×

Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours. (English) Zbl 1294.81270

Summary: The antenna subtraction formalism allows to calculate QCD corrections to jet observables. Within this formalism, the subtraction terms are constructed using antenna functions describing all unresolved radiation between a pair of hard radiator partons. In this paper, we focus on the subtraction terms for double real radiation contributions to jet observables in hadron-hadron collisions evaluated at NNLO. An essential ingredient to these subtraction terms are the four-parton antenna functions with both radiators in the initial state. We outline the construction of the double real subtraction terms, classify all relevant antenna functions and describe their integration over the relevant antenna phase space. For the initial-initial antenna functions with two quark flavours, we derive the phase space master integrals and obtain the integrated antennae.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81V35 Nuclear physics
81U05 \(2\)-body potential quantum scattering theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys.3 (1962) 650 [SPIRES]. · Zbl 0118.44501 · doi:10.1063/1.1724268
[2] T.D. Lee and M. Nauenberg, Degenerate Systems And Mass Singularities, Phys. Rev.B 133 (1964) 1549 [SPIRES]. · doi:10.1103/PhysRev.133.B1549
[3] S. Catani and M.H. Seymour, A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys.B 485 (1997) 291 [hep-ph/9605323] [SPIRES]. · doi:10.1016/S0550-3213(96)00589-5
[4] S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys.B 467 (1996) 399 [hep-ph/9512328] [SPIRES]. · doi:10.1016/0550-3213(96)00110-1
[5] Z. Nagy and Z. Trócsányi, Calculation of QCD jet cross sections at next-to-leading order, Nucl. Phys.B 486 (1997) 189 [hep-ph/9610498] [SPIRES]. · doi:10.1016/S0550-3213(96)00657-8
[6] S. Frixione, A General approach to jet cross-sections in QCD, Nucl. Phys.B 507 (1997) 295 [hep-ph/9706545] [SPIRES]. · doi:10.1016/S0550-3213(97)00574-9
[7] G. Somogyi and Z. Trócsányi, A new subtraction scheme for computing QCD jet cross sections at next-to-leading order accuracy, hep-ph/0609041 [SPIRES]. · Zbl 1214.81293
[8] R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: the FKS subtraction, JHEP10 (2009) 003 [arXiv:0908.4272] [SPIRES]. · doi:10.1088/1126-6708/2009/10/003
[9] T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J.C 53 (2008) 501 [arXiv:0709.2881] [SPIRES]. · doi:10.1140/epjc/s10052-007-0495-0
[10] M.H. Seymour and C. Tevlin, TeVJet: A general framework for the calculation of jet observables in NLO QCD, arXiv:0803.2231 [SPIRES].
[11] K. Hasegawa, S. Moch and P. Uwer, Automating dipole subtraction, Nucl. Phys. Proc. Suppl.183 (2008) 268 [arXiv:0807.3701] [SPIRES]. · doi:10.1016/j.nuclphysbps.2008.09.115
[12] K. Hasegawa, S. Moch and P. Uwer, AutoDipole — Automated generation of dipole subtraction terms -, Comput. Phys. Commun.181 (2010) 1802 [arXiv:0911.4371] [SPIRES]. · Zbl 1219.81244 · doi:10.1016/j.cpc.2010.06.044
[13] R. Frederix, T. Gehrmann and N. Greiner, Automation of the Dipole Subtraction Method in MadGraph/MadEvent, JHEP09 (2008) 122 [arXiv:0808.2128] [SPIRES]. · doi:10.1088/1126-6708/2008/09/122
[14] M. Czakon, C.G. Papadopoulos and M. Worek, Polarizing the Dipoles, JHEP08 (2009) 085 [arXiv:0905.0883] [SPIRES]. · doi:10.1088/1126-6708/2009/08/085
[15] C.F. Berger et al., An Automated Implementation of On-Shell Methods for One-Loop Amplitudes, Phys. Rev.D 78 (2008) 036003 [arXiv:0803.4180] [SPIRES].
