×

zbMATH — the first resource for mathematics

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel. (English) Zbl 1214.81294
Summary: We evaluate the two-loop QCD diagrams contributing to the leading color coefficient of the heavy-quark pair production cross section in the gluon fusion channel. We obtain an analytic expression, which is valid for any value of the Mandelstam invariants \(s\) and \(t\) and of the heavy-quark mass \(m\). Our findings agree with previous analytic results in the small-mass limit and with recent results for the coefficients of the IR poles.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81U35 Inelastic and multichannel quantum scattering
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
Software:
FORM; GiNaC; HPL; Reduze; sunem
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] CDF and D0 collaboration, Combination of CDF and D0 results on the mass of the top quark, arXiv:1007.3178 [SPIRES].
[2] CDF collaboration; Aaltonen, T.; etal., Top quark mass measurement in the lepton + jets channel using a matrix element method and in situ jet energy calibration, Phys. Rev. Lett., 105, 252001, (2010)
[3] D0 collaboration; Abazov, VM; etal., Combination of \( t\bar{t} \) cross section measurements and constraints on the mass of the top quark and its decays into charged Higgs bosons, Phys. Rev., D 80, 071102, (2009)
[4] CDF collaboration; Aaltonen, T.; etal., First measurement of the ratio \( {{{{σ_{t\bar{t}}}}} \left/ {{{σ_{{{Z} \left/ {{{γ^*} → ll}} \right.}}}}} \right.} \) and precise extraction of the \( t\bar{t} \) cross section, Phys. Rev. Lett., 105, 012001, (2010)
[5] CDF collaboration; Aaltonen, T.; etal., First measurement of the \( t\bar{t} \) differential cross section \( {{{dσ }} \left/ {{d{M_{t\bar{t}}}}} \right.} \) in \( p\bar{p} \) collisions at \( \sqrt {s} = 1.96\;{\text{TeV}} \), Phys. Rev. Lett., 102, 222003, (2009)
[6] D0 collaboration; Abazov, VM; etal., Dependence of the \( t\bar{t} \) production cross section on the transverse momentum of the top quark, Phys. Lett., B 693, 515, (2010)
[7] R. Frederix, Top quark phenomenology, arXiv:1009.6199 [SPIRES].
[8] W. Bernreuther, Keynote: some remarks on top, arXiv:1008.3819 [SPIRES].
[9] Bernreuther, W., Top quark physics at the LHC, J. Phys., G 35, 083001, (2008)
[10] Nason, P.; Dawson, S.; Ellis, RK, The total cross-section for the production of heavy quarks in hadronic collisions, Nucl. Phys., B 303, 607, (1988)
[11] Nason, P.; Dawson, S.; Ellis, RK, The one particle inclusive differential cross-section for heavy quark production in hadronic collisions, Nucl. Phys., B 327, 49, (1989)
[12] Beenakker, W.; Kuijf, H.; Neerven, WL; Smith, J., QCD corrections to heavy quark production in \( p\bar{p} \) collisions, Phys. Rev., D 40, 54, (1989)
[13] Beenakker, W.; Neerven, WL; Meng, R.; Schuler, GA; Smith, J., QCD corrections to heavy quark production in hadron hadron collisions, Nucl. Phys., B 351, 507, (1991)
[14] Mangano, ML; Nason, P.; Ridolfi, G., Heavy quark correlations in hadron collisions at next-to-leading order, Nucl. Phys., B 373, 295, (1992)
[15] Korner, JG; Merebashvili, Z., One-loop corrections to four-point functions with two external massive fermions and two external massless partons, Phys. Rev., D 66, 054023, (2002)
[16] Bernreuther, W.; Brandenburg, A.; Si, Z-G; Uwer, P., Top quark pair production and decay at hadron colliders, Nucl. Phys., B 690, 81, (2004)
[17] Czakon, M.; Mitov, A., Inclusive heavy flavor hadroproduction in NLO QCD: the exact analytic result, Nucl. Phys., B 824, 111, (2010)
[18] Melnikov, K.; Schulze, M., NLO QCD corrections to top quark pair production and decay at hadron colliders, JHEP, 08, 049, (2009)
[19] Bernreuther, W.; Si, Z-G, Distributions and correlations for top quark pair production and decay at the tevatron and LHC, Nucl. Phys., B 837, 90, (2010)
