The H-graph with equal masses in terms of multiple polylogarithms

Abstract

The initial phase of the inspiral process of a binary system producing gravitational waves can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph contributes. We consider the case where the two objects making up the binary system have equal masses. We express all master integrals related to the equal-mass H-graph up to weight four in terms of multiple polylogarithms. We provide a numerical program which evaluates all master integrals up to weight four in the physical regions with arbitrary precision.

arXiv comment19 pages, v2: version to be published, v3: boundary value for $J_{25}^{(4)}$ corrected

References in corpus (46)

• Effective one-body approach to general relativistic two-body dynamics
• Multiloop integrals in dimensional regularization made simple
• Cuba - a library for multidimensional numerical integration
• Transition from inspiral to plunge in binary black hole coalescences
• An Effective Field Theory of Gravity for Extended Objects
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Numerical evaluation of multiple polylogarithms
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• The Effective Field Theorist's Approach to Gravitational Dynamics
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• Integral Reduction with Kira 2.0 and Finite Field Methods
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• General Relativity from Scattering Amplitudes
• Reduze 2 - Distributed Feynman Integral Reduction
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• On Post-Minkowskian Hamiltonians in General Relativity
• Resolution of singularities for multi-loop integrals
• The massless higher-loop two-point function
• Gravitational Bremsstrahlung from Reverse Unitarity
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Static two-body potential at fifth post-Newtonian order
• Classical Gravity from Loop Amplitudes
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• RationalizeRoots: Software Package for the Rationalization of Square Roots
• FORM version 4.2
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• On the four-loop static contribution to the gravitational interaction potential of two point masses
• The General Relativistic Two Body Problem and the Effective One Body Formalism
• Loopedia, a Database for Loop Integrals
• Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics
• A $QQ\to QQ$ planar doublebox in canonical form
• Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell--Yan scattering

Cited by in corpus (7)

• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Machine Learning Post-Minkowskian Integrals
• Analytic two-loop master integrals for $tW$ production at hadron colliders. Part II
• Analytic results for two-loop planar master integrals for Bhabha scattering