×

zbMATH — the first resource for mathematics

The real radiation antenna function for \( S \to Q\bar{Q}q\bar{q} \) at NNLO QCD. (English) Zbl 1298.81368
Summary: As a first step towards the application of the antenna subtraction formalism to NNLO QCD reactions with massive quarks, we determine the real radiation antenna function and its integrated counterpart for reactions of the type \( S \to Q\bar{Q}q\bar{q} \), where \(S\) denotes an uncolored initial state and \(Q\), \(q\) a massive and massless quark, respectively. We compute the corresponding integrated antenna function in terms of harmonic polylogarithms. As an application and check of our results we calculate the contribution proportional to \(\alpha_{s}^{2}e_{Q}^{2}N_{f}\) to the inclusive heavy-quark pair production cross section in \(e^{+}e^{-}\) annihilation.
MSC:
81V05 Strong interaction, including quantum chromodynamics
81U35 Inelastic and multichannel quantum scattering
11G55 Polylogarithms and relations with \(K\)-theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Catani, S.; Seymour, MH, A general algorithm for calculating jet cross sections in NLO QCD, Nucl. Phys., B 485, 291, (1997)
[2] Catani, S.; Dittmaier, S.; Trocsanyi, Z., One loop singular behavior of QCD and SUSY QCD amplitudes with massive partons, Phys. Lett., B 500, 149, (2001)
[3] Phaf, L.; Weinzierl, S., Dipole formalism with heavy fermions, JHEP, 04, 006, (2001)
[4] Catani, S.; Dittmaier, S.; Seymour, MH; Trocsanyi, Z., The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys., B 627, 189, (2002)
[5] Nagy, Z.; Trócsányi, Z., Next-to-leading order calculation of four-jet observables in electron positron annihilation, Phys. Rev., D 59, 014020, (1999)
[6] Campbell, JM; Ellis, RK; Tramontano, F., Single top production and decay at next-to-leading order, Phys. Rev., D 70, 094012, (2004)
[7] Czakon, M.; Papadopoulos, CG; Worek, M., Polarizing the dipoles, JHEP, 08, 085, (2009)
[8] Bevilacqua, G.; Czakon, M.; Papadopoulos, CG; Pittau, R.; Worek, M., Assault on the NLO wishlist: pp → ttbb, JHEP, 09, 109, (2009)
[9] Frederix, R.; Gehrmann, T.; Greiner, N., Integrated dipoles with maddipole in the madgraph framework, JHEP, 06, 086, (2010)
[10] Gleisberg, T.; Krauss, F., Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J., C 53, 501, (2008)
[11] M.H. Seymour and C. Tevlin, TeVJet: a general framework for the calculation of jet observables in NLO QCD, arXiv:0803.2231 [SPIRES].
[12] Hasegawa, K.; Moch, S.; Uwer, P., Autodipole — automated generation of dipole subtraction terms, Comput. Phys. Commun., 181, 1802, (2010)
[13] Frixione, S.; Kunszt, Z.; Signer, A., Three jet cross-sections to next-to-leading order, Nucl. Phys., B 467, 399, (1996)
[14] Nagy, Z.; Trócsányi, Z., Calculation of QCD jet cross sections at next-to-leading order, Nucl. Phys., B 486, 189, (1997)
[15] Frixione, S., A general approach to jet cross-sections in QCD, Nucl. Phys., B 507, 295, (1997)
[16] C.-H. Chung, M. Krämer and T. Robens, An alternative subtraction scheme for next-to-leading order QCD calculations, arXiv:1012.4948 [SPIRES].