[20] Beenakker, W.; etal., Electroweak one loop contributions to top pair production in hadron colliders, Nucl. Phys., B 411, 343, (1994)
[21] Kühn, JH; Scharf, A.; Uwer, P., Electroweak corrections to top-quark pair production in quark-antiquark annihilation, Eur. Phys. J., C 45, 139, (2006)
[22] Kühn, JH; Scharf, A.; Uwer, P., Electroweak effects in top-quark pair production at hadron colliders, Eur. Phys. J., C 51, 37, (2007)
[23] Bernreuther, W.; Fücker, M.; Si, Z-G, Weak interaction corrections to hadronic top quark pair production, Phys. Rev., D 74, 113005, (2006)
[24] Bernreuther, W.; Fücker, M.; Si, Z-G, Weak interaction corrections to hadronic top quark pair production: contributions from quark-gluon and \( b\bar{b} \) induced reactions, Phys. Rev., D 78, 017503, (2008)
[25] Laenen, E.; Smith, J.; Neerven, WL, All order resummation of soft gluon contributions to heavy quark production in hadron hadron collisions, Nucl. Phys., B 369, 543, (1992)
[26] Laenen, E.; Smith, J.; Neerven, WL, Top quark production cross-section, Phys. Lett., B 321, 254, (1994)
[27] Berger, EL; Contopanagos, H., Perturbative gluon resummation of the top quark production cross-section, Phys. Lett., B 361, 115, (1995)
[28] Berger, EL; Contopanagos, H., The perturbative resummed series for top quark production in hadron reactions, Phys. Rev., D 54, 3085, (1996)
[29] Berger, EL; Contopanagos, H., Threshold resummation of the total cross-section for heavy quark production in hadronic collisions, Phys. Rev., D 57, 253, (1998)
[30] Catani, S.; Mangano, ML; Nason, P.; Trentadue, L., The top cross-section in hadronic collisions, Phys. Lett., B 378, 329, (1996)
[31] Catani, S.; Mangano, ML; Nason, P.; Trentadue, L., The resummation of soft gluon in hadronic collisions, Nucl. Phys., B 478, 273, (1996)
[32] Kidonakis, N.; Sterman, GF, Subleading logarithms in QCD hard scattering, Phys. Lett., B 387, 867, (1996)
[33] Kidonakis, N.; Sterman, GF, Resummation for QCD hard scattering, Nucl. Phys., B 505, 321, (1997)
[34] Kidonakis, N.; Oderda, G.; Sterman, GF, Evolution of color exchange in QCD hard scattering, Nucl. Phys., B 531, 365, (1998)
[35] Laenen, E.; Oderda, G.; Sterman, GF, Resummation of threshold corrections for single particle inclusive cross-sections, Phys. Lett., B 438, 173, (1998)
[36] Bonciani, R.; Catani, S.; Mangano, ML; Nason, P., NLL resummation of the heavy-quark hadroproduction cross-section, Nucl. Phys., B 529, 424, (1998)
[37] Bonciani, R.; Catani, S.; Mangano, ML; Nason, P., Sudakov resummation of multiparton QCD cross sections, Phys. Lett., B 575, 268, (2003)
[38] Czakon, M.; Mitov, A., On the soft-gluon resummation in top quark pair production at hadron colliders, Phys. Lett., B 680, 154, (2009)
[39] Beneke, M.; Falgari, P.; Schwinn, C., Soft radiation in heavy-particle pair production: all-order colour structure and two-loop anomalous dimension, Nucl. Phys., B 828, 69, (2010)
[40] Czakon, M.; Mitov, A.; Sterman, GF, Threshold resummation for top-pair hadroproduction to next-to-next-to-leading log, Phys. Rev., D 80, 074017, (2009)
[41] Ahrens, V.; Ferroglia, A.; Neubert, M.; Pecjak, BD; Yang, LL, Top-quark pair production beyond next-to-leading order, Nucl. Phys. Proc. Suppl., 205-206, 48, (2010)
[42] Ferroglia, A.; Neubert, M.; Pecjak, BD; Yang, LL, Infrared singularities and soft gluon resummation with massive partons, Nucl. Phys. Proc. Suppl., 205-206, 98, (2010)
[43] Kidonakis, N., Next-to-next-to-leading soft-gluon corrections for the top quark cross section and transverse momentum distribution, Phys. Rev., D 82, 114030, (2010)
[44] Moch, S.; Uwer, P., Theoretical status and prospects for top-quark pair production at hadron colliders, Phys. Rev., D 78, 034003, (2008)
[45] Langenfeld, U.; Moch, S.; Uwer, P., Measuring the running top-quark mass, Phys. Rev., D 80, 054009, (2009)
[46] U. Langenfeld, S. Moch and P. Uwer, New results for\( t\bar{t} \)production at hadron colliders, arXiv:0907.2527 [SPIRES].
