Gehrmann, Thomas; Tancredi, Lorenzo Two-loop QCD helicity amplitudes for \(q\overline{q} \to W^{{\pm}}{\gamma}\) and \(q\overline{q} \to Z^{0}{\gamma}\). (English) Zbl 1309.81273 J. High Energy Phys. 2012, No. 2, Paper No. 004, 37 p. (2012). Summary: The self-couplings of the electroweak gauge bosons are probed at hadron colliders through the production of a massive gauge boson and a photon. To extend the theoretical description of this type of final states towards next-to-next-to-leading order (NNLO) in QCD, we derive the two-loop QCD corrections to the helicity amplitudes describing the production of a massive gauge boson in association with a real photon. Our results are obtained by applying projectors to the general parton-level tensor structure. The leptonic decay of the vector boson is included, thus allowing for a fully exclusive description of the final state. The infrared poles of the amplitudes are described by an infrared factorization formula. We provide an analytic expression for the finite remainder of the amplitude in terms of one- and two-dimensional harmonic polylogarithms. The amplitudes are expressed in the physical kinematics relevant to gauge-boson-plus-photon production at hadron colliders. As a by-product, we also derive the two-loop QCD amplitudes for vector-boson-plus-jet production at hadron colliders. Cited in 4 Documents MSC: 81V05 Strong interaction, including quantum chromodynamics 81V22 Unified quantum theories 81V35 Nuclear physics 81U35 Inelastic and multichannel quantum scattering 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 81T18 Feynman diagrams Keywords:hadronic colliders; QCD Software:HPL; SecDec; FORM; Reduze; CHAPLIN PDFBibTeX XMLCite \textit{T. Gehrmann} and \textit{L. Tancredi}, J. High Energy Phys. 2012, No. 2, Paper No. 004, 37 p. (2012; Zbl 1309.81273) Full Text: DOI arXiv References: [1] U. Baur and E.L. Berger, Probing the WW γ vertex at the Fermilab Tevatron collider, Phys. Rev.D 41 (1990) 1476 [INSPIRE]. [2] U. Baur and E.L. Berger, Probing the weak boson sector in Zγ production at hadron colliders, Phys. Rev.D 47 (1993) 4889 [INSPIRE]. [3] L.J. Dixon, Z. Kunszt and A. Signer, Vector boson pair production in hadronic collisions at order αs: lepton correlations and anomalous couplings, Phys. Rev.D 60 (1999) 114037 [hep-ph/9907305] [INSPIRE]. [4] D0 collaboration, V. Abazov et al., Measurement of the p −\( \overline p → W\) γ+X cross section at \(\sqrt{s} = 1.96\;TeV\) and WWγ anomalous coupling limits, Phys. Rev.D 71 (2005) 091108 [hep-ex/0503048] [INSPIRE]. [5] D0 collaboration, V. Abazov et al., Zγ production and limits on anomalous ZZγ and Zγγ couplings in \(p\overline p\) collisions at \(\sqrt{s} = 1.96\;TeV \), Phys. Lett.B 653 (2007) 378 [arXiv:0705.1550] [INSPIRE]. [6] D0 collaboration, V. Abazov et al., First study of the radiation-amplitude zero in W γ production and limits on anomalous WW γ couplings at \(\sqrt{s} = 1.96\;TeV \), Phys. Rev. Lett.100 (2008) 241805 [arXiv:0803.0030] [INSPIRE]. [7] D0 collaboration, V. Abazov et al., Measurement of the Zγ → \( \nu \overline \nu \gamma\) cross section and limits on anomalous ZZγ and Zγγ couplings in \(p\overline p\) collisions at \(\sqrt{s} = 1.96\;TeV \), Phys. Rev. Lett.102 (2009) 201802 [arXiv:0902.2157] [INSPIRE]. [8] CDF II collaboration, D. Acosta et al., Measurement of W γ and Zγ production in \(p\overline p\) collisions at \(\sqrt{s} = 1.96\;TeV \), Phys. Rev. Lett.94 (2005) 041803 [hep-ex/0410008] [INSPIRE]. [9] CDF collaboration, T. Aaltonen