Abstract
We present a novel method for resummation of event shapes to next-to-next-to-leading-logarithmic (NNLL) accuracy. We discuss the technique and describe its implementation in a numerical program in the case of e + e − collisions where the resummed prediction is matched to NNLO. We reproduce all the existing predictions and present new results for oblateness and thrust major.
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M. Dasgupta and G.P. Salam, Event shapes in e + e − annihilation and deep inelastic scattering, J. Phys. G 30 (2004) R143 [hep-ph/0312283] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
M. Dasgupta and G.P. Salam, Accounting for coherence in interjet E t flow: a case study, JHEP 03 (2002) 017 [hep-ph/0203009] [INSPIRE].
A. Banfi, G. Marchesini and G. Smye, Away from jet energy flow, JHEP 08 (2002) 006 [hep-ph/0206076] [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].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Jet rates in electron-positron annihilation at O(α 3 s ) in QCD, Phys. Rev. Lett. 100 (2008) 172001 [arXiv:0802.0813] [INSPIRE].
S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett. 101 (2008) 162001 [arXiv:0807.3241] [INSPIRE].
S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP 06 (2009) 041 [arXiv:0904.1077] [INSPIRE].
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].
S. Catani, L. Trentadue, G. Turnock and B.R. Webber, Resummation of large logarithms in e + e − event shape distributions, Nucl. Phys. B 407 (1993) 3 [INSPIRE].
R. Bonciani, S. Catani, M.L. Mangano and P. Nason, Sudakov resummation of multiparton QCD cross-sections, Phys. Lett. B 575 (2003) 268 [hep-ph/0307035] [INSPIRE].
S. Catani, G. Turnock, B.R. Webber and L. Trentadue, Thrust distribution in e + e − annihilation, Phys. Lett. B 263 (1991) 491 [INSPIRE].
S. Catani, G. Turnock and B.R. Webber, Heavy jet mass distribution in e + e − annihilation, Phys. Lett. B 272 (1991) 368 [INSPIRE].
S. Catani and B.R. Webber, Resummed C parameter distribution in e + e − annihilation, Phys. Lett. B 427 (1998) 377 [hep-ph/9801350] [INSPIRE].
S. Catani, G. Turnock and B.R. Webber, Jet broadening measures in e + e − annihilation, Phys. Lett. B 295 (1992) 269 [INSPIRE].
Y.L. Dokshitzer, A. Lucenti, G. Marchesini and G.P. Salam, On the QCD analysis of jet broadening, JHEP 01 (1998) 011 [hep-ph/9801324] [INSPIRE].
S. Catani, Y.L. Dokshitzer, M. Olsson, G. Turnock and B.R. Webber, New clustering algorithm for multi-jet cross-sections in e + e − annihilation, Phys. Lett. B 269 (1991) 432 [INSPIRE].
S. Catani, Y.L. Dokshitzer and B.R. Webber, Average number of jets in deep inelastic scattering, Phys. Lett. B 322 (1994) 263 [INSPIRE].
G. Dissertori and M. SchMelling, An improved theoretical prediction for the two jet rate in e + e − annihilation, Phys. Lett. B 361 (1995) 167 [INSPIRE].
C.F. Berger, T. Kucs and G.F. Sterman, Interjet energy flow/event shape correlations, Int. J. Mod. Phys. A 18 (2003) 4159 [hep-ph/0212343] [INSPIRE].
C.F. Berger, T. Kucs and G.F. Sterman, Event shape/energy flow correlations, Phys. Rev. D 68 (2003) 014012 [hep-ph/0303051] [INSPIRE].
A.J. Larkoski, D. Neill and J. Thaler, Jet shapes with the broadening axis, JHEP 04 (2014) 017 [arXiv:1401.2158] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Semi-numerical resummation of event shapes, JHEP 01 (2002) 018 [hep-ph/0112156] [INSPIRE].
A.J. Larkoski and J. Thaler, Unsafe but calculable: ratios of angularities in perturbative QCD, JHEP 09 (2013) 137 [arXiv:1307.1699] [INSPIRE].
A.J. Larkoski, I. Moult and D. Neill, Toward multi-differential cross sections: measuring two angularities on a single jet, JHEP 09 (2014) 046 [arXiv:1401.4458] [INSPIRE].
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].
A. Banfi, G.P. Salam and G. Zanderighi, Principles of general final-state resummation and automated implementation, JHEP 03 (2005) 073 [hep-ph/0407286] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Phenomenology of event shapes at hadron colliders, JHEP 06 (2010) 038 [arXiv:1001.4082] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Resummed event shapes at hadron-hadron colliders, JHEP 08 (2004) 062 [hep-ph/0407287] [INSPIRE].
T. Becher and M.D. Schwartz, A precise determination of α s from LEP thrust data using effective field theory, JHEP 07 (2008) 034 [arXiv:0803.0342] [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].
Y.-T. Chien and M.D. Schwartz, Resummation of heavy jet mass and comparison to LEP data, JHEP 08 (2010) 058 [arXiv:1005.1644] [INSPIRE].
T. Becher and G. Bell, NNLL resummation for jet broadening, JHEP 11 (2012) 126 [arXiv:1210.0580] [INSPIRE].
S. Alioli et al., Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA, JHEP 09 (2013) 120 [arXiv:1211.7049] [INSPIRE].
D. de Florian and M. Grazzini, The back-to-back region in e + e − energy-energy correlation, Nucl. Phys. B 704 (2005) 387 [hep-ph/0407241] [INSPIRE].
