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Summing threshold logs in a parton shower. (English) Zbl 1390.81364
Summary: When parton distributions are falling steeply as the momentum fractions of the partons increases, there are effects that occur at each order in \(\alpha_{s}\) that combine to affect hard scattering cross sections and need to be summed. We show how to accomplish this in a leading approximation in the context of a parton shower Monte Carlo event generator.
MSC:
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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[1] Sterman, GF, Summation of large corrections to short distance hadronic cross-sections, Nucl. Phys., B 281, 310, (1987)
[2] Appell, D.; Sterman, GF; Mackenzie, PB, Soft gluons and the normalization of the Drell-Yan cross-section, Nucl. Phys., B 309, 259, (1988)
[3] Catani, S.; Trentadue, L., Resummation of the QCD perturbative series for hard processes, Nucl. Phys., B 327, 323, (1989)
[4] Catani, S.; Webber, BR; Marchesini, G., QCD coherent branching and semiinclusive processes at large x, Nucl. Phys., B 349, 635, (1991)
[5] Magnea, L., All order summation and two loop results for the Drell-Yan cross-section, Nucl. Phys., B 349, 703, (1991)
[6] Korchemsky, GP; Marchesini, G., Resummation of large infrared corrections using Wilson loops, Phys. Lett., B 313, 433, (1993)
[7] S. Catani, M.L. Mangano, P. Nason and L. Trentadue, The resummation of soft gluons in hadronic collisions, Nucl. Phys.B 478 (1996) 273 [hep-ph/9604351] [INSPIRE].
[8] H. Contopanagos, E. Laenen and G.F. Sterman, Sudakov factorization and resummation, Nucl. Phys.B 484 (1997) 303 [hep-ph/9604313] [INSPIRE].
[9] N. Kidonakis and G.F. Sterman, Resummation for QCD hard scattering, Nucl. Phys.B 505 (1997) 321 [hep-ph/9705234] [INSPIRE].
[10] N. Kidonakis, G. Oderda and G.F. Sterman, Threshold resummation for dijet cross-sections, Nucl. Phys.B 525 (1998) 299 [hep-ph/9801268] [INSPIRE].
[11] 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].
[12] 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].
[13] S. Catani, M.L. Mangano and P. Nason, Sudakov resummation for prompt photon production in hadron collisions, JHEP07 (1998) 024 [hep-ph/9806484] [INSPIRE].
[14] H.-n. Li, Unification of the k_{\(T\)}and threshold resummations, Phys. Lett.B 454 (1999) 328 [hep-ph/9812363] [INSPIRE].
[15] N. Kidonakis and J.F. Owens, Soft gluon resummation and NNLO corrections for direct photon production, Phys. Rev.D 61 (2000) 094004 [hep-ph/9912388] [INSPIRE].
[16] G.F. Sterman and W. Vogelsang, Threshold resummation and rapidity dependence, JHEP02 (2001) 016 [hep-ph/0011289] [INSPIRE].
[17] 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].
[18] E. Laenen, G.F. Sterman and W. Vogelsang, Recoil and threshold corrections in short distance cross-sections, Phys. Rev.D 63 (2001) 114018 [hep-ph/0010080] [INSPIRE].
[19] A. Kulesza, G.F. Sterman and W. Vogelsang, Joint resummation in electroweak boson production, Phys. Rev.D 66 (2002) 014011 [hep-ph/0202251] [INSPIRE].
[20] N. Kidonakis, Next-to-next-to-next-to-leading-order soft-gluon corrections in hard-scattering processes near threshold, Phys. Rev.D 73 (2006) 034001 [hep-ph/0509079] [INSPIRE].
[21] A. Mukherjee and W. Vogelsang, Threshold resummation for W-boson production at RHIC, Phys. Rev.D 73 (2006) 074005 [hep-ph/0601162] [INSPIRE].
[22] P. Bolzoni, Threshold resummation of Drell-Yan rapidity distributions, Phys. Lett.B 643 (2006) 325 [hep-ph/0609073] [INSPIRE].
[23] Florian, D.; Vogelsang, W., Resummed cross-section for jet production at hadron colliders, Phys. Rev., D 76, 074031, (2007)
[24] V. Ravindran, J. Smith and W.L. van Neerven, QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N\^{2}LO, Nucl. Phys.B 767 (2007) 100 [hep-ph/0608308] [INSPIRE].
