Master integrals of a planar double-box family for top-quark pair production

Abstract

We calculate analytically the master integrals of a planar double-box family for top-quark pair production using the method of differential equations. With a proper choice of the bases, the differential equations can be transformed to the $d$-log form. The square roots of the kinematic variables in the differential equations can be rationalized by defining two dimensionless variables. We find that all the boundary conditions can be fully fixed either by simple integrals or regularity conditions at some special kinematic points. The analytic results for thirty-three master integrals at general kinematics are all expressed in terms of multiple polylogarithms up to transcendental weight four.

arXiv comment11 pages, 4 figures

References in corpus (25)

• The total top quark pair production cross-section at hadron colliders through O(alpha_S^4)
• Multiloop integrals in dimensional regularization made simple
• Percent level precision physics at the Tevatron: first genuine NNLO QCD corrections to q qbar -> t tbar + X
• Numerical evaluation of multiple polylogarithms
• FIRE5: a C++ implementation of Feynman Integral REduction
• Automatized analytic continuation of Mellin-Barnes integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• High-precision differential predictions for top-quark pairs at the LHC
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Top-quark pair hadroproduction at next-to-next-to-leading order in QCD
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• Virtual amplitudes and threshold behaviour of hadronic top-quark pair-production cross sections
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• Analytic Continuation of Massless Two-Loop Four-Point Functions
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the non-planar graphs
• Higher order corrections to spin correlations in top quark pair production at the LHC
• Master integrals for the NNLO virtual corrections to $\mu e$ scattering in QED: the planar graphs
• Two-Loop Leading Color Corrections to Heavy-Quark Pair Production in the Gluon Fusion Channel
• Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel
• Measurement of the t t-bar production cross section using events with one lepton and at least one jet in pp collisions at sqrt(s) = 13 TeV
• Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language
• Massive planar and non-planar double box integrals for light Nf contributions to gg->tt
• Two-Loop integrals for CP-even heavy quarkonium production and decays

Cited by in corpus (7)

• Constructing Canonical Feynman Integrals with Intersection Theory
• Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel
• Two-loop diagrams in non-relativistic QCD with elliptics
• Master integrals for the NNLO virtual corrections to $q\bar{q}\to t\bar{t}$ scattering in QCD: the non-planar graphs
• Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel
• Sunrise integral with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms
• Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay