Three-loop planar master integrals for heavy-to-light form factors

TL;DR

This paper analytically computes three-loop planar master integrals for heavy-to-light form factors using differential equations and harmonic polylogarithms, simplifying boundary conditions through a canonical basis.

Contribution

It introduces a canonical basis approach to simplify the calculation of three-loop master integrals for heavy-to-light form factors.

Findings

All 71 master integrals expressed in harmonic polylogarithms.

Simplified boundary conditions for differential equations.

Enhanced analytical methods for high-loop integrals.

Abstract

We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be determined, and the solution of differential equations is greatly simplified. The results for seventy-one master integrals at general kinematics are all expressed in terms of harmonic polylogarithms.