[47] Cacciari, M.; Frixione, S.; Mangano, ML; Nason, P.; Ridolfi, G., Updated predictions for the total production cross sections of top and of heavier quark pairs at the tevatron and at the LHC, JHEP, 09, 127, (2008)
[48] Kidonakis, N.; Vogt, R., The theoretical top quark cross section at the tevatron and the LHC, Phys. Rev., D 78, 074005, (2008)
[49] Dittmaier, S.; Uwer, P.; Weinzierl, S., NLO QCD corrections to \( t\bar{t} \) + jet production at hadron colliders, Phys. Rev. Lett., 98, 262002, (2007)
[50] Dittmaier, S.; Uwer, P.; Weinzierl, S., Hadronic top-quark pair production in association with a hard jet at next-to-leading order QCD: phenomenological studies for the tevatron and the LHC, Eur. Phys. J., C 59, 625, (2009)
[51] Bevilacqua, G.; Czakon, M.; Papadopoulos, CG; Worek, M., Dominant QCD backgrounds in Higgs boson analyses at the LHC: a study of \( pp → t\bar{t} + 2 \) jets at next-to-leading order, Phys. Rev. Lett., 104, 162002, (2010)
[52] Melnikov, K.; Schulze, M., NLO QCD corrections to top quark pair production in association with one hard jet at hadron colliders, Nucl. Phys., B 840, 129, (2010)
[53] Binoth, T.; Heinrich, G., An automatized algorithm to compute infrared divergent multi-loop integrals, Nucl. Phys., B 585, 741, (2000)
[54] Binoth, T.; Heinrich, G., Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys., B 693, 134, (2004)
[55] Heinrich, G., A numerical method for NNLO calculations, Nucl. Phys. Proc. Suppl., 116, 368, (2003)
[56] Heinrich, G., A numerical approach to infrared divergent multi-parton phase space integrals, Nucl. Phys. Proc. Suppl., 135, 290, (2004)
[57] Heinrich, G., Towards \(e\)\^{+}\(e\)\^{−} → 3 jets at NNLO by sector decomposition, Eur. Phys. J., C 48, 25, (2006)
[58] Heinrich, G., Sector decomposition, Int. J. Mod. Phys., A 23, 1457, (2008)
[59] Gehrmann-De Ridder, A.; Gehrmann, T.; Heinrich, G., Four-particle phase space integrals in massless QCD, Nucl. Phys., B 682, 265, (2004)
[60] Anastasiou, C.; Melnikov, K.; Petriello, F., A new method for real radiation at NNLO, Phys. Rev., D 69, 076010, (2004)
[61] Kosower, DA, Multiple singular emission in gauge theories, Phys. Rev., D 67, 116003, (2003)
[62] Daleo, A.; Gehrmann, T.; Maître, D., Antenna subtraction with hadronic initial states, JHEP, 04, 016, (2007)
[63] Gehrmann-De Ridder, A.; Ritzmann, M., NLO antenna subtraction with massive fermions, JHEP, 07, 041, (2009)
[64] Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, EWN, Antenna subtraction at NNLO, JHEP, 09, 056, (2005)
[65] Nigel Glover, EW; Pires, J., Antenna subtraction for gluon scattering at NNLO, JHEP, 06, 096, (2010)
[66] R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, NNLO antenna subtraction with two hadronic initial states, PoS(RADCOR2009)052 [arXiv:1001.2396] [SPIRES].
[67] 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)
[68] Czakon, M., A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett., B 693, 259, (2010)
[69] C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, arXiv:1011.4867 [SPIRES].