[25] Ravindran, V.; Smith, J., threshold corrections to rapidity distributions of Z and \(W\)\^{±}bosons beyond N\^{2}LO at hadron colliders, Phys. Rev., D 76, 114004, (2007)
[26] Bonvini, M.; Forte, S.; Ridolfi, G., Soft gluon resummation of Drell-Yan rapidity distributions: theory and phenomenology, Nucl. Phys., B 847, 93, (2011) · Zbl 1208.81200
[27] Bonvini, M.; Forte, S.; Ridolfi, G., The threshold region for Higgs production in gluon fusion, Phys. Rev. Lett., 109, 102002, (2012)
[28] Florian, D.; Hinderer, P.; Mukherjee, A.; Ringer, F.; Vogelsang, W., Approximate next-to-next-to-leading order corrections to hadronic jet production, Phys. Rev. Lett., 112, 082001, (2014)
[29] Catani, S.; Cieri, L.; Florian, D.; Ferrera, G.; Grazzini, M., threshold resummation at N\^{3}LL accuracy and soft-virtual cross sections at N\^{3}LO, Nucl. Phys., B 888, 75, (2014) · Zbl 1326.81267
[30] Ahmed, T.; Mandal, MK; Rana, N.; Ravindran, V., Rapidity distributions in Drell-Yan and Higgs productions at threshold to third order in QCD, Phys. Rev. Lett., 113, 212003, (2014)
[31] Bonvini, M.; Marzani, S., resummed Higgs cross section at N\^{3}LL, JHEP, 09, 007, (2014)
[32] Bonvini, M.; etal., Parton distributions with threshold resummation, JHEP, 09, 191, (2015)
[33] A.V. Manohar, Deep inelastic scattering as x → 1 using soft collinear effective theory, Phys. Rev.D 68 (2003) 114019 [hep-ph/0309176] [INSPIRE].
[34] A. Idilbi and X.-d. Ji, Threshold resummation for Drell-Yan process in soft-collinear effective theory, Phys. Rev.D 72 (2005) 054016 [hep-ph/0501006] [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] T. Becher, M. Neubert and B.D. Pecjak, Factorization and Momentum-Space Resummation in Deep-Inelastic Scattering, JHEP01 (2007) 076 [hep-ph/0607228] [INSPIRE].
[37] Becher, T.; Neubert, M.; Xu, G., Dynamical threshold enhancement and resummation in Drell-Yan production, JHEP, 07, 030, (2008)
[38] Becher, T.; Schwartz, MD, Direct photon production with effective field theory, JHEP, 02, 040, (2010) · Zbl 1270.81215
[39] Stewart, IW; Tackmann, FJ; Waalewijn, WJ, Factorization at the LHC: from PDFs to initial state jets, Phys. Rev., D 81, 094035, (2010)
[40] Beneke, M.; Falgari, P.; Schwinn, C., Threshold resummation for pair production of coloured heavy (s)particles at hadron colliders, Nucl. Phys., B 842, 414, (2011) · Zbl 1207.81192
[41] Bauer, CW; Tackmann, FJ; Walsh, JR; Zuberi, S., Factorization and resummation for dijet invariant mass spectra, Phys. Rev., D 85, 074006, (2012)
[42] Wang, Y.; Li, CS; Liu, ZL; Shao, DY, threshold resummation for W\^{±}Z and ZZ pair production at the LHC, Phys. Rev., D 90, 034008, (2014)
[43] Y. Li, D. Neill and H.X. Zhu, An Exponential Regulator for Rapidity Divergences, submitted to Phys. Rev. D (2016) [arXiv:1604.00392] [INSPIRE].
[44] G. Lustermans, W.J. Waalewijn and L. Zeune, Joint transverse momentum and threshold resummation beyond NLL, arXiv:1605.02740 [INSPIRE]. · Zbl 1390.81643
[45] Bonvini, M.; Forte, S.; Ghezzi, M.; Ridolfi, G., Threshold resummation in SCET vs. perturbative QCD: an analytic comparison, Nucl. Phys., B 861, 337, (2012) · Zbl 1246.81423
[46] Sterman, G.; Zeng, M., Quantifying comparisons of threshold resummations, JHEP, 05, 132, (2014)
[47] M. Bonvini, S. Forte, G. Ridolfi and L. Rottoli, Resummation prescriptions and ambiguities in SCET vs. direct QCD: Higgs production as a case study, JHEP01 (2015) 046 [arXiv:1409.0864] [INSPIRE].
[48] Sjöstrand, T., A model for initial state parton showers, Phys. Lett., B 157, 321, (1985)
[49] Marchesini, G.; Webber, BR, Simulation of QCD jets including soft gluon interference, Nucl. Phys., B 238, 1, (1984)
[50] Gustafson, G., Dual description of a confined color field, Phys. Lett., B 175, 453, (1986)
[51] R.K. Ellis, G. Marchesini and B.R. Webber, Soft Radiation in Parton Parton Scattering, Nucl. Phys.B 286 (1987) 643 [Erratum ibid.B 294 (1987) 1180] [INSPIRE].
[52] Gustafson, G.; Pettersson, U., Dipole formulation of QCD cascades, Nucl. Phys., B 306, 746, (1988)
[53] G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, M.H. Seymour and L. Stanco, HERWIG: A Monte Carlo event generator for simulating hadron emission reactions with interfering gluons. Version 5.1 — April 1991, Comput. Phys. Commun.67 (1992) 465 [INSPIRE]. · Zbl 0875.65018
[54] Sjöstrand, T., High-energy physics event generation with PYTHIA 5.7 and JETSET 7.4, Comput. Phys. Commun., 82, 74, (1994)
[55] T. Gleisberg, S. Hoeche, F. Krauss, A. Schalicke, S. Schumann and J.-C. Winter, SHERPA 1. alpha: A proof of concept version, JHEP02 (2004) 056 [hep-ph/0311263] [INSPIRE].
