Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs

Di Vita, Stefano; Laporta, Stefano; Mastrolia, Pierpaolo; Primo, Amedeo; Schubert, Ulrich

doi:10.1007/JHEP09(2018)016

Title: Master integrals for the NNLO virtual corrections to μe scattering in QED: The non-planar graphs

Journal Article · 04 September 2018 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP09(2018)016 · OSTI ID:1494707

^[1]; Laporta, Stefano ^[2]; Mastrolia, Pierpaolo ^[2]; Primo, Amedeo ^[3]; Schubert, Ulrich ^[4]

INFN, Sezione di Milano, Milano (Italy)
Univ. di Padova, Padova (Italy); INFN, Sezione di Padova, Padova (Italy)
Univ. of Zurich, Zurich (Switzerland)
Argonne National Lab. (ANL), Argonne, IL (United States)

In this study, we evaluate the master integrals for the two-loop non-planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to-leading order in QED. We adopt the method of differential equations and the Magnus exponential to determine a canonical set of integrals, finally expressed as a Taylor series around four space-time dimensions, with coefficients written as combination of generalized polylogarithms. The electron is treated as massless, while we retain full dependence on the muon mass. The considered integrals are also relevant for crossing-related processes, such as di-muon production at e⁺e^– colliders, as well as for the QCD corrections to top-pair production at hadron colliders. In particular our results, together with the planar master integrals recently computed, represent the complete set of functions needed for the evaluation of the photonic two-loop virtual next-to-next-to-leading order QED corrections to μe → μe and e⁺e^– → μ⁺μ^–.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Swiss National Science Foundation (SNSF)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1494707

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (62)