[17] Campbell, JM; Glover, EWN, Double unresolved approximations to multiparton scattering amplitudes, Nucl. Phys., B 527, 264, (1998)
[18] Catani, S., The singular behaviour of QCD amplitudes at two-loop order, Phys. Lett., B 427, 161, (1998)
[19] Catani, S.; Grazzini, M., Collinear factorization and splitting functions for next-to-next-to-leading order QCD calculations, Phys. Lett., B 446, 143, (1999)
[20] Catani, S.; Grazzini, M., Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond, Nucl. Phys., B 570, 287, (2000)
[21] Catani, S.; Grazzini, M., The soft-gluon current at one-loop order, Nucl. Phys., B 591, 435, (2000)
[22] Bern, Z.; Duca, V.; Schmidt, CR, The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order, Phys. Lett., B 445, 168, (1998)
[23] Bern, Z.; Duca, V.; Kilgore, WB; Schmidt, CR, The infrared behavior of one-loop QCD amplitudes at next-to-next-to-leading order, Phys. Rev., D 60, 116001, (1999)
[24] Kosower, DA, Multiple singular emission in gauge theories, Phys. Rev., D 67, 116003, (2003)
[25] Heinrich, G., A numerical method for NNLO calculations, Nucl. Phys. Proc. Suppl., 116, 368, (2003)
[26] Binoth, T.; Heinrich, G., Numerical evaluation of multi-loop integrals by sector decomposition, Nucl. Phys., B 680, 375, (2004)
[27] Binoth, T.; Heinrich, G., Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys., B 693, 134, (2004)
[28] Anastasiou, C.; Melnikov, K.; Petriello, F., A new method for real radiation at NNLO, Phys. Rev., D 69, 076010, (2004)
[29] Heinrich, G., The sector decomposition approach to real radiation at NNLO, Nucl. Phys. Proc. Suppl., 157, 43, (2006)
[30] Kosower, DA, Antenna factorization of gauge-theory amplitudes, Phys. Rev., D 57, 5410, (1998)
[31] Kosower, DA, Antenna factorization in strongly-ordered limits, Phys. Rev., D 71, 045016, (2005)
[32] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN, Antenna subtraction at NNLO, JHEP, 09, 056, (2005)
[33] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN, Quark-gluon antenna functions from neutralino decay, Phys. Lett., B 612, 36, (2005)
[34] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN, Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett., B 612, 49, (2005)
[35] Duhr, C.; Maltoni, F., Antenna functions from MHV rules, JHEP, 11, 002, (2008)
[36] Weinzierl, S., Subtraction terms at NNLO, JHEP, 03, 062, (2003)
[37] Weinzierl, S., Subtraction terms for one-loop amplitudes with one unresolved parton, JHEP, 07, 052, (2003)
[38] Frixione, S.; Grazzini, M., Subtraction at NNLO, JHEP, 06, 010, (2005)
[39] Somogyi, G.; Trócsányi, Z.; Duca, V., Matching of singly-and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP, 06, 024, (2005)
[40] Somogyi, G.; Trócsányi, Z., A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission, JHEP, 01, 052, (2007)
[41] Somogyi, G.; Trócsányi, Z.; Duca, V., A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions, JHEP, 01, 070, (2007)
[42] Somogyi, G.; Trócsányi, Z., A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms I, JHEP, 08, 042, (2008)
[43] Aglietti, U.; Duca, V.; Duhr, C.; Somogyi, G.; Trocsanyi, Z., Analytic integration of real-virtual counterterms in NNLO jet cross sections. I, JHEP, 09, 107, (2008)
[44] Bolzoni, P.; Moch, S-O; Somogyi, G.; Trocsanyi, Z., Analytic integration of real-virtual counterterms in NNLO jet cross sections. II, JHEP, 08, 079, (2009)
[45] Somogyi, G., Subtraction with hadronic initial states: an NNLO-compatible scheme, JHEP, 05, 016, (2009)
[46] Bolzoni, P.; Somogyi, G.; Trócsányi, Z., A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, JHEP, 01, 059, (2011)
[47] Catani, S.; Grazzini, M., An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett., 98, 222002, (2007)
[48] Czakon, M., A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett., B 693, 259, (2010)
[49] M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, arXiv:1101.0642 [SPIRES].
[50] Anastasiou, C.; Melnikov, K.; Petriello, F., Higgs boson production at hadron colliders: differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett., 93, 262002, (2004)
[51] Melnikov, K.; Petriello, F., The W boson production cross section at the LHC through \(O\)(\(α\)_{\(s\)}\^{}{2}), Phys. Rev. Lett., 96, 231803, (2006)
[52] Catani, S.; Cieri, L.; Ferrera, G.; Florian, D.; Grazzini, M., Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett., 103, 082001, (2009)
[53] Catani, S.; Ferrera, G.; Grazzini, M., W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD, JHEP, 05, 006, (2010)
[54] Anastasiou, C.; Melnikov, K.; Petriello, F., Real radiation at NNLO: \(e\)\^{}{+}\(e\)\^{}{−} → 2 jets through \(O\)(\(α\)_{\(s\)}\^{}{2}), Phys. Rev. Lett., 93, 032002, (2004)
[55] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN, Infrared structure of \(e\)\^{}{+}\(e\)\^{}{−} → 2 jets at NNLO, Nucl. Phys., B 691, 195, (2004)
[56] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN; Heinrich, G., Infrared structure of \(e\)\^{}{+}\(e\)\^{}{−} → 3 jets at NNLO, JHEP, 11, 058, (2007)
[57] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN; Heinrich, G., NNLO corrections to event shapes in \(e\)\^{}{+}\(e\)\^{}{−} annihilation, JHEP, 12, 094, (2007)
