Massive Two-Loop Heavy Particle Diagrams

TL;DR

This paper analytically evaluates two-loop master integrals involving heavy particles in effective field theories using differential equations and recurrence relations, advancing computational techniques in quantum field theory.

Contribution

It introduces a method to compute two-loop integrals with heavy lines analytically, expanding the toolkit for effective field theory calculations.

Findings

Master integrals for heavy particle diagrams are derived analytically.

The methods improve accuracy and efficiency in multi-loop calculations.

Results facilitate more precise predictions in theories with heavy fields.

Abstract

We determine the master integrals for vertex and propagator diagrams that appear in effective field theories containing heavy fields. The integrals involve at least one heavy line, and the standard lines include an arbitrary mass scale. The evaluation is done analytically with modern techniques. We employ the methods of differential equations and dimensional recurrence relations to evaluate said integrals up to two-loop order.