Abstract
We present a systematic study of differences between NLL resummation and parton showers. We first construct a Markovian Monte-Carlo algorithm for resummation of additive observables in electron-positron annihilation. Approximations intrinsic to the pure NLL result are then removed, in order to obtain a traditional, momentum and probability conserving parton shower based on the coherent branching formalism. The impact of each approximation is studied, and an overall comparison is made between the parton shower and pure NLL resummation. Differences compared to modern parton-shower algorithms formulated in terms of color dipoles are analyzed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y.L. Dokshitzer, D. Diakonov and S.I. Troian, Hard Processes in Quantum Chromodynamics, Phys. Rept. 58 (1980) 269 [INSPIRE].
G. Parisi and R. Petronzio, Small Transverse Momentum Distributions in Hard Processes, Nucl. Phys. B 154 (1979) 427 [INSPIRE].
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].
G.F. Sterman, Summation of Large Corrections to Short Distance Hadronic Cross-Sections, Nucl. Phys. B 281 (1987) 310 [INSPIRE].
S. Catani and L. Trentadue, Resummation of the QCD Perturbative Series for Hard Processes, Nucl. Phys. B 327 (1989) 323 [INSPIRE].
S. Catani and L. Trentadue, Comment on QCD exponentiation at large x, Nucl. Phys. B 353 (1991) 183 [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].
S. Catani et al., QCD, in proceedings of the CERN Workshop on Standard Model Physics (and more) at the LHC (Final Plenary Meeting), Geneva, Switzerland, 14-15 October 1999, CERN-TH-2000-131 [hep-ph/0005025] [INSPIRE].
G. Dissertori et al., Determination of the strong coupling constant using matched NNLO + NLLA predictions for hadronic event shapes in e + e − annihilations, JHEP 08 (2009) 036 [arXiv:0906.3436] [INSPIRE].
T. Gehrmann, M. Jaquier and G. Luisoni, Hadronization effects in event shape moments, Eur. Phys. J. C 67 (2010) 57 [arXiv:0911.2422] [INSPIRE].
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].
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].
N. Kidonakis and G.F. Sterman, Resummation for QCD hard scattering, Nucl. Phys. B 505 (1997) 321 [hep-ph/9705234] [INSPIRE].
N. Kidonakis, G. Oderda and G.F. Sterman, Evolution of color exchange in QCD hard scattering, Nucl. Phys. B 531 (1998) 365 [hep-ph/9803241] [INSPIRE].
E. Laenen, G. Oderda and G.F. Sterman, Resummation of threshold corrections for single particle inclusive cross-sections, Phys. Lett. B 438 (1998) 173 [hep-ph/9806467] [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].
A. Banfi, G.P. Salam and G. Zanderighi, Semi-numerical resummation of event shapes, JHEP 01 (2002) 018 [hep-ph/0112156] [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, H. McAslan, P.F. Monni and G. Zanderighi, A general method for the resummation of event-shape distributions in e + e − annihilation, JHEP 05 (2015) 102 [arXiv:1412.2126] [INSPIRE].
E. Gerwick, S. Höche, S. Marzani and S. Schumann, Soft evolution of multi-jet final states, JHEP 02 (2015) 106 [arXiv:1411.7325] [INSPIRE].
G.C. Fox and S. Wolfram, A Model for Parton Showers in QCD, Nucl. Phys. B 168 (1980) 285 [INSPIRE].
G. Marchesini and B.R. Webber, Simulation of QCD Jets Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 1 [INSPIRE].
T. Sjöstrand, A Model for Initial State Parton Showers, Phys. Lett. B 157 (1985) 321 [INSPIRE].
G. Marchesini and B.R. Webber, Monte Carlo Simulation of General Hard Processes with Coherent QCD Radiation, Nucl. Phys. B 310 (1988) 461 [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].
V.N. Gribov and L.N. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [INSPIRE].
L.N. Lipatov, The parton model and perturbation theory, Sov. J. Nucl. Phys. 20 (1975) 94 [INSPIRE].
Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e + e − Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
D. Amati, A. Bassetto, M. Ciafaloni, G. Marchesini and G. Veneziano, A Treatment of Hard Processes Sensitive to the Infrared Structure of QCD, Nucl. Phys. B 173 (1980) 429 [INSPIRE].
J. Botts and G.F. Sterman, Hard Elastic Scattering in QCD: Leading Behavior, Nucl. Phys. B 325 (1989) 62 [INSPIRE].
N. Kidonakis and G.F. Sterman, Subleading logarithms in QCD hard scattering, Phys. Lett. B 387 (1996) 867 [INSPIRE].
N. Kidonakis, G. Oderda and G.F. Sterman, Threshold resummation for dijet cross-sections, Nucl. Phys. B 525 (1998) 299 [hep-ph/9801268] [INSPIRE].
G. Oderda, Dijet rapidity gaps in photoproduction from perturbative QCD, Phys. Rev. D 61 (2000) 014004 [hep-ph/9903240] [INSPIRE].
N. Kidonakis and J.F. Owens, Effects of higher order threshold corrections in high-E T jet production, Phys. Rev. D 63 (2001) 054019 [hep-ph/0007268] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
S. Höche, S. Schumann and F. Siegert, Hard photon production and matrix-element parton-shower merging, Phys. Rev. D 81 (2010) 034026 [arXiv:0912.3501] [INSPIRE].
L. Lönnblad, Fooling Around with the Sudakov Veto Algorithm, Eur. Phys. J. C 73 (2013) 2350 [arXiv:1211.7204] [INSPIRE].
E. Farhi, A QCD Test for Jets, Phys. Rev. Lett. 39 (1977) 1587 [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].
S. Höche, Introduction to parton-shower event generators, in proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics: Journeys Through the Precision Frontier: Amplitudes for Colliders. (TASI 2014), Boulder, Colorado, 2-27 June 2014, World Scientific (2015), p. 235 [arXiv:1411.4085] [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].
S. Höche and S. Prestel, The midpoint between dipole and parton showers, Eur. Phys. J. C 75 (2015) 461 [arXiv:1506.05057] [INSPIRE].
R.K. Ellis, D.A. Ross and A.E. Terrano, The Perturbative Calculation of Jet Structure in e + e − Annihilation, Nucl. Phys. B 178 (1981) 421 [INSPIRE].
S. Höche and S. Prestel, Triple collinear emissions in parton showers, Phys. Rev. D 96 (2017) 074017 [arXiv:1705.00742] [INSPIRE].
S. Jadach and M. Skrzypek, Exact solutions of the QCD evolution equations using Monte Carlo method, Acta Phys. Polon. B 35 (2004) 745 [hep-ph/0312355] [INSPIRE].
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].
A. Jain, M. Procura and W.J. Waalewijn, Parton Fragmentation within an Identified Jet at NNLL, JHEP 05 (2011) 035 [arXiv:1101.4953] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1711.03497
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Höche, S., Reichelt, D. & Siegert, F. Momentum conservation and unitarity in parton showers and NLL resummation. J. High Energ. Phys. 2018, 118 (2018). https://doi.org/10.1007/JHEP01(2018)118
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2018)118