[70] Czakon, M.; Mitov, A.; Moch, S., Heavy-quark production in massless quark scattering at two loops in QCD, Phys. Lett., B 651, 147, (2007)
[71] Czakon, M.; Mitov, A.; Moch, S., Heavy-quark production in gluon fusion at two loops in QCD, Nucl. Phys., B 798, 210, (2008)
[72] Czakon, M., Tops from light quarks: full mass dependence at two-loops in QCD, Phys. Lett., B 664, 307, (2008)
[73] Bonciani, R.; Ferroglia, A.; Gehrmann, T.; Maître, D.; Studerus, C., Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel, JHEP, 07, 129, (2008)
[74] Bonciani, R.; Ferroglia, A.; Gehrmann, T.; Studerus, C., Two-loop planar corrections to heavy-quark pair production in the quark-antiquark channel, JHEP, 08, 067, (2009)
[75] Laporta, S.; Remiddi, E., The analytical value of the electron (g-2) at order alpha 3 in QED, Phys. Lett., B 379, 283, (1996)
[76] Laporta, S., High-precision calculation of multi-loop Feynman integrals by difference equations, Int. J. Mod. Phys., A 15, 5087, (2000)
[77] Tkachov, FV, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett., B 100, 65, (1981)
[78] Chetyrkin, KG; Tkachov, FV, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys., B 192, 159, (1981)
[79] Kotikov, AV, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett., B 254, 158, (1991)
[80] Kotikov, AV, Differential equations method: the calculation of vertex type Feynman diagrams, Phys. Lett., B 259, 314, (1991)
[81] Kotikov, AV, Differential equation method: the calculation of N point Feynman diagrams, Phys. Lett., B 267, 123, (1991)
[82] Remiddi, E., Differential equations for Feynman graph amplitudes, Nuovo Cim., A 110, 1435, (1997)
[83] Caffo, M.; Czyz, H.; Laporta, S.; Remiddi, E., Master equations for master amplitudes, Acta Phys. Polon., B 29, 2627, (1998)
[84] Caffo, M.; Czyz, H.; Laporta, S.; Remiddi, E., The master differential equations for the 2-loop sunrise selfmass amplitudes, Nuovo Cim., A 111, 365, (1998)
[85] Gehrmann, T.; Remiddi, E., Differential equations for two-loop four-point functions, Nucl. Phys., B 580, 485, (2000)
[86] Argeri, M.; Mastrolia, P., Feynman diagrams and differential equations, Int. J. Mod. Phys., A 22, 4375, (2007)
[87] Körner, JG; Merebashvili, Z.; Rogal, M., One-loop amplitudes for four-point functions with two external massive quarks and two external massless partons up to \( \mathcal{O}\left( {{ε^2}} \right) \), Phys. Rev., D 73, 034030, (2006)
[88] Körner, JG; Merebashvili, Z.; Rogal, M., NNLO \( \mathcal{O}\left( {α_s^4} \right) \) results for heavy quark pair production in quark-antiquark collisions: the one-loop squared contributions, Phys. Rev., D 77, 094011, (2008)
[89] Anastasiou, C.; Aybat, SM, The one-loop gluon amplitude for heavy-quark production at NNLO, Phys. Rev., D 78, 114006, (2008)
[90] Kniehl, B.; Merebashvili, Z.; Körner, JG; Rogal, M., Heavy quark pair production in gluon fusion at next-to-next-to-leading \( \mathcal{O}\left( {α_s^4} \right) \) order: one-loop squared contributions, Phys. Rev., D 78, 094013, (2008)
[91] Becher, T.; Neubert, M., Infrared singularities of QCD amplitudes with massive partons, Phys. Rev., D 79, 125004, (2009)
[92] Ferroglia, A.; Neubert, M.; Pecjak, BD; Yang, LL, Two-loop divergences of scattering amplitudes with massive partons, Phys. Rev. Lett., 103, 201601, (2009)
[93] Ferroglia, A.; Neubert, M.; Pecjak, BD; Yang, LL, Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories, JHEP, 11, 062, (2009)
[94] Nogueira, P., Automatic Feynman graph generation, J. Comput. Phys., 105, 279, (1993)
[95] A. von Manteuffel and C. Studerus, Reduze 2, to appear.
