Abstract
We compute the three-loop QCD corrections to the massive quark form factors with external vector, axial-vector, scalar and pseudo-scalar currents. All corrections with closed loops of massless fermions are included. The non-fermionic part is computed in the large-Nc limit, where only planar Feynman diagrams contribute.
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K.G. Chetyrkin, J.H. Kuhn and A. Kwiatkowski, QCD corrections to the e + e − cross-section and the Z boson decay rate, hep-ph/9503396 [INSPIRE].
P. Mastrolia and E. Remiddi, Two loop form-factors in QED, Nucl. Phys. B 664 (2003) 341 [hep-ph/0302162] [INSPIRE].
R. Bonciani, P. Mastrolia and E. Remiddi, QED vertex form-factors at two loops, Nucl. Phys. B 676 (2004) 399 [hep-ph/0307295] [INSPIRE].
W. Bernreuther et al., Two-loop QCD corrections to the heavy quark form-factors: The Vector contributions, Nucl. Phys. B 706 (2005) 245 [hep-ph/0406046] [INSPIRE].
A.H. Hoang and T. Teubner, Analytic calculation of two loop corrections to heavy quark pair production vertices induced by light quarks, Nucl. Phys. B 519 (1998) 285 [hep-ph/9707496] [INSPIRE].
J. Gluza, A. Mitov, S. Moch and T. Riemann, The QCD form factor of heavy quarks at NNLO, JHEP 07 (2009) 001 [arXiv:0905.1137] [INSPIRE].
J. Henn, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Massive three-loop form factor in the planar limit, JHEP 01 (2017) 074 [arXiv:1611.07535] [INSPIRE].
T. Ahmed, J.M. Henn and M. Steinhauser, High energy behaviour of form factors, JHEP 06 (2017) 125 [arXiv:1704.07846] [INSPIRE].
J. Ablinger et al., The Heavy Quark Form Factors at Two Loops, Phys. Rev. D 97 (2018) 094022 [arXiv:1712.09889] [INSPIRE].
R.N. Lee, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Three-loop massive form factors: complete light-fermion corrections for the vector current, JHEP 03 (2018) 136 [arXiv:1801.08151] [INSPIRE].
A. Mitov and S. Moch, The singular behavior of massive QCD amplitudes, JHEP 05 (2007) 001 [hep-ph/0612149] [INSPIRE].
W. Bernreuther et al., Two-loop QCD corrections to the heavy quark form-factors: Axial vector contributions, Nucl. Phys. B 712 (2005) 229 [hep-ph/0412259] [INSPIRE].
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, T. Leineweber and E. Remiddi, Two-loop QCD corrections to the heavy quark form-factors: Anomaly contributions, Nucl. Phys. B 723 (2005) 91 [hep-ph/0504190] [INSPIRE].
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, P. Mastrolia and E. Remiddi, Decays of scalar and pseudoscalar Higgs bosons into fermions: Two-loop QCD corrections to the Higgs-quark-antiquark amplitude, Phys. Rev. D 72 (2005) 096002 [hep-ph/0508254] [INSPIRE].
J.M. Henn, A.V. Smirnov and V.A. Smirnov, Analytic results for planar three-loop integrals for massive form factors, JHEP 12 (2016) 144 [arXiv:1611.06523] [INSPIRE].
A. Grozin, Heavy-quark form factors in the large β 0 limit, Eur. Phys. J. C 77 (2017) 453 [arXiv:1704.07968] [INSPIRE].
S.A. Larin, The Renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2015) 182 [arXiv:1408.2372] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998) 497 [arXiv:1105.2076] [INSPIRE].
R.N. Lee, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Three-loop massive form factors: complete light-fermion corrections for the vector current, JHEP 03 (2018) 136 [arXiv:1801.08151] [INSPIRE].
K. Melnikov and T. van Ritbergen, The three loop on-shell renormalization of QCD and QED, Nucl. Phys. B 591 (2000) 515 [hep-ph/0005131] [INSPIRE].
P. Marquard, L. Mihaila, J.H. Piclum and M. Steinhauser, Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order, Nucl. Phys. B 773 (2007) 1 [hep-ph/0702185] [INSPIRE].
