Non-analytic terms of string amplitudes from partial waves

TL;DR

This paper introduces a formalism using partial-wave decomposition to analyze non-analytic terms in string amplitudes, providing new insights into their structure and contributions at various loop orders.

Contribution

It presents a novel approach to compute the iterative s-channel discontinuity of four-point amplitudes at any loop order, with applications to low-energy superstring expansions.

Findings

New results for leading and sub-leading logarithmic contributions beyond genus one.

Elucidation of the structure of non-analytic threshold terms.

Efficient computation of contributions from different worldsheet topologies.

Abstract

We describe a general formalism based on the partial-wave decomposition to compute the iterative $s$-channel discontinuity of four-point amplitudes at any loop order. As an application, we focus on the low-energy expansions of type I and II superstring amplitudes. Besides providing new results for their leading and sub-leading logarithmic contributions beyond genus one, our approach elucidates the general structure of non-analytic threshold terms. In the case of open strings, the use of orthogonal colour projectors allows us to efficiently compute all contributions from different worldsheet topologies at a given loop order.