Abstract
We consider soft-gluon evolution at the amplitude level. Our evolution algorithm applies to generic hard-scattering processes involving any number of coloured partons and we present a reformulation of the algorithm in such a way as to make the cancellation of infrared divergences explicit. We also emphasise the special role played by a Lorentz-invariant evolution variable, which coincides with the transverse momentum of the latest emission in a suitably defined dipole zero-momentum frame. Handling large colour matrices presents the most significant challenge to numerical implementations and we present a means to expand systematically about the leading colour approximation. Specifically, we present a systematic procedure to calculate the resulting colour traces, which is based on the colour flow basis. Identifying the leading contribution leads us to re-derive the Banfi-Marchesini-Smye equation. However, our formalism is more general and can systematically perform resummation of contributions enhanced by the t’Hooft coupling αsN ∼ 1, along with successive perturbations that are parametrically suppressed by powers of 1/N . We also discuss how our approach relates to earlier work.
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References
M. Bähr et al., HERWIG++ Physics and Manual, Eur. Phys. J. C 58 (2008) 639 [arXiv:0803.0883] [INSPIRE].
J. Bellm et al., HERWIG 7.0/HERWIG++ 3.0 release note, Eur. Phys. J. C 76 (2016) 196 [arXiv:1512.01178] [INSPIRE].
T. Sjöstrand et al., An Introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
T. Becher, A. Broggio and A. Ferroglia, Introduction to Soft-Collinear Effective Theory, Lect. Notes Phys. 896 (2015) 1 [arXiv:1410.1892] [INSPIRE].
M. Dasgupta and G.P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B 512 (2001) 323 [hep-ph/0104277] [INSPIRE].
H. Weigert, Nonglobal jet evolution at finite N c, Nucl. Phys. B 685 (2004) 321 [hep-ph/0312050] [INSPIRE].
K. Khelifa-Kerfa and Y. Delenda, Non-global logarithms at finite N c beyond leading order, JHEP 03 (2015) 094 [arXiv:1501.00475] [INSPIRE].
Y. Delenda and K. Khelifa-Kerfa, Eikonal gluon bremsstrahlung at finite N c beyond two loops, Phys. Rev. D 93 (2016) 054027 [arXiv:1512.05401] [INSPIRE].
M.D. Schwartz and H.X. Zhu, Nonglobal logarithms at three loops, four loops, five loops and beyond, Phys. Rev. D 90 (2014) 065004 [arXiv:1403.4949] [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].
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, M. Neubert, L. Rothen and D.Y. Shao, Factorization and Resummation for Jet Processes, JHEP 11 (2016) 019 [Erratum ibid. 1705 (2017) 154] [arXiv:1605.02737] [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].
Y. Hagiwara, Y. Hatta and T. Ueda, Hemisphere jet mass distribution at finite N c, Phys. Lett. B 756 (2016) 254 [arXiv:1507.07641] [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].
S. Plätzer and M. Sjödahl, Subleading N c improved Parton Showers, JHEP 07 (2012) 042 [arXiv:1201.0260] [INSPIRE].
Z. Nagy and D.E. Soper, A parton shower based on factorization of the quantum density matrix, JHEP 06 (2014) 097 [arXiv:1401.6364] [INSPIRE].
Z. Nagy and D.E. Soper, Effects of subleading color in a parton shower, JHEP 07 (2015) 119 [arXiv:1501.00778] [INSPIRE].
Z. Nagy and D.E. Soper, What is a parton shower?, arXiv:1705.08093 [INSPIRE].
J.R. Forshaw, A. Kyrieleis and M.H. Seymour, Super-leading logarithms in non-global observables in QCD, JHEP 08 (2006) 059 [hep-ph/0604094] [INSPIRE].
J.R. Forshaw, A. Kyrieleis and M.H. Seymour, Super-leading logarithms in non-global observables in QCD: Colour basis independent calculation, JHEP 09 (2008) 128 [arXiv:0808.1269] [INSPIRE].
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].
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].
M.D. Schwartz, K. Yan and H.X. Zhu, Collinear factorization violation and effective field theory, Phys. Rev. D 96 (2017) 056005 [arXiv:1703.08572] [INSPIRE].
R. Ángeles Martínez, J.R. Forshaw and M.H. Seymour, Ordering multiple soft gluon emissions, Phys. Rev. Lett. 116 (2016) 212003 [arXiv:1602.00623] [INSPIRE].
S. Plätzer, Summing Large-N Towers in Colour Flow Evolution, Eur. Phys. J. C 74 (2014) 2907 [arXiv:1312.2448] [INSPIRE].
A. Banfi, G.P. Salam and G. Zanderighi, Phenomenology of event shapes at hadron colliders, JHEP 06 (2010) 038 [arXiv:1001.4082] [INSPIRE].
S. Caron-Huot and M. Herranen, High-energy evolution to three loops, JHEP 02 (2018) 058 [arXiv:1604.07417] [INSPIRE].
S. Keppeler and M. Sjödahl, Orthogonal multiplet bases in SU(N C ) color space, JHEP 09 (2012) 124 [arXiv:1207.0609] [INSPIRE].
R. Ángeles Martínez, J.R. Forshaw and M.H. Seymour, Coulomb gluons and the ordering variable, JHEP 12 (2015) 091 [arXiv:1510.07998] [INSPIRE].
S. Catani and M. Grazzini, The soft gluon current at one loop order, Nucl. Phys. B 591 (2000) 435 [hep-ph/0007142] [INSPIRE].
Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one loop QCD amplitudes at next-to-next-to leading order, Phys. Rev. D 60 (1999) 116001 [hep-ph/9903516] [INSPIRE].
I. Feige and M.D. Schwartz, Hard-Soft-Collinear Factorization to All Orders, Phys. Rev. D 90 (2014) 105020 [arXiv:1403.6472] [INSPIRE].
F. Maltoni, K. Paul, T. Stelzer and S. Willenbrock, Color flow decomposition of QCD amplitudes, Phys. Rev. D 67 (2003) 014026 [hep-ph/0209271] [INSPIRE].
G. Gustafson and U. Pettersson, Dipole Formulation of QCD Cascades, Nucl. Phys. B 306 (1988) 746 [INSPIRE].
L. Lönnblad, ARIADNE version 4: A Program for simulation of QCD cascades implementing the color dipole model, Comput. Phys. Commun. 71 (1992) 15 [INSPIRE].
S. Plätzer and S. Gieseke, Coherent Parton Showers with Local Recoils, JHEP 01 (2011) 024 [arXiv:0909.5593] [INSPIRE].
S. Höche and S. Prestel, The midpoint between dipole and parton showers, Eur. Phys. J. C 75 (2015) 461 [arXiv:1506.05057] [INSPIRE].
A. Banfi, G. Marchesini and G. Smye, Away from jet energy flow, JHEP 08 (2002) 006 [hep-ph/0206076] [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
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Martínez, R.Á., De Angelis, M., Forshaw, J.R. et al. Soft gluon evolution and non-global logarithms. J. High Energ. Phys. 2018, 44 (2018). https://doi.org/10.1007/JHEP05(2018)044
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DOI: https://doi.org/10.1007/JHEP05(2018)044