W. Bernreuther et al., QCD corrections to static heavy quark form-factors, Phys. Rev. Lett. 95 (2005) 261802 [hep-ph/0509341] [INSPIRE].
A.G. Grozin, P. Marquard, J.H. Piclum and M. Steinhauser, Three-Loop Chromomagnetic Interaction in HQET, Nucl. Phys. B 789 (2008) 277 [arXiv:0707.1388] [INSPIRE].
S. Laporta and E. Remiddi, The Analytical value of the electron (g − 2) at order α 3 in QED, Phys. Lett. B 379 (1996) 283 [hep-ph/9602417] [INSPIRE].
J.P. Archambault and A. Czarnecki, Three-loop QCD corrections and b-quark decays, Phys. Rev. D 70 (2004) 074016 [hep-ph/0408021] [INSPIRE].
V.V. Sudakov, Vertex parts at very high-energies in quantum electrodynamics, Sov. Phys. JETP 3 (1956) 65 [INSPIRE].
J. Frenkel and J.C. Taylor, Exponentiation of Leading Infrared Divergences in Massless Yang-Mills Theories, Nucl. Phys. B 116 (1976) 185 [INSPIRE].
A.A. Penin, High-Energy Limit of Quantum Electrodynamics beyond Sudakov Approximation, Phys. Lett. B 745 (2015) 69 [Erratum ibid. B 751 (2015) 596] [Erratum ibid. B 771 (2017) 633] [arXiv:1412.0671] [INSPIRE].
T. Liu, A.A. Penin and N. Zerf, Three-loop quark form factor at high energy: the leading mass corrections, Phys. Lett. B 771 (2017) 492 [arXiv:1705.07910] [INSPIRE].
T. Liu and A.A. Penin, High-Energy Limit of QCD beyond the Sudakov Approximation, Phys. Rev. Lett. 119 (2017) 262001 [arXiv:1709.01092] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, Heavy quark current correlators to O(α 2 S ), Nucl. Phys. B 505 (1997) 40 [hep-ph/9705254] [INSPIRE].
L.D. Landau and E.M. Lifschitz, Lehrbuch der Theoretischen Physik III, Quantenmechanik, Akademie-Verlag Berlin (1988), section 36, eq. (24).
A. Messiah, Quantenmechanik 1, Walter de Gruyter (1991), eq. (B32/2).
V.S. Fadin and V.A. Khoze, Production of a pair of \( t\overline{t} \) quarks near threshold, Sov. J. Nucl. Phys. 53 (1991) 692 [INSPIRE].
A.M. Polyakov, Gauge Fields as Rings of Glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].
R.A. Brandt, F. Neri and M.-a. Sato, Renormalization of Loop Functions for All Loops, Phys. Rev. D 24 (1981) 879 [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson Loops Beyond the Leading Order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, Three Loop Cusp Anomalous Dimension in QCD, Phys. Rev. Lett. 114 (2015) 062006 [arXiv:1409.0023] [INSPIRE].
A. Grozin, J.M. Henn, G.P. Korchemsky and P. Marquard, The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions, JHEP 01 (2016) 140 [arXiv:1510.07803] [INSPIRE].
A.V. Smirnov, FIESTA4: Optimized Feynman integral calculations with GPU support, Comput. Phys. Commun. 204 (2016) 189 [arXiv:1511.03614] [INSPIRE].
C.W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2000) 1 [cs/0004015] [INSPIRE].
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun. 167 (2005) 177 [hep-ph/0410259] [INSPIRE].
J.A.M. Vermaseren, Axodraw, Comput. Phys. Commun. 83 (1994) 45 [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
J. Ablinger, J. Blümlein, P. Marquard, N. Rana and C. Schneider, Heavy Quark Form Factors at Three Loops in the Planar Limit, DESY-18-052 [arXiv:1804.07313] [INSPIRE].
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Lee, R.N., Smirnov, A.V., Smirnov, V.A. et al. Three-loop massive form factors: complete light-fermion and large-Nc corrections for vector, axial-vector, scalar and pseudo-scalar currents. J. High Energ. Phys. 2018, 187 (2018). https://doi.org/10.1007/JHEP05(2018)187
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DOI: https://doi.org/10.1007/JHEP05(2018)187