Calculation of 1-loop Hexagon Amplitudes in the Yukawa Model

TL;DR

The paper addresses the challenge of computing one-loop multi-particle amplitudes by employing string-inspired worldline master formulas for the Yukawa model, focusing on the massless hexagon (N=6) as a representative case. It shows that all tensor structures collapse to scalar integrals and demonstrates explicit cancellations of spurious poles during reduction from hexagon to pentagon to boxes, ultimately expressing the amplitude in terms of a finite combination involving a triangle integral and logarithms. The authors establish the equivalence with the Feynman-diagram approach and obtain a compact, infrared-finite result that holds after summing over orientation-preserving permutations. This work suggests a scalable framework for higher-N amplitudes and motivates extensions to off-shell, massive, and gauge-theory scenarios, potentially enabling efficient multi-particle one-loop computations.

Abstract

We calculate a class of one-loop six-point amplitudes in the Yukawa model. The construction of multi-particle amplitudes is done in the string inspired formalism and compared to the Feynman diagrammatic approach. We show that there exists a surprisingly efficient way of calculating such amplitudes by using cyclic identities of kinematic coefficients and discuss in detail cancellation mechanisms of spurious terms. A collection of formulas