T. Becher and M. Neubert, Drell-Yan production at small q T , transverse parton distributions and the collinear anomaly, Eur. Phys. J. C 71 (2011) 1665 [arXiv:1007.4005] [INSPIRE].
D. Kang, C. Lee and I.W. Stewart, Using 1-jettiness to measure 2 jets in DIS 3 ways, Phys. Rev. D 88 (2013) 054004 [arXiv:1303.6952] [INSPIRE].
Z.-B. Kang, X. Liu, S. Mantry and J.-W. Qiu, Probing nuclear dynamics in jet production with a global event shape, Phys. Rev. D 88 (2013) 074020 [arXiv:1303.3063] [INSPIRE].
Z.-B. Kang, X. Liu and S. Mantry, 1-jettiness DIS event shape: NNLL+NLO results, Phys. Rev. D 90 (2014) 014041 [arXiv:1312.0301] [INSPIRE].
G. Bozzi, S. Catani, D. de Florian and M. Grazzini, Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC, Nucl. Phys. B 737 (2006) 73 [hep-ph/0508068] [INSPIRE].
A. Banfi, M. Dasgupta and S. Marzani, QCD predictions for new variables to study dilepton transverse momenta at hadron colliders, Phys. Lett. B 701 (2011) 75 [arXiv:1102.3594] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The beam thrust cross section for Drell-Yan at NNLL order, Phys. Rev. Lett. 106 (2011) 032001 [arXiv:1005.4060] [INSPIRE].
C.F. Berger, C. Marcantonini, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Higgs production with a central jet veto at NNLL+NNLO, JHEP 04 (2011) 092 [arXiv:1012.4480] [INSPIRE].
T. Becher and M. Neubert, Factorization and NNLL resummation for Higgs production with a jet veto, JHEP 07 (2012) 108 [arXiv:1205.3806] [INSPIRE].
T. Becher, M. Neubert and L. Rothen, Factorization and N 3 LL p + N N LO predictions for the Higgs cross section with a jet veto, JHEP 10 (2013) 125 [arXiv:1307.0025] [INSPIRE].
A. Banfi, P.F. Monni, G.P. Salam and G. Zanderighi, Higgs and Z-boson production with a jet veto, Phys. Rev. Lett. 109 (2012) 202001 [arXiv:1206.4998] [INSPIRE].
I.W. Stewart, F.J. Tackmann, J.R. Walsh and S. Zuberi, Jet p T resummation in Higgs production at N N LL ′ + N N LO, Phys. Rev. D 89 (2014) 054001 [arXiv:1307.1808] [INSPIRE].
H.X. Zhu, C.S. Li, H.T. Li, D.Y. Shao and L.L. Yang, Transverse-momentum resummation for top-quark pairs at hadron colliders, Phys. Rev. Lett. 110 (2013) 082001 [arXiv:1208.5774] [INSPIRE].
S. Catani, M. Grazzini and A. Torre, Transverse-momentum resummation for heavy-quark hadroproduction, Nucl. Phys. B 890 (2014) 518 [arXiv:1408.4564] [INSPIRE].
I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, N -jettiness: an inclusive event shape to veto jets, Phys. Rev. Lett. 105 (2010) 092002 [arXiv:1004.2489] [INSPIRE].
T.T. Jouttenus, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, The soft function for exclusive N -jet production at hadron colliders, Phys. Rev. D 83 (2011) 114030 [arXiv:1102.4344] [INSPIRE].
J. Fan, M. Reece and L.-T. Wang, Possible futures of electroweak precision: ILC, FCC-ee and CEPC, arXiv:1411.1054 [INSPIRE].
R. Brock et al., Planning the future of U.S. particle physics (Snowmass 2013). Section 3: energy frontier, arXiv:1401.6081 [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].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, EERAD3: event shapes and jet rates in electron-positron annihilation at order α 3 s , Comput. Phys. Commun. 185 (2014) 3331 [arXiv:1402.4140] [INSPIRE].
S. Catani and M. Grazzini, QCD transverse-momentum resummation in gluon fusion processes, Nucl. Phys. B 845 (2011) 297 [arXiv:1011.3918] [INSPIRE].
S. Catani, B.R. Webber and G. Marchesini, QCD coherent branching and semiinclusive processes at large x, Nucl. Phys. B 349 (1991) 635 [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, N LL + N N LO predictions for jet-veto efficiencies in Higgs-boson and Drell-Yan production, JHEP 06 (2012) 159 [arXiv:1203.5773] [INSPIRE].
Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummed event shape variables in DIS, JHEP 08 (2002) 032 [hep-ph/0208073] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of the jet broadening in DIS, Eur. Phys. J. C 24 (2002) 213 [hep-ph/0110213] [INSPIRE].
A.H. Hoang, D.W. Kolodrubetz, V. Mateu and I.W. Stewart, C parameter distribution at N 3 LL ′ including power corrections, arXiv:1411.6633 [INSPIRE].
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Banfi, A., McAslan, H., Monni, P.F. et al. A general method for the resummation of event-shape distributions in e + e − annihilation. J. High Energ. Phys. 2015, 102 (2015). https://doi.org/10.1007/JHEP05(2015)102
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DOI: https://doi.org/10.1007/JHEP05(2015)102