Three-loop master integrals for ladder-box diagrams with one massive leg

Abstract

The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type integrals, as well as of the tower of vertex- and bubble-type master integrals associated to subtopologies, are given as a Taylor series expansion in the dimensional regulator parameter epsilon = (4-d)/2. The coefficients of the series are expressed in terms of uniform weight combinations of multiple polylogarithms and transcendental constants up to weight six. The considered integrals enter the next-to-next-to-next-to-leading order virtual corrections to scattering processes like the three-jet production mediated by vector boson decay, V* -> jjj, as well as the Higgs plus one-jet production in gluon fusion, pp -> Hj.

44 pages, 5 figures, 2 ancillary files

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• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
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• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the non-planar graphs
• Theory for muon-electron scattering @ 10ppm: A report of the MUonE theory initiative
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the planar graphs
• Cluster algebras for Feynman integrals
• A Three-Point Form Factor Through Five Loops
• Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering
• Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production
• Master integrals for the two-loop penguin contribution in non-leptonic B-decays
• Exact Top Yukawa corrections to Higgs boson decay into bottom quarks
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Muon-electron scattering at NNLO
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• Two-loop Master Integrals with the Simplified Differential Equations approach
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
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• NNLO virtual and real leptonic corrections to muon-electron scattering
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• First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production
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• Two-loop master integrals for the leading QCD corrections to the Higgs coupling to a $W$ pair and to the triple gauge couplings $ZWW$ and ${\gamma }^{\ast }WW$
• Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel
• Two-loop helicity amplitudes for $H+$jet production to higher orders in the dimensional regulator
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Two-loop master integrals for non-leptonic heavy-to-heavy decays
• On the calculation of soft phase space integral
• Dissecting polytopes: Landau singularities and asymptotic expansions in $2\to 2$ scattering
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• Two-loop running effects in Higgs physics in Standard Model Effective Field Theory
• Resummation methods for Master Integrals
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• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• Integration-by-parts identities in FDR
• Three-loop planar master integrals for heavy-to-light form factors
• A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• Two-Loop Four-Fermion Scattering Amplitude in QED
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Higgs-boson production in top-quark fragmentation
• Two-photon exchange in leptophilic dark matter scenarios
• Mixed QCD-EW corrections to $W$-pair production at electron-positron colliders