DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions

157

115

We propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory approach to general relativity, without the need of subtracting iteration terms. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required D-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in D dimensions.

Section: A1 the General Methodologymentioning

confidence: 99%

Classical gravitational scattering from a gauge-invariant double copy

Brandhuber

Chen

Travaglini

et al. 2021

157

115

“…This is possible using a basis of independent special functions recently identified in the context of W b b production [50]. We obtain numerical results valid across the full phase space by applying the generalised series expansion approach [47,87,88] to the differential equations satisfied by the special functions appearing in the finite remainders.…”

Section: Jhep11(2021)012mentioning

confidence: 99%

Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC

Badger

Hartanto

Kryś

et al. 2021

We compute the two-loop QCD helicity amplitudes for the production of a Higgs boson in association with a bottom quark pair at a hadron collider. We take the approximations of leading colour and work in the five flavour scheme, where the bottom quarks are massless while the Yukawa coupling is non-zero. We extract analytic expressions from multiple numerical evaluations over finite fields and present the results in terms of an independent set of special functions that can be reliably evaluated over the full phase space.

“…[54] to deal with complicated multidimensional problems, see for example [55,56]. This strategy has also been implemented into the public code DiffExp [57]. 3 The input data for this code are the matrices that define the differential equations, and the boundary conditions in some limit, e.g., at some point (x 0 , y 0 ).…”

Section: Integration Of the Differential Equations In Terms Of Mplsmentioning

confidence: 99%

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

Duhr¹,

Smirnov

Tancredi

2021

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.