Magnus and Dyson Series for Master Integrals Mastrolia, Pierpaolo; Argeri, Mario; Di Vita, Stefano Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014) https://doi.org/10.22323/1.211.0007	conference	August 2014
Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Springer https://doi.org/10.5167/uzh-41374	text	January 2011
Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering Bonciani, Roberto; Di Vita, Stefano; Mastrolia, Pierpaolo arXiv https://doi.org/10.48550/arxiv.1604.08581	text	January 2016
QED vertex form factors at two loops Bonciani, R.; Mastrolia, P.; Remiddi, E. Nuclear Physics B, Vol. 676, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2003.10.031	journal	January 2004
Multiloop integrals in dimensional regularization made simple Henn, Johannes M. arXiv https://doi.org/10.48550/arxiv.1304.1806	text	January 2013
Measuring the leading hadronic contribution to the muon g-2 via $$\mu e$$ μ e scattering Abbiendi, G.; Calame, C. M. Carloni; Marconi, U. The European Physical Journal C, Vol. 77, Issue 3 https://doi.org/10.1140/epjc/s10052-017-4633-z	journal	March 2017
Integration by parts: The algorithm to calculate β-functions in 4 loops Chetyrkin, K. G.; Tkachov, F. V. Nuclear Physics B, Vol. 192, Issue 1 https://doi.org/10.1016/0550-3213(81)90199-1	journal	November 1981
Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D Lee, R. N. arXiv https://doi.org/10.48550/arxiv.0911.0252	text	January 2009
Two-loop planar corrections to heavy-quark pair production in the quark-antiquark channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Institute of Physics Publishing https://doi.org/10.5167/uzh-30915	text	January 2009
Chow polylogarithms and regulators Goncharov, A. B. Mathematical Research Letters, Vol. 2, Issue 1 https://doi.org/10.4310/MRL.1995.v2.n1.a9	journal	January 1995
Multiloop Integrals in Dimensional Regularization Made Simple Henn, Johannes M. Physical Review Letters, Vol. 110, Issue 25 https://doi.org/10.1103/PhysRevLett.110.251601	journal	June 2013
Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)102	journal	January 2011
Status of R(s) measurements by energy scan method Ignatov, Fedor EPJ Web of Conferences, Vol. 179 https://doi.org/10.1051/epjconf/201817901005	journal	January 2018
NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels Czakon, Michal; Mitov, Alexander Journal of High Energy Physics, Vol. 2012, Issue 12 https://doi.org/10.1007/JHEP12(2012)054	journal	December 2012
Three-loop master integrals for ladder-box diagrams with one massive leg Di Vita, Stefano; Mastrolia, Pierpaolo; Schubert, Ulrich arXiv https://doi.org/10.48550/arxiv.1408.3107	text	January 2014
A quasi-finite basis for multi-loop Feynman integrals von Manteuffel, Andreas; Panzer, Erik; Schabinger, Robert M. arXiv https://doi.org/10.48550/arxiv.1411.7392	text	January 2014
Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Springer https://doi.org/10.5167/uzh-90656	text	January 2013
Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Institute of Physics Publishing https://doi.org/10.5167/uzh-13578	text	January 2008
High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations Laporta, S. International Journal of Modern Physics A, Vol. 15, Issue 32 https://doi.org/10.1142/S0217751X00002159	journal	December 2000
Percent-Level-Precision Physics at the Tevatron: Next-to-Next-to-Leading Order QCD Corrections to q q ¯ → t t ¯ + X Bärnreuther, Peter; Czakon, Michał; Mitov, Alexander Physical Review Letters, Vol. 109, Issue 13 https://doi.org/10.1103/PhysRevLett.109.132001	journal	September 2012
Two-loop planar corrections to heavy-quark pair production in the quark-antiquark channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Journal of High Energy Physics, Vol. 2009, Issue 08 https://doi.org/10.1088/1126-6708/2009/08/067	journal	August 2009
Harmonic Polylogarithms Remiddi, E.; Vermaseren, J. A. M. arXiv https://doi.org/10.48550/arxiv.hep-ph/9905237	text	January 1999
Master integrals for the NNLO virtual corrections to μe scattering in QED: the planar graphs Mastrolia, Pierpaolo; Passera, Massimo; Primo, Amedeo Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)198	journal	November 2017
Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through O ( α S 4 ) Czakon, Michał; Fiedler, Paul; Mitov, Alexander Physical Review Letters, Vol. 110, Issue 25 https://doi.org/10.1103/PhysRevLett.110.252004	journal	June 2013
Two-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Journal of High Energy Physics, Vol. 2008, Issue 07 https://doi.org/10.1088/1126-6708/2008/07/129	journal	July 2008
NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels Czakon, Michal; Mitov, Alexander arXiv https://doi.org/10.48550/arxiv.1207.0236	text	January 2012
Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. arXiv https://doi.org/10.48550/arxiv.1309.4450	text	January 2013
Magnus and Dyson Series for Master Integrals Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo arXiv https://doi.org/10.48550/arxiv.1401.2979	text	January 2014
A non-planar two-loop three-point function beyond multiple polylogarithms Manteuffel, A. Von; Tancredi, L. Karlsruhe https://doi.org/10.5445/ir/1000072078	text	January 2017
A non-planar two-loop three-point function beyond multiple polylogarithms Manteuffel, A. Von; Tancredi, L. Karlsruhe https://doi.org/10.5445/ir/1000072078#verlagsausgabe	text	January 2017
Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to Lee, R. N. Nuclear Physics B, Vol. 830, Issue 3 https://doi.org/10.1016/j.nuclphysb.2009.12.025	journal	May 2010
Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD Czakon, M. arXiv https://doi.org/10.48550/arxiv.0803.1400	text	January 2008