[58] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN; Heinrich, G., Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett., 99, 132002, (2007)
[59] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN; Heinrich, G., Jet rates in electron-positron annihilation at \(O\)(\(α\)_{\(s\)}\^{}{3}) in QCD, Phys. Rev. Lett., 100, 172001, (2008)
[60] Weinzierl, S., NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett., 101, 162001, (2008)
[61] Weinzierl, S., The infrared structure of \(e\)\^{}{+}\(e\)\^{}{−} → 3 jets at NNLO reloaded, JHEP, 07, 009, (2009)
[62] Daleo, A.; Gehrmann, T.; Maître, D., Antenna subtraction with hadronic initial states, JHEP, 04, 016, (2007)
[63] Daleo, A.; Gehrmann-De Ridder, A.; Gehrmann, T.; Luisoni, G., Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP, 01, 118, (2010)
[64] Nigel Glover, EW; Pires, J., Antenna subtraction for gluon scattering at NNLO, JHEP, 06, 096, (2010)
[65] Boughezal, R.; Gehrmann-De Ridder, A.; Ritzmann, M., Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP, 02, 098, (2011)
[66] Gehrmann-De Ridder, A.; Ritzmann, M., NLO antenna subtraction with massive fermions, JHEP, 07, 041, (2009)
[67] Abelof, G.; Gehrmann-De Ridder, A., Antenna subtraction for the production of heavy particles at hadron colliders, JHEP, 04, 063, (2011)
[68] Bernreuther, W.; etal., Two-loop QCD corrections to the heavy quark form factors: the vector contributions, Nucl. Phys., B 706, 245, (2005)
[69] Gluza, J.; Mitov, A.; Moch, S.; Riemann, T., The QCD form factor of heavy quarks at NNLO, JHEP, 07, 001, (2009)
[70] Bernreuther, W.; etal., Two-loop QCD corrections to the heavy quark form factors: axial vector contributions, Nucl. Phys., B 712, 229, (2005)
[71] Bernreuther, W.; etal., Two-loop QCD corrections to the heavy quark form factors: anomaly contributions, Nucl. Phys., B 723, 91, (2005)
[72] Bernreuther, W.; etal., Decays of scalar and pseudoscalar Higgs bosons into fermions: two-loop QCD corrections to the Higgs-quark-antiquark amplitude, Phys. Rev., D 72, 096002, (2005)
[73] Brandenburg, A.; Uwer, P., Next-to-leading order QCD corrections and massive quarks in \(e\)\^{}{+}\(e\)\^{}{−} → 3 jets, Nucl. Phys., B 515, 279, (1998)
[74] Nason, P.; Oleari, C., Next-to-leading-order corrections to the production of heavy-flavour jets in \(e\)\^{}{+}\(e\)\^{}{−} collisions, Nucl. Phys., B 521, 237, (1998)
[75] Rodrigo, G.; Bilenky, MS; Santamaria, A., Quark-mass effects for jet production in \(e\)\^{}{+}\(e\)\^{}{−} collisions at the next-to-leading order: results and applications, Nucl. Phys., B 554, 257, (1999)
[76] Wetzel, W.; Bernreuther, W., The effect of massive quarks on the electromagnetic vacuum polarization by massless quarks, Phys. Rev., D 24, 2724, (1981)
[77] Chetyrkin, KG; Tkachov, FV, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys., B 192, 159, (1981)
[78] Anastasiou, C.; Melnikov, K., Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys., B 646, 220, (2002)
[79] Gehrmann-De Ridder, A.; Gehrmann, T.; Heinrich, G., Four-particle phase space integrals in massless QCD, Nucl. Phys., B 682, 265, (2004)
[80] Cutkosky, RE, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys., 1, 429, (1960)
[81] Anastasiou, C.; Lazopoulos, A., Automatic integral reduction for higher order perturbative calculations, JHEP, 07, 046, (2004)
[82] Laporta, S., High-precision calculation of multi-loop Feynman integrals by difference equations, Int. J. Mod. Phys., A 15, 5087, (2000)
[83] Smirnov, AV, Algorithm FIRE — Feynman integral reduction, JHEP, 10, 107, (2008)
[84] A.P. Prudnikov, Y.A. Brychkov and O.I. Marichev, Integrals and series: more special functions, volume 3, Taylor and Francis Ltd., U.S.A. (1989).
[85] Huber, T.; Maître, D., Hypexp2, expanding hypergeometric functions about half-integer parameters, Comput. Phys. Commun., 178, 755, (2008)
[86] Remiddi, E.; Vermaseren, JAM, Harmonic polylogarithms, Int. J. Mod. Phys., A 15, 725, (2000)
[87] Gehrmann, T.; Remiddi, E., Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun., 141, 296, (2001)
[88] Kotikov, AV, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett., B 254, 158, (1991)
[89] Remiddi, E., Differential equations for Feynman graph amplitudes, Nuovo Cim., A 110, 1435, (1997)
[90] Gehrmann, T.; Remiddi, E., Differential equations for two-loop four-point functions, Nucl. Phys., B 580, 485, (2000)
[91] Argeri, M.; Mastrolia, P., Feynman diagrams and differential equations, Int. J. Mod. Phys., A 22, 4375, (2007)
[92] Maître, D., HPL, a Mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun., 174, 222, (2006)
[93] Lepage, GP, A new algorithm for adaptive multidimensional integration, J. Comput. Phys., 27, 192, (1978)
[94] Hoang, AH; Kuhn, JH; Teubner, T., Radiation of light fermions in heavy fermion production, Nucl. Phys., B 452, 173, (1995)
[95] Binosi, D.; Theussl, L., Jaxodraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun., 161, 76, (2004)
[96] Vermaseren, JAM, Axodraw, Comput. Phys. Commun., 83, 45, (1994)
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.