zbMATH — the first resource for mathematics

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.
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.