[16] W.T. Giele and G. Zanderighi, On the Numerical Evaluation of One-Loop Amplitudes: The Gluonic Case, JHEP06 (2008) 038 [arXiv:0805.2152] [SPIRES]. · doi:10.1088/1126-6708/2008/06/038
[17] G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes, JHEP03 (2008) 042 [arXiv:0711.3596] [SPIRES]. · doi:10.1088/1126-6708/2008/03/042
[18] T. Binoth, J.P. Guillet, G. Heinrich, E. Pilon and T. Reiter, Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs, Comput. Phys. Commun.180 (2009) 2317 [arXiv:0810.0992] [SPIRES]. · Zbl 1197.81004 · doi:10.1016/j.cpc.2009.06.024
[19] J.M. Campbell and R.K. Ellis, An update on vector boson pair production at hadron colliders, Phys. Rev.D 60 (1999) 113006 [hep-ph/9905386] [SPIRES].
[20] J.M. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2 jet and Z + 2 jet production at hadron colliders, Phys. Rev.D 65 (2002) 113007 [hep-ph/0202176] [SPIRES].
[21] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna Subtraction at NNLO, JHEP09 (2005) 056 [hep-ph/0505111] [SPIRES]. · doi:10.1088/1126-6708/2005/09/056
[22] S. Weinzierl, Subtraction terms at NNLO, JHEP03 (2003) 062 [hep-ph/0302180] [SPIRES]. · doi:10.1088/1126-6708/2003/03/062
[23] S. Frixione and M. Grazzini, Subtraction at NNLO, JHEP06 (2005) 010 [hep-ph/0411399] [SPIRES]. · doi:10.1088/1126-6708/2005/06/010
[24] G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP06 (2005) 024 [hep-ph/0502226] [SPIRES]. · doi:10.1088/1126-6708/2005/06/024
[25] G. Somogyi, Z. Trócsányi and V. Del Duca, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions, JHEP01 (2007) 070 [hep-ph/0609042] [SPIRES]. · doi:10.1088/1126-6708/2007/01/070
[26] G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission, JHEP01 (2007) 052 [hep-ph/0609043] [SPIRES]. · doi:10.1088/1126-6708/2007/01/052
[27] G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms I, JHEP08 (2008) 042 [arXiv:0807.0509] [SPIRES]. · doi:10.1088/1126-6708/2008/08/042
[28] U. Aglietti, V. Del Duca, C. Duhr, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections I, JHEP09 (2008) 107 [arXiv:0807.0514] [SPIRES]. · doi:10.1088/1126-6708/2008/09/107
[29] G. Somogyi, Subtraction with hadronic initial states: an NNLO- compatible scheme, JHEP05 (2009) 016 [arXiv:0903.1218] [SPIRES]. · doi:10.1088/1126-6708/2009/05/016
[30] P. Bolzoni, S.-O. Moch, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections II, JHEP08 (2009) 079 [arXiv:0905.4390] [SPIRES]. · doi:10.1088/1126-6708/2009/08/079
[31] M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett.B 693 (2010) 259 [arXiv:1005.0274] [SPIRES].
[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] [SPIRES]. · doi:10.1103/PhysRevLett.98.222002
[33] M. Grazzini, NNLO predictions for the Higgs boson signal in the H → WW → lνlν and H → ZZ → 4l decay channels, JHEP02 (2008) 043 [arXiv:0801.3232] [SPIRES]. · doi:10.1088/1126-6708/2008/02/043
[34] S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett.103 (2009) 082001 [arXiv:0903.2120] [SPIRES]. · doi:10.1103/PhysRevLett.103.082001
[35] S. Catani, G. Ferrera and M. Grazzini, W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD, JHEP05 (2010) 006 [arXiv:1002.3115] [SPIRES]. · doi:10.1007/JHEP05(2010)006
[36] T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multi-loop integrals, Nucl. Phys.B 585 (2000) 741 [hep-ph/0004013] [SPIRES]. · Zbl 1042.81565 · doi:10.1016/S0550-3213(00)00429-6
[37] T. Binoth and G. Heinrich, Numerical evaluation of multi-loop integrals by sector decomposition, Nucl. Phys.B 680 (2004) 375 [hep-ph/0305234] [SPIRES]. · Zbl 1043.81630 · doi:10.1016/j.nuclphysb.2003.12.023
[38] G. Heinrich, Sector Decomposition, Int. J. Mod. Phys.A 23 (2008) 1457 [arXiv:0803.4177] [SPIRES]. · Zbl 1153.81522
[39] G. Heinrich, A numerical method for NNLO calculations, Nucl. Phys. Proc. Suppl.116 (2003) 368 [hep-ph/0211144] [SPIRES]. · Zbl 1037.81585 · doi:10.1016/S0920-5632(03)80201-3
[40] C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev.D 69 (2004) 076010 [hep-ph/0311311] [SPIRES].