et al., Measurement of Zγ production in \(p\overline p\) collisions at \(\sqrt{s} = 1.96\;TeV \) , Phys. Rev.D 82 (2010) 031103 [arXiv:1004.1140] [INSPIRE]. [10] CMS collaboration, S. Chatrchyan et al., Measurement of W γ and Zγ production in pp collisions at \(\sqrt{s} = 7\;TeV \), Phys. Lett.B 701 (2011) 535 [arXiv:1105.2758] [INSPIRE]. [11] ATLAS collaboration, G. Aad et al., Measurement of W γ and Zγ production in proton-proton collisions at \(\sqrt{s} = 7\;TeV\) with the ATLAS Detector, JHEP09 (2011) 072 [arXiv:1106.1592] [INSPIRE]. [12] J. Ohnemus, Order αscalculations of hadronic W±γ and Zγ production, Phys. Rev.D 47 (1993) 940 [INSPIRE]. [13] U. Baur, T. Han and J. Ohnemus, QCD corrections to hadronic W γ production with nonstandard WW γ couplings, Phys. Rev.D 48 (1993) 5140 [hep-ph/9305314] [INSPIRE]. [14] U. Baur, T. Han and J. Ohnemus, QCD corrections and anomalous couplings in Zγ production at hadron colliders, Phys. Rev.D 57 (1998) 2823 [hep-ph/9710416] [INSPIRE]. [15] L.J. Dixon, Z. Kunszt and A. Signer, Helicity amplitudes for O(αs) production of W+W−, W±Z, ZZ, W±γ, or Zγ pairs at hadron colliders, Nucl. Phys.B 531 (1998) 3 [hep-ph/9803250] [INSPIRE]. [16] E. Accomando, A. Denner and C. Meier, Electroweak corrections to W γ and Zγ production at the LHC, Eur. Phys. J.C 47 (2006) 125 [hep-ph/0509234] [INSPIRE]. [17] V. Del Duca, F. Maltoni, Z. Nagy and Z. Trócsányi, QCD radiative corrections to prompt diphoton production in association with a jet at hadron colliders, JHEP04 (2003) 059 [hep-ph/0303012] [INSPIRE]. [18] F. Campanario, C. Englert, M. Spannowsky and D. Zeppenfeld, NLO-QCD corrections to Wγ j production, Europhys. Lett.88 (2009) 11001 [arXiv:0908.1638] [INSPIRE]. [19] F. Campanario, C. Englert and M. Spannowsky, Precise predictions for (non-standard) Wγ+jet production, Phys. Rev.D 83 (2011) 074009 [arXiv:1010.1291] [INSPIRE]. [20] S. Dittmaier, S. Kallweit and P. Uwer, NLO QCD corrections to WW+jet production at hadron colliders, Phys. Rev. Lett.100 (2008) 062003 [arXiv:0710.1577] [INSPIRE]. [21] S. Dittmaier, S. Kallweit and P. Uwer, NLO QCD corrections to pp/\( p\overline p \)→ WW+jet+X including leptonic W-boson decays, Nucl. Phys.B 826 (2010) 18 [arXiv:0908.4124] [INSPIRE]. · Zbl 1203.81174 [22] J.M. Campbell, R. Ellis and G. Zanderighi, Next-to-leading order predictions for WW+1 jet distributions at the LHC, JHEP12 (2007) 056 [arXiv:0710.1832] [INSPIRE]. [23] T. Binoth, T. Gleisberg, S. Karg, N. Kauer and G. Sanguinetti, NLO QCD corrections to ZZ+jet production at hadron colliders,Phys. Lett.B 683 (2010) 154 [arXiv:0911.3181] [INSPIRE]. [24] F. Campanario, C. Englert, S. Kallweit, M. Spannowsky and D. Zeppenfeld, NLO QCD corrections to W Z+jet production with leptonic decays, JHEP07 (2010) 076 [arXiv:1006.0390] [INSPIRE]. [25] T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys.B 585 (2000) 741 [hep-ph/0004013] [INSPIRE]. · Zbl 1042.81565 [26] T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys.B 693 (2004) 134 [hep-ph/0402265] [INSPIRE]. · Zbl 1151.81352 [27] C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev.D 69 (2004) 076010 [hep-ph/0311311] [INSPIRE]. [28] G. Heinrich, Sector decomposition, Int. J. Mod. Phys.A 23 (2008) 1457 [arXiv:0803.4177] [INSPIRE]. · Zbl 1153.81522 [29] J. Carter and G. Heinrich, SecDec: a general program for sector decomposition, Comput. Phys. Commun.182 (2011) 1566 [arXiv:1011.5493] [INSPIRE]. · Zbl 1262.81119 [30] C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, JHEP03 (2011) 038 [arXiv:1011.4867] [INSPIRE]. · Zbl 1301.81284 [31] C. Anastasiou, F. Herzog and A. Lazopoulos, The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD, arXiv:1110.2368 [INSPIRE]. · Zbl 1309.81257 [32] S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett.98 (2007) 222002 [hep-ph/0703012] [INSPIRE]. [33] A. Gehrmann-De Ridder, T. Gehrmann and E. Glover, Antenna subtraction at NNLO, JHEP09 (2005) 056 [hep-ph/0505111] [INSPIRE]. [34] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Infrared structure of e+e−→3 jets at NNLO, JHEP11 (2007) 058 [arXiv:0710.0346] [INSPIRE]. [35] A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP04 (2007) 016 [hep-ph/0612257] [INSPIRE]. [36] A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP01 (2010) 118 [arXiv:0912.0374] [INSPIRE]. · Zbl 1269.81194 [37] R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP02 (2011) 098 [arXiv:1011.6631] [INSPIRE]. · Zbl 1294.81270 [38] T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP12 (2011) 049 [arXiv:1107.4037] [INSPIRE]. · Zbl 1306.81339 [39] E. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP06 (2010) 096 [arXiv:1003.2824] [INSPIRE]. · Zbl 1288.81147 [40] S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, arXiv:1110.2375 [INSPIRE]. · Zbl 1284.81281 [41] C. Anastasiou, E. Glover and M. Tejeda-Yeomans, Two loop QED and QCD corrections to massless fermion boson scattering, Nucl. Phys.B 629 (2002) 255 [hep-ph/0201274] [INSPIRE]. [42] Z. Bern, A. De Freitas and L.J. Dixon, Two loop amplitudes for gluon fusion into two photons, JHEP09 (2001) 037 [hep-ph/0109078] [INSPIRE]. [43] G. Chachamis, M. Czakon and D. Eiras, W pair production at the LHC. I. Two-loop corrections in the high energy limit, JHEP12 (2008) 003 [arXiv:0802.4028] [INSPIRE]. [44] L. Garland, T. Gehrmann, E. Glover, A. Koukoutsakis and E. Remiddi, The two loop QCD matrix element for e+e−→3 jets, Nucl. Phys.B 627 (2002) 107 [hep-ph/0112081] [INSPIRE]. [45] L. Garland, T. Gehrmann, E. Glover, A. Koukoutsakis and E. Remiddi, Two loop QCD helicity amplitudes for e+e−→3 jets, Nucl. Phys.B 642 (2002) 227 [hep-ph/0206067] [INSPIRE]. [46] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett.99 (2007) 132002 [arXiv:0707.1285] [INSPIRE]. [47] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, NNLO corrections to event shapes in e+e−annihilation, JHEP12 (2007) 094 [arXiv:0711.4711] [INSPIRE]. [48] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Jet rates in electron-positron annihilation at \(O( \alpha_s^3 )\) in QCD, Phys. Rev. Lett.100 (2008) 172001 [arXiv:0802.0813] [INSPIRE]. [49] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, NNLO moments of event shapes in e+e−annihilation, JHEP05 (2009) 106 [arXiv:0903.4658] [INSPIRE]. [50] S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett.101 (2008) 162001 [arXiv:0807.3241] [INSPIRE]. [51] S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP06 (2009) 041 [arXiv:0904.1077] [INSPIRE]. [52] S. Weinzierl, The Infrared structure of e+e−→3 jets at NNLO reloaded, JHEP07 (2009) 009 [arXiv:0904.1145] [INSPIRE]. [53] S. Weinzierl, Moments of event shapes in electron-positron annihilation at NNLO, Phys. Rev.D 80 (2009) 094018 [arXiv:0909.5056] [INSPIRE]. [54] S. Weinzierl, Jet algorithms in electron-positron annihilation: Perturbative higher order predictions, Eur. Phys. J.C 71 (2011) 1565 [Erratum ibid.C 71 (2011) 1717] [arXiv:1011.6247] [INSPIRE]. [55] T. Gehrmann and E. Remiddi, Analytic continuation of massless two loop four point