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.
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References
Y. Hatta, Relating e + e − annihilation to high energy scattering at weak and strong coupling, JHEP 11 (2008) 057 [arXiv:0810.0889] [INSPIRE].
E. Avsar, Y. Hatta and T. Matsuo, Soft gluons away from jets: distribution and correlation, JHEP 06 (2009) 011 [arXiv:0903.4285] [INSPIRE].
Y. Hatta and T. Ueda, Resummation of non-global logarithms at finite N c, Nucl. Phys. B 874 (2013) 808 [arXiv:1304.6930] [INSPIRE].
S. Caron-Huot, Resummation of non-global logarithms and the BFKL equation, JHEP 03 (2018) 036 [arXiv:1501.03754] [INSPIRE].
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].
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].
D. Neill, The edge of jets and subleading non-global logs, arXiv:1508.07568 [INSPIRE].
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].
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].
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].
D. Neill, The asymptotic form of non-global logarithms, black disc saturation and gluonic deserts, JHEP 01 (2017) 109 [arXiv:1610.02031] [INSPIRE].
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].
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].
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].
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].
D. Neill and V. Vaidya, Soft evolution after a hard scattering process, arXiv:1803.02372 [INSPIRE].
D. Neill, Non-global and clustering effects for groomed multi-prong jet shapes, JHEP 02 (2019) 114 [arXiv:1808.04897] [INSPIRE].
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].
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].
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].
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].
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].
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].
T. Becher and G. Bell, The gluon jet function at two-loop order, Phys. Lett. B 695 (2011) 252 [arXiv:1008.1936] [INSPIRE].
R. Brüser, Z.L. Liu and M. Stahlhofen, Three-loop quark jet function, Phys. Rev. Lett. 121 (2018) 072003 [arXiv:1804.09722] [INSPIRE].
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].
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].
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].
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].
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].
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].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
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].
P. Cal, F. Ringer and W.J. Waalewijn, The jet shape at NLL′, arXiv:1901.06389 [INSPIRE].
T. Becher and M. Neubert, Threshold resummation in momentum space from effective field theory, Phys. Rev. Lett. 97 (2006) 082001 [hep-ph/0605050] [INSPIRE].
ALEPH collaboration, Properties of hadronic Z decays and test of QCD generators, Z. Phys. C 55 (1992) 209 [INSPIRE].
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].
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].
S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP 06 (2009) 041 [arXiv:0904.1077] [INSPIRE].
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].
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].
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].
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].
G.P. Korchemsky and G.F. Sterman, Power corrections to event shapes and factorization, Nucl. Phys. B 555 (1999) 335 [hep-ph/9902341] [INSPIRE].
S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029 [hep-ph/0204244] [INSPIRE].
P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, JHEP 11 (2004) 040 [hep-ph/0409146] [INSPIRE].
H.T. Li and P. Skands, A framework for second-order parton showers, Phys. Lett. B 771 (2017) 59 [arXiv:1611.00013] [INSPIRE].
S. Höche and S. Prestel, Triple collinear emissions in parton showers, Phys. Rev. D 96 (2017) 074017 [arXiv:1705.00742] [INSPIRE].
S. Höche, F. Krauss and S. Prestel, Implementing NLO DGLAP evolution in parton showers, JHEP 10 (2017) 093 [arXiv:1705.00982] [INSPIRE].
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].
Z. Nagy and D.E. Soper, Parton showers with quantum interference, JHEP 09 (2007) 114 [arXiv:0706.0017] [INSPIRE].
S. Plätzer and M. Sjödahl, Subleading N c improved parton showers, JHEP 07 (2012) 042 [arXiv:1201.0260] [INSPIRE].
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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