[41] T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys.B 693 (2004) 134 [hep-ph/0402265] [SPIRES]. · Zbl 1151.81352 · doi:10.1016/j.nuclphysb.2004.06.005
[42] G. Heinrich, The sector decomposition approach to real radiation at NNLO, Nucl. Phys. Proc. Suppl.157 (2006) 43 [hep-ph/0601232] [SPIRES]. · doi:10.1016/j.nuclphysbps.2006.03.034
[43] C. Anastasiou, K. Melnikov and F. Petriello, Real radiation at NNLO: e+e− → 2 jets through O(αs2), Phys. Rev. Lett.93 (2004) 032002 [hep-ph/0402280] [SPIRES]. · doi:10.1103/PhysRevLett.93.032002
[44] C. Anastasiou, K. Melnikov and F. Petriello, Higgs boson production at hadron colliders: Differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett.93 (2004) 262002 [hep-ph/0409088] [SPIRES]. · doi:10.1103/PhysRevLett.93.262002
[45] C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys.B 724 (2005) 197 [hep-ph/0501130] [SPIRES]. · doi:10.1016/j.nuclphysb.2005.06.036
[46] K. Melnikov and F. Petriello, The W boson production cross section at the LHC through O(αs2), Phys. Rev. Lett.96 (2006) 231803 [hep-ph/0603182] [SPIRES]. · doi:10.1103/PhysRevLett.96.231803
[47] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Infrared structure of e+e− → 3 jets at NNLO, JHEP11 (2007) 058 [arXiv:0710.0346] [SPIRES]. · doi:10.1088/1126-6708/2007/11/058
[48] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Jet rates in electron-positron annihilation at O(αs3) in QCD, Phys. Rev. Lett.100 (2008) 172001 [arXiv:0802.0813] [SPIRES]. · doi:10.1103/PhysRevLett.100.172001
[49] S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett.101 (2008) 162001 [arXiv:0807.3241] [SPIRES]. · doi:10.1103/PhysRevLett.101.162001
[50] S. Weinzierl, The infrared structure of e+e− → 3 jets at NNLO reloaded, JHEP07 (2009) 009 [arXiv:0904.1145] [SPIRES]. · doi:10.1088/1126-6708/2009/07/009
[51] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett.99 (2007) 132002 [arXiv:0707.1285] [SPIRES]. · doi:10.1103/PhysRevLett.99.132002
[52] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO corrections to event shapes in e+e−annihilation, JHEP12 (2007) 094 [arXiv:0711.4711] [SPIRES]. · doi:10.1088/1126-6708/2007/12/094
[53] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO moments of event shapes in e+e−annihilation, JHEP05 (2009) 106 [arXiv:0903.4658] [SPIRES]. · doi:10.1088/1126-6708/2009/05/106
[54] S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP06 (2009) 041 [arXiv:0904.1077] [SPIRES]. · doi:10.1088/1126-6708/2009/06/041
[55] S. Weinzierl, Moments of event shapes in electron-positron annihilation at NNLO, Phys. Rev.D 80 (2009) 094018 [arXiv:0909.5056] [SPIRES].