functions, Nucl. Phys.B 640 (2002) 379 [hep-ph/0207020] [INSPIRE]. · Zbl 0997.81070 [56] L.J. Dixon, Calculating scattering amplitudes efficiently, Proceedings of TASI’95: QCD & Beyond, Theoretical Advanced Study Institute, Boulder U.S.A. (1995), D. Soper eds., World Scientific, Singapore (1995), pg. 539 [hep-ph/9601359] [INSPIRE]. [57] P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys.105 (1993) 279 [INSPIRE]. · Zbl 0782.68091 [58] S. Moch, J. Vermaseren and A. Vogt, Three-loop results for quark and gluon form-factors, Phys. Lett.B 625 (2005) 245 [hep-ph/0508055] [INSPIRE]. [59] P. Baikov, K. Chetyrkin, A. Smirnov, V. Smirnov and M. Steinhauser, Quark and gluon form factors to three loops, Phys. Rev. Lett.102 (2009) 212002 [arXiv:0902.3519] [INSPIRE]. [60] R. Lee, A. Smirnov and V. Smirnov, Analytic results for massless three-loop form factors, JHEP04 (2010) 020 [arXiv:1001.2887] [INSPIRE]. · Zbl 1272.81196 [61] T. Gehrmann, E. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP06 (2010) 094 [arXiv:1004.3653] [INSPIRE]. · Zbl 1288.81146 [62] F. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett.B 100 (1981) 65 [INSPIRE]. [63] K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 Loops, Nucl. Phys.B 192 (1981) 159 [INSPIRE]. [64] S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys.A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE]. · Zbl 0973.81082 [65] C. Studerus, Reduze-Feynman integral reduction in C++, Comput. Phys. Commun.181 (2010) 1293 [arXiv:0912.2546] [INSPIRE]. · Zbl 1219.81133 [66] T. Gehrmann and E. Remiddi, Two loop master integrals for γ∗→3 jets: the planar topologies, Nucl. Phys.B 601 (2001) 248 [hep-ph/0008287] [INSPIRE]. [67] T. Gehrmann and E. Remiddi, Two loop master integrals for γ∗→3 jets: the nonplanar topologies, Nucl. Phys.B 601 (2001) 287 [hep-ph/0101124] [INSPIRE]. [68] T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys.B 580 (2000) 485 [hep-ph/9912329] [INSPIRE]. · Zbl 1071.81089 [69] E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys.A 15 (2000) 725 [hep-ph/9905237] [INSPIRE]. · Zbl 0951.33003 [70] T. Gehrmann and E. Remiddi, Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun.141 (2001) 296 [hep-ph/0107173] [INSPIRE]. · Zbl 0991.65022 [71] T. Gehrmann and E. Remiddi, Numerical evaluation of two-dimensional harmonic polylogarithms, Comput. Phys. Commun.144 (2002) 200 [hep-ph/0111255] [INSPIRE]. · Zbl 1001.65020 [72] J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun.167 (2005) 177 [hep-ph/0410259] [INSPIRE]. · Zbl 1196.65045 [73] D. Maître, HPL, a mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun.174 (2006) 222 [hep-ph/0507152] [INSPIRE]. · Zbl 1196.68330 [74] D. Maitre, Extension of HPL to complex arguments, Comput. Phys. Commun.183 (2012) 846 [hep-ph/0703052] [INSPIRE]. [75] S. Buehler and C. Duhr, CHAPLIN — Complex Harmonic Polylogarithms in Fortran, arXiv:1106.5739 [INSPIRE]. · Zbl 1360.33002 [76] J. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE]. [77] J.A.M. Vermaseren, The FORM project, Nucl. Phys. Proc. Suppl.183 (2008) 19 [arXiv:0806.4080] [INSPIRE]. [78] S. Catani, The Singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE]. [79] R. Ellis, D. Ross and A. Terrano, The perturbative calculation of jet structure in e+e−annihilation, Nucl. Phys.B 178 (1981) 421 [INSPIRE]. [80] W. Giele and E. Glover, Higher order corrections to jet cross-sections in e+e−annihilation, Phys. Rev.D 46 (1992) 1980 [INSPIRE]. 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.