Threshold expansion of the sunset diagram

TL;DR

This paper presents an algorithm for analytically expanding the two-loop sunset diagram near its threshold using threshold expansion and dimensional regularization, enabling precise calculations of complex Feynman integrals.

Contribution

It introduces a systematic algorithm with recurrence relations for evaluating the sunset diagram's expansion at threshold with arbitrary masses and propagator powers.

Findings

Provides explicit recurrence relations for sunset diagrams.

Enables analytical calculation of arbitrary order expansions.

Applicable to diagrams with general masses and propagator powers.

Abstract

By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its threshold, i.e. in any given order in the difference between the external momentum squared and its threshold value, (m_1+m_2+m_3)^2. In particular, this algorithm includes an explicit recurrence procedure to analytically calculate sunset diagrams with arbitrary integer powers of propagators at the threshold.