The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions

TL;DR

This paper introduces a novel approach combining the Dimensional Recurrence and Analyticity (DRA) method with unitarity cuts to efficiently construct homogeneous solutions for multicomponent master integrals, enhancing computational techniques in quantum field theory.

Contribution

It establishes a connection between unitarity cuts and the homogeneous solutions of the DRA method, enabling systematic construction of solutions for coupled difference equations in multicomponent integrals.

Findings

Maximally cut integrals solve the homogeneous DRA equations.

The method simplifies the construction of solutions for complex integral systems.

Enhanced computational framework for multicomponent master integrals.

Abstract

We consider the application of the DRA method to the case of several master integrals in a given sector. We establish a connection between the homogeneous part of dimensional recurrence and maximal unitarity cuts of the corresponding integrals: a maximally cut master integral appears to be a solution of the homogeneous part of the dimensional recurrence relation. This observation allows us to make a necessary step of the DRA method, the construction of the general solution of the homogeneous equation, which, in this case, is a coupled system of difference equations.