[56] T. Sjöstrand and P.Z. Skands, Transverse-momentum-ordered showers and interleaved multiple interactions, Eur. Phys. J.C 39 (2005) 129 [hep-ph/0408302] [INSPIRE].
[57] Z. Nagy and D.E. Soper, A new parton shower algorithm: Shower evolution, matching at leading and next-to-leading order level, in New trends in HERA physics: Proceedings of the Ringberg Workshop, Tegernsee, Germany, 2-7 October 2005, G. Grindhammer et al. eds., World Scientific, Hackensack, U.S.A. (2006), hep-ph/0601021 [INSPIRE].
[58] Dinsdale, M.; Ternick, M.; Weinzierl, S., Parton showers from the dipole formalism, Phys. Rev., D 76, 094003, (2007)
[59] Schumann, S.; Krauss, F., A parton shower algorithm based on catani-seymour dipole factorisation, JHEP, 03, 038, (2008)
[60] Bahr, M.; etal., HERWIG++ physics and manual, Eur. Phys. J., C 58, 639, (2008)
[61] T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP02 (2009) 007 [arXiv:0811.4622] [INSPIRE].
[62] Platzer, S.; Gieseke, S., Coherent parton showers with local recoils, JHEP, 01, 024, (2011) · Zbl 1214.81306
[63] Platzer, S.; Gieseke, S., Dipole showers and automated NLO matching in HERWIG++, Eur. Phys. J., C 72, 2187, (2012)
[64] Stichel, PC; Zakrzewski, WJ, General relativistic, nonstandard model for the dark sector of the universe, Eur. Phys. J., C 75, 9, (2015) · Zbl 1251.83072
[65] T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun.191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
[66] Nagy, Z.; Soper, DE, On the transverse momentum in Z-boson production in a virtuality ordered parton shower, JHEP, 03, 097, (2010) · Zbl 1271.81180
[67] Nagy, Z.; Soper, DE, Parton showers with quantum interference, JHEP, 09, 114, (2007)
[68] Nagy, Z.; Soper, DE, Parton showers with quantum interference: leading color, spin averaged, JHEP, 03, 030, (2008)
[69] Nagy, Z.; Soper, DE, Parton showers with quantum interference: leading color, with spin, JHEP, 07, 025, (2008)
[70] Nagy, Z.; Soper, DE, Parton shower evolution with subleading color, JHEP, 06, 044, (2012)
[71] Nagy, Z.; Soper, DE, A parton shower based on factorization of the quantum density matrix, JHEP, 06, 097, (2014)
[72] Nagy, Z.; Soper, DE, Ordering variable for parton showers, JHEP, 06, 178, (2014)
[73] Nagy, Z.; Soper, DE, Parton distribution functions in the context of parton showers, JHEP, 06, 179, (2014)
[74] Nagy, Z.; Soper, DE, Effects of subleading color in a parton shower, JHEP, 07, 119, (2015)
[75] Collins, JC; Soper, DE, Parton distribution and decay functions, Nucl. Phys., B 194, 445, (1982)
[76] Dulat, S.; etal., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev., D 93, 033006, (2016)
[77] J.M. Campbell and R.K. Ellis, Radiative corrections to\( Zb\overline{b} \)production, Phys. Rev.D 62 (2000) 114012 [hep-ph/0006304] [INSPIRE].
[78] Collins, JC; Soper, DE; Sterman, GF, Transverse momentum distribution in Drell-Yan pair and W and Z boson production, Nucl. Phys., B 250, 199, (1985)
[79] G.A. Ladinsky and C.P. Yuan, The Nonperturbative regime in QCD resummation for gauge boson production at hadron colliders, Phys. Rev.D 50 (1994) R4239 [hep-ph/9311341] [INSPIRE].
[80] F. Landry, R. Brock, P.M. Nadolsky and C.P. Yuan, Tevatron Run-1 Z boson data and Collins-Soper-Sterman resummation formalism, Phys. Rev.D 67 (2003) 073016 [hep-ph/0212159] [INSPIRE].
[81] Cacciari, M.; Salam, GP; Soyez, G., The anti-k_{t} jet clustering algorithm, JHEP, 04, 063, (2008) · Zbl 1369.81100
[82] Cacciari, M.; Salam, GP; Soyez, G., Fastjet user manual, Eur. Phys. J., C 72, 1896, (2012) · Zbl 1393.81007
[83] Ellis, SD; Kunszt, Z.; Soper, DE, The one jet inclusive cross-section at order \(α\)_{\(s\)}\^{3} quarks and gluons, Phys. Rev. Lett., 64, 2121, (1990)
[84] J.R. Forshaw, A. Kyrieleis and M.H. Seymour, Gaps between jets in the high energy limit, JHEP06 (2005) 034 [hep-ph/0502086] [INSPIRE].
[85] M. Krämer and D.E. Soper, Next-to-leading order numerical calculations in Coulomb gauge, Phys. Rev.D 66 (2002) 054017 [hep-ph/0204113] [INSPIRE]. · Zbl 1045.81560
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