scholarly journals Analytic results for two-loop planar master integrals for Bhabha scattering

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Claude Duhr ◽  
Vladimir A. Smirnov ◽  
Lorenzo Tancredi
Keyword(s):  
Differential Equations ◽  
Canonical Bases ◽  
Bhabha Scattering ◽  
Multiple Polylogarithms

Abstract We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equations with canonical bases. We obtain results in terms of multiple polylogarithms for all the master integrals but one, for which we derive a compact result in terms of elliptic multiple polylogarithms. As a byproduct, we also provide a compact analytic result in terms of elliptic multiple polylogarithms for an integral belonging to the first family of planar Bhabha integrals, whose computation in terms of polylogarithms was addressed previously in the literature.

scholarly journals The diagrammatic coaction beyond one loop

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Samuel Abreu ◽  
Ruth Britto ◽  
Claude Duhr ◽  
Einan Gardi ◽  
James Matthew
Keyword(s):  
Differential Equations ◽  
Hypergeometric Functions ◽  
Differential Forms ◽  
Feynman Graph ◽  
Loop Order ◽  
Feynman Integrals ◽  
Mathematical Properties ◽  
Multiple Polylogarithms ◽  
Complete Set ◽  
General Tool

Abstract The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions. The coaction on the functions is constructed by pairing a basis of differential forms, corresponding to master integrals, with a basis of integration contours, corresponding to independent cut integrals. At one loop, a general diagrammatic coaction was established using dimensional regularisation, which may be realised in terms of a global coaction on hypergeometric functions, or equivalently, order by order in the ϵ expansion, via a local coaction on multiple polylogarithms. The present paper takes the first steps in generalising the diagrammatic coaction beyond one loop. We first establish general properties that govern the diagrammatic coaction at any loop order. We then focus on examples of two-loop topologies for which all integrals expand into polylogarithms. In each case we determine bases of master integrals and cuts in terms of hypergeometric functions, and then use the global coaction to establish the diagrammatic coaction of all master integrals in the topology. The diagrammatic coaction encodes the complete set of discontinuities of Feynman integrals, as well as the differential equations they satisfy, providing a general tool to understand their physical and mathematical properties.

scholarly journals Differential equations and massive two-loop Bhabha scattering: the B5l2m3 case

2006 ◽  
Vol 157 (1) ◽  
pp. 16-20 ◽  
Author(s):  
M. Czakon ◽  
J. Gluza ◽  
K. Kajda ◽  
T. Riemann
Keyword(s):  
Differential Equations ◽  
Bhabha Scattering

scholarly journals Mixed QCD-EW corrections for Higgs leptonic decay via HW+W− vertex

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Chichuan Ma ◽  
Yuxuan Wang ◽  
Xiaofeng Xu ◽  
Li Lin Yang ◽  
Bin Zhou
Keyword(s):  
Differential Equations ◽  
Production Process ◽  
Canonical Basis ◽  
Intersection Theory ◽  
Leptonic Decay ◽  
Decay Rates ◽  
Decay Process ◽  
Higgs Production ◽  
Multiple Polylogarithms ◽  
Analytic Expressions

Abstract We consider the two-loop corrections to the HW+W− vertex at order ααs. We construct a canonical basis for the two-loop integrals using the Baikov representation and the intersection theory. By solving the ϵ-form differential equations, we obtain fully analytic expressions for the master integrals in terms of multiple polylogarithms, which allow fast and accurate numeric evaluation for arbitrary configurations of external momenta. We apply our analytic results to the decay process H → νeeW, and study both the integrated and differential decay rates. Our results can also be applied to the Higgs production process via W boson fusion.

scholarly journals Differential equations for Feynman integrals beyond multiple polylogarithms

2018 ◽  
Author(s):  
Stefan Weinzierl ◽  
Luise Adams ◽  
Christian Bogner ◽  
Ekta Chaubey ◽  
Armin Schweitzer
Keyword(s):  
Differential Equations ◽  
Feynman Integrals ◽  
Multiple Polylogarithms

scholarly journals Two-loop mixed QCD-EW corrections to gg → Hg

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marco Bonetti ◽  
Erik Panzer ◽  
Vladimir A. Smirnov ◽  
Lorenzo Tancredi
Keyword(s):  
Higgs Boson ◽  
Differential Equations ◽  
Helicity Amplitude ◽  
Numerical Evaluation ◽  
Gluon Fusion ◽  
Physical Region ◽  
Multiple Polylogarithms ◽  
Helicity Amplitudes ◽  
Weight Drop

Abstract We compute the two-loop mixed QCD-Electroweak (QCD-EW) corrections to the production of a Higgs boson and a gluon in gluon fusion through a loop of light quarks. The relevant four-point functions with internal massive propagators are expressed as multiple polylogarithms with algebraic arguments. We perform the calculation by integration over Feynman parameters and, independently, by the method of differential equations. We compute the two independent helicity amplitudes for the process and we find that they are both finite. Moreover, we observe a weight drop when all gluons have the same helicity. We also provide a simplified expression for the all-plus helicity amplitude, which is optimised for fast and reliable numerical evaluation in the physical region.

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