03645] [INSPIRE].

    ADS  Article  Google Scholar 

  23. T. Becher and M. Neubert, Toward a NNLO calculation of the \( \overline{B}\to {X}_s\gamma \) decay rate with a cut on photon energy. II. Two-loop result for the jet function, Phys. Lett. B 637 (2006) 251 [hep-ph/0603140] [INSPIRE].

  24. T. Becher and G. Bell, The gluon jet function at two-loop order, Phys. Lett. B 695 (2011) 252 [arXiv:1008.1936] [INSPIRE].

    ADS  Article  Google Scholar 

  25. R. Brüser, Z.L. Liu and M. Stahlhofen, Three-loop quark jet function, Phys. Rev. Lett. 121 (2018) 072003 [arXiv:1804.09722] [INSPIRE].

    ADS  Article  Google Scholar 

  26. P. Banerjee, P.K. Dhani and V. Ravindran, Gluon jet function at three loops in QCD, Phys. Rev. D 98 (2018) 094016 [arXiv:1805.02637] [INSPIRE].

    ADS  Google Scholar 

  27. 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].

  28. R. Kelley, M.D. Schwartz, R.M. Schabinger and H.X. Zhu, The two-loop hemisphere soft function, Phys. Rev. D 84 (2011) 045022 [arXiv:1105.3676] [INSPIRE].

    ADS  Google Scholar 

  29. A. Hornig, C. Lee, I.W. Stewart, J.R. Walsh and S. Zuberi, Non-global structure of the O(α 2 s ) dijet soft function, JHEP 08 (2011) 054 [Erratum ibid. 10 (2017) 101] [arXiv:1105.4628] [INSPIRE].

  30. P.F. Monni, T. Gehrmann and G. Luisoni, Two-loop soft corrections and resummation of the thrust distribution in the dijet region, JHEP 08 (2011) 010 [arXiv:1105.4560] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  31. J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].

    ADS  Article  Google Scholar 

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

  33. A. Banfi, M. Dasgupta, K. Khelifa-Kerfa and S. Marzani, Non-global logarithms and jet algorithms in high-p T jet shapes, JHEP 08 (2010) 064 [arXiv:1004.3483] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  34. P. Cal, F. Ringer and W.J. Waalewijn, The jet shape at NLL′, arXiv:1901.06389 [INSPIRE].

  35. T. Becher and M. Neubert, Threshold resummation in momentum space from effective field theory, Phys. Rev. Lett. 97 (2006) 082001 [hep-ph/0605050] [INSPIRE].

  36. ALEPH collaboration, Properties of hadronic Z decays and test of QCD generators, Z. Phys. C 55 (1992) 209 [INSPIRE].

  37. R. Abbate, M. Fickinger, A.H. Hoang, V. Mateu and I.W. Stewart, Thrust at N 3 LL with power corrections and a precision global fit for α s(m Z), Phys. Rev. D 83 (2011) 074021 [arXiv:1006.3080] [INSPIRE].

    ADS  Google Scholar 

  38. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO corrections to event shapes in e + e − annihilation, JHEP 12 (2007) 094 [arXiv:0711.4711] [INSPIRE].

    ADS  Article  Google Scholar 

  39. S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP 06 (2009) 041 [arXiv:0904.1077] [INSPIRE].

    ADS  Article  Google Scholar 

  40. V. Del Duca, C. Duhr, A. Kardos, G. Somogyi and Z. Trócsányi, Three-jet production in electron-positron collisions at next-to-next-to-leading order accuracy, Phys. Rev. Lett. 117 (2016) 152004 [arXiv:1603.08927] [INSPIRE].

    ADS  Article  Google Scholar 

  41. T. Sjöstrand, S. Mrenna and P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].

  42. W.T. Giele, D.A. Kosower and P.Z. Skands, A simple shower and matching algorithm, Phys. Rev. D 78 (2008) 014026 [arXiv:0707.3652] [INSPIRE].

    ADS  Google Scholar 

  43. G.P. Korchemsky, Shape functions and power corrections to the event shapes, in QCD and high energy hadronic interactions. Proceedings, 33rd Rencontres de Moriond, Les Arcs, France, 21–28 March 1998, pg. 489 [hep-ph/9806537] [INSPIRE].

  44. G.P. Korchemsky and G.F. Sterman, Power corrections to event shapes and factorization, Nucl. Phys. B 555 (1999) 335 [hep-ph/9902341] [INSPIRE].

  45. S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].

  46. P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].

  47. H.T. Li and P. Skands, A framework for second-order parton showers, Phys. Lett. B 771 (2017) 59 [arXiv:1611.00013] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  48. S. Höche and S. Prestel, Triple collinear emissions in parton showers, Phys. Rev. D 96 (2017) 074017 [arXiv:1705.00742] [INSPIRE].

    ADS  Google Scholar 

  49. S. Höche, F. Krauss and S. Prestel, Implementing NLO DGLAP evolution in parton showers, JHEP 10 (2017) 093 [arXiv:1705.00982] [INSPIRE].

    Article  ADS  Google Scholar 

  50. F. Dulat, S. Höche and S. Prestel, Leading-color fully differential two-loop soft corrections to QCD dipole showers, Phys. Rev. D 98 (2018) 074013 [arXiv:1805.03757] [INSPIRE].

    ADS  Google Scholar 

  51. Z. Nagy and D.E. Soper, Parton showers with quantum interference, JHEP 09 (2007) 114 [arXiv:0706.0017] [INSPIRE].

    ADS  Article  Google Scholar 

  52. S. Plätzer and M. Sjödahl, Subleading N c improved parton showers, JHEP 07 (2012) 042 [arXiv:1201.0260] [INSPIRE].

    ADS  Article  Google Scholar 

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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.

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Authors and Affiliations

  1. Albert Einstein Center for Fundamental Physics, Institut für Theoretische Physik, Universität Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland

    Marcel Balsiger & Thomas Becher

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

    Ding Yu Shao

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  1. Marcel Balsiger
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  2. Thomas Becher
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Correspondence to Ding Yu Shao.

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ArXiv ePrint: 1901.09038

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Balsiger, M., Becher, T. & Shao, D.Y. NLL′ resummation of jet mass. J. High Energ. Phys. 2019, 20 (2019). https://doi.org/10.1007/JHEP04(2019)020

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  • DOI: https://doi.org/10.1007/JHEP04(2019)020

Keywords

  • Perturbative QCD
  • Resummation