[56] G. Dissertori et al., First determination of the strong coupling constant using NNLO predictions for hadronic event shapes in e+e−annihilations, JHEP02 (2008) 040 [arXiv:0712.0327] [SPIRES]. · doi:10.1088/1126-6708/2008/02/040
[57] G. Dissertori et al., Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e−annihilations, JHEP08 (2009) 036 [arXiv:0906.3436] [SPIRES]. · doi:10.1088/1126-6708/2009/08/036
[58] G. Dissertori et al., Precise determination of the strong coupling constant at NNLO in QCD from the three-jet rate in electron-positron annihilation at LEP, Phys. Rev. Lett.104 (2010) 072002 [arXiv:0910.4283] [SPIRES]. · doi:10.1103/PhysRevLett.104.072002
[59] JADE collaboration, S. Bethke, S. Kluth, C. Pahl and J. Schieck, Determination of the Strong Coupling αsfrom hadronic Event Shapes with O(alphas3) and resummed QCD predictions using JADE Data, Eur. Phys. J.C 64 (2009) 351 [arXiv:0810.1389] [SPIRES]. · doi:10.1140/epjc/s10052-009-1149-1
[60] T. Gehrmann, M. Jaquier and G. Luisoni, Hadronization effects in event shape moments, Eur. Phys. J.C 67 (2010) 57 [arXiv:0911.2422] [SPIRES]. · doi:10.1140/epjc/s10052-010-1288-4
[61] A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP04 (2007) 016 [hep-ph/0612257] [SPIRES]. · doi:10.1088/1126-6708/2007/04/016
[62] 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] [SPIRES]. · Zbl 1269.81194 · doi:10.1007/JHEP01(2010)118
[63] R. Boughezal, A. G.-D. Ridder and M. Ritzmann, NNLO antenna subtraction with two hadronic initial states, PoS(RADCOR2009)052 [arXiv:1001.2396] [SPIRES]. · Zbl 1294.81270
[64] E.W. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP06 (2010) 096 [arXiv:1003.2824] [SPIRES]. · Zbl 1288.81147 · doi:10.1007/JHEP06(2010)096
[65] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Infrared Structure of e+e− → 2 jets at NNLO, Nucl. Phys. B 691 (2004) 195 [hep-ph/0403057] [SPIRES]. · doi:10.1016/j.nuclphysb.2004.05.017
[66] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, quark-gluon Antenna Functions from Neutralino Decay, Phys. Lett.B 612 (2005) 36 [hep-ph/0501291] [SPIRES].
[67] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Gluon-Gluon Antenna Functions from Higgs Boson Decay, Phys. Lett.B 612 (2005) 49 [hep-ph/0502110] [SPIRES].
[68] D. de Florian and M. Grazzini, The structure of large logarithmic corrections at small transverse momentum in hadronic collisions, Nucl. Phys.B 616 (2001) 247 [hep-ph/0108273] [SPIRES]. · doi:10.1016/S0550-3213(01)00460-6
[69] C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys.B 646 (2002) 220 [hep-ph/0207004] [SPIRES]. · doi:10.1016/S0550-3213(02)00837-4
[70] C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev.D 69 (2004) 094008 [hep-ph/0312266] [SPIRES].
[71] C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD, Phys. Rev. Lett.91 (2003) 182002 [hep-ph/0306192] [SPIRES]. · doi:10.1103/PhysRevLett.91.182002
[72] F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett.B 100 (1981) 65 [SPIRES].
[73] K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys.B 192 (1981) 159 [SPIRES]. · doi:10.1016/0550-3213(81)90199-1
[74] T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions, Nucl. Phys.B 580 (2000) 485 [hep-ph/9912329] [SPIRES]. · Zbl 1071.81089 · doi:10.1016/S0550-3213(00)00223-6
[75] S. Laporta, High-precision calculation of multi-loop Feynman integrals by difference equations, Int. J. Mod. Phys.A 15 (2000) 5087 [hep-ph/0102033] [SPIRES]. · Zbl 0973.81082
[76] A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP10 (2008) 107 [arXiv:0807.3243] [SPIRES]. · Zbl 1245.81033 · doi:10.1088/1126-6708/2008/10/107
[77] A.V. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation, Phys. Lett.B 254 (1991) 158 [SPIRES].
[78] A.V. Kotikov, Differential equations method: The Calculation of vertex type Feynman diagrams, Phys. Lett.B 259 (1991) 314 [SPIRES].
[79] A.V. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams, Phys. Lett.B 267 (1991) 123 [SPIRES].
[80] E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim.A 110 (1997) 1435 [hep-th/9711188] [SPIRES].
[81] M. Caffo, H. Czyz, S. Laporta and E. Remiddi, Master equations for master amplitudes, Acta Phys. Polon.B 29 (1998) 2627 [hep-th/9807119] [SPIRES].
[82] M. Caffo, H. Czyz, S. Laporta and E. Remiddi, The master differential equations for the 2-loop sunrise selfmass amplitudes, Nuovo Cim.A 111 (1998) 365 [hep-th/9805118] [SPIRES].
[83] 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] [SPIRES]. · doi:10.1016/S0550-3213(01)00057-8
[84] T. Gehrmann and E. Remiddi, Numerical evaluation of two-dimensional harmonic polylogarithms, Comput. Phys. Commun.144 (2002) 200 [hep-ph/0111255] [SPIRES]. · Zbl 1001.65020 · doi:10.1016/S0010-4655(02)00139-X
[85] E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys.A 15 (2000) 725 [hep-ph/9905237] [SPIRES]. · Zbl 0951.33003
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.