[96] Anastasiou, C.; Lazopoulos, A., Automatic integral reduction for higher order perturbative calculations, JHEP, 07, 046, (2004)
[97] Smirnov, AV, Algorithm FIRE — Feynman integral reduction, JHEP, 10, 107, (2008)
[98] Studerus, C., Reduze — Feynman integral reduction in C++, Comput. Phys. Commun., 181, 1293, (2010)
[99] Bauer, CW; Frink, A.; Kreckel, R., Introduction to the ginac framework for symbolic computation within the C++ programming language, J. Symb. Comput., 33, 1, (2002)
[100] Argeri, M.; Mastrolia, P.; Remiddi, E., The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass, Nucl. Phys., B 631, 388, (2002)
[101] Bonciani, R.; Mastrolia, P.; Remiddi, E., Vertex diagrams for the QED form factors at the 2-loop level, Nucl. Phys., B 661, 289, (2003)
[102] Bonciani, R.; Mastrolia, P.; Remiddi, E., Master integrals for the 2-loop QCD virtual corrections to the forward-backward asymmetry, Nucl. Phys., B 690, 138, (2004)
[103] Bonciani, R.; Mastrolia, P.; Remiddi, E., QED vertex form factors at two loops, Nucl. Phys., B 676, 399, (2004)
[104] Fleischer, J.; Kotikov, AV; Veretin, OL, Analytic two-loop results for selfenergy-and vertex-type diagrams with one non-zero mass, Nucl. Phys., B 547, 343, (1999)
[105] Aglietti, U.; Bonciani, R., Master integrals with one massive propagator for the two-loop electroweak form factor, Nucl. Phys., B 668, 3, (2003)
[106] Davydychev, AI; Kalmykov, MY, Massive Feynman diagrams and inverse binomial sums, Nucl. Phys., B 699, 3, (2004)
[107] Aglietti, U.; Bonciani, R., Master integrals with 2 and 3 massive propagators for the 2-loop electroweak form factor: planar case, Nucl. Phys., B 698, 277, (2004)
[108] R. Bonciani, G. Degrassi and A. Vicini, On the generalized harmonic polylogarithms of one complex variable, arXiv:1007.1891 [SPIRES].
[109] Czakon, M.; Gluza, J.; Riemann, T., Master integrals for massive two-loop Bhabha scattering in QED, Phys. Rev., D 71, 073009, (2005)
[110] G. Bell, Higher order QCD corrections in exclusive charmless B decays, arXiv:0705.3133 [SPIRES].
[111] Bonciani, R.; Ferroglia, A., Two-loop QCD corrections to the heavy-to-light quark decay, JHEP, 11, 065, (2008)
[112] Asatrian, HM; Greub, C.; Pecjak, BD, NNLO corrections to \( \bar{B} → {X_u}l\bar{ν } \) in the shape-function region, Phys. Rev., D 78, 114028, (2008)
[113] Beneke, M.; Huber, T.; Li, XQ, Two-loop QCD correction to differential semi-leptonic b → u decays in the shape-function region, Nucl. Phys., B 811, 77, (2009)
[114] Goncharov, AB, Multiple polylogarithms, ciclotomy and modular complexes, Math. Res. Lett., 5, 497, (1998)
[115] Broadhurst, DJ, Massive 3-loop Feynman diagrams reducible to SC\^{*} primitives of algebras of the sixth root of unity, Eur. Phys. J., C 8, 311, (1999)
[116] Remiddi, E.; Vermaseren, JAM, Harmonic polylogarithms, Int. J. Mod. Phys., A 15, 725, (2000)
[117] Gehrmann, T.; Remiddi, E., Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun., 141, 296, (2001)
[118] Maître, D., HPL, a Mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun., 174, 222, (2006)
[119] D. Maître, Extension of HPL to complex arguments, hep-ph/0703052 [SPIRES].
[120] Vollinga, J.; Weinzierl, S., Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun., 167, 177, (2005)
[121] Gehrmann, T.; Remiddi, E., Two-loop master integrals for \(γ\)\^{*} → 3 jets: the planar topologies, Nucl. Phys., B 601, 248, (2001)
[122] Gehrmann, T.; Remiddi, E., Two-loop master integrals for \(γ\)\^{*} → 3 jets: the non-planar topologies, Nucl. Phys., B 601, 287, (2001)
[123] Gehrmann, T.; Remiddi, E., Numerical evaluation of two-dimensional harmonic polylogarithms, Comput. Phys. Commun., 144, 200, (2002)
[124] Melnikov, K.; Ritbergen, T., The three-loop on-shell renormalization of QCD and QED, Nucl. Phys., B 591, 515, (2000)
[125] Laporta, S.; Remiddi, E., Analytic treatment of the two loop equal mass sunrise graph, Nucl. Phys., B 704, 349, (2005)
[126] Pozzorini, S.; Remiddi, E., Precise numerical evaluation of the two loop sunrise graph master integrals in the equal mass case, Comput. Phys. Commun., 175, 381, (2006)
[127] Aglietti, U.; Bonciani, R.; Grassi, L.; Remiddi, E., The two loop crossed ladder vertex diagram with two massive exchanges, Nucl. Phys., B 789, 45, (2008)
[128] J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [SPIRES].
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.