Surfaceology for Colored Yukawa Theory

TL;DR

This paper extends the surface integral formalism to colored Yukawa theories, providing a compact all-loop amplitude formula that simplifies the structure and computation of scattering amplitudes involving colored fermions.

Contribution

It introduces a new curve integral formalism for colored Yukawa theories, enabling compact all-loop amplitude expressions and efficient computation methods.

Findings

Derived a compact all-loop amplitude integrand formula.

Extended the formalism to include colored fermionic matter.

Provided an efficient sum-over-determinants formula for loop amplitudes.

Abstract

Arkani-Hamed and collaborators have recently shown that scattering amplitudes for colored theories can be expressed as integrals over combinatorial objects simply constructed from surfaces decorated by kinematic data. In this paper we extend the curve integral formalism to theories with colored fermionic matter and present a compact formula for the all-loop, all-genus, all-multiplicity amplitude integrand of a colored Yukawa theory. The curve integral formalism makes certain properties of the amplitudes manifest and repackages non-trivial numerators into a single combinatorial object. We also present an efficient formula for $L$-loop integrated amplitudes in terms of a sum over $2^L$ combinatorial determinants.