A systematic and efficient method to compute multi-loop master integrals Liu, Xiao; Ma, Yan-Qing; Wang, Chen-Yu Physics Letters B, Vol. 779 https://doi.org/10.1016/j.physletb.2018.02.026	journal	April 2018
Differential equations method. New technique for massive Feynman diagram calculation Kotikov, A. V. Physics Letters B, Vol. 254, Issue 1-2 https://doi.org/10.1016/0370-2693(91)90413-K	journal	January 1991
SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop Borowka, S.; Heinrich, G.; Jones, S. P. Computer Physics Communications, Vol. 196 https://doi.org/10.1016/j.cpc.2015.05.022	journal	November 2015
Magnus and Dyson series for Master Integrals Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)082	journal	March 2014
Harmonic Polylogarithms Remiddi, E.; Vermaseren, J. A. M. International Journal of Modern Physics A, Vol. 15, Issue 05 https://doi.org/10.1142/S0217751X00000367	journal	February 2000
Two-loop correction to Bhabha scattering Bern, Z.; Dixon, L.; Ghinculov, A. Physical Review D, Vol. 63, Issue 5 https://doi.org/10.1103/PhysRevD.63.053007	journal	February 2001
Numerical evaluation of multiple polylogarithms Vollinga, Jens; Weinzierl, Stefan Computer Physics Communications, Vol. 167, Issue 3 https://doi.org/10.1016/j.cpc.2004.12.009	journal	May 2005
Massive planar and non-planar double box integrals for light N f contributions to $ gg\to t\overline{t} $ von Manteuffel, Andreas; Studerus, Cedric Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)037	journal	October 2013
A theorem on analytical calculability of 4-loop renormalization group functions Tkachov, F. V. Physics Letters B, Vol. 100, Issue 1 https://doi.org/10.1016/0370-2693(81)90288-4	journal	March 1981
The Anomalous Magnetic Moment of the Muon Jegerlehner, Friedrich Springer Tracts in Modern Physics https://doi.org/10.1007/978-3-319-63577-4	book	January 2017
Two-loop form factors in QED Mastrolia, P.; Remiddi, E. Nuclear Physics B, Vol. 664, Issue 1-2 https://doi.org/10.1016/S0550-3213(03)00405-X	journal	August 2003
Three-loop master integrals for ladder-box diagrams with one massive leg Di Vita, Stefano; Mastrolia, Pierpaolo; Schubert, Ulrich Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)148	journal	September 2014
Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering Bonciani, Roberto; Di Vita, Stefano; Mastrolia, Pierpaolo Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)091	journal	September 2016
A new approach to evaluate the leading hadronic corrections to the muon g -2 Carloni Calame, C. M.; Passera, M.; Trentadue, L. Physics Letters B, Vol. 746 https://doi.org/10.1016/j.physletb.2015.05.020	journal	June 2015
Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel Bonciani, R.; Ferroglia, A.; Gehrmann, T. Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)038	journal	December 2013
Differential equations for two-loop four-point functions Gehrmann, T.; Remiddi, E. Nuclear Physics B, Vol. 580, Issue 1-2 https://doi.org/10.1016/S0550-3213(00)00223-6	journal	July 2000
NLO electroweak radiative corrections for four-fermionic process at Belle II Aleksejevs, A.; Barkanova, S.; Zykunov, V. arXiv https://doi.org/10.48550/arxiv.1701.07047	text	January 2017
Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a W pair and to the triple gauge couplings ZW W and γ∗ W W Di Vita, Stefano; Mastrolia, Pierpaolo; Primo, Amedeo Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)008	journal	April 2017
LiteRed 1.4: a powerful tool for reduction of multiloop integrals Lee, Roman N. Journal of Physics: Conference Series, Vol. 523 https://doi.org/10.1088/1742-6596/523/1/012059	journal	June 2014
Tops from light quarks: Full mass dependence at two-loops in QCD Czakon, M. Physics Letters B, Vol. 664, Issue 4-5 https://doi.org/10.1016/j.physletb.2008.05.028	journal	June 2008
NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction Czakon, Michal; Mitov, Alexander Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)080	journal	January 2013
Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language Bauer, Christian; Frink, Alexander; Kreckel, Richard Journal of Symbolic Computation, Vol. 33, Issue 1 https://doi.org/10.1006/jsco.2001.0494	journal	January 2002
A quasi-finite basis for multi-loop Feynman integrals von Manteuffel, Andreas; Panzer, Erik; Schabinger, Robert M. Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)120	journal	February 2015
Numerical evaluation of harmonic polylogarithms Gehrmann, T.; Remiddi, E. Computer Physics Communications, Vol. 141, Issue 2 https://doi.org/10.1016/S0010-4655(01)00411-8	journal	November 2001
NLO electroweak radiative corrections for four-fermionic process at Belle II Aleksejevs, Aleksandrs; Barkanova, Svetlana; Zykunov, Vladimir EPJ Web of Conferences, Vol. 138 https://doi.org/10.1051/epjconf/201713806001	journal	January 2017
NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction Czakon, Michal; Mitov, Alexander arXiv https://doi.org/10.48550/arxiv.1210.6832	text	January 2012
Magnus and Dyson series for Master Integrals Argeri, Mario; Di Vita, Stefano; Mastrolia, Pierpaolo Springer https://doi.org/10.5167/uzh-107578	text	January 2014
Vertex diagrams for the QED form factors at the 2-loop level Bonciani, R.; Mastrolia, P.; Remiddi, E. Nuclear Physics B, Vol. 661, Issue 1-2 https://doi.org/10.1016/S0550-3213(03)00299-2	journal	June 2003
On μe-scattering at NNLO in QED Mastrolia, P.; Passera, M.; Primo, A. EPJ Web of Conferences, Vol. 179 https://doi.org/10.1051/epjconf/201817901014	journal	January 2018
Differential equations for Feynman graph amplitudes Remiddi, E. Il Nuovo Cimento A, Vol. 110, Issue 12 https://doi.org/10.1007/BF03185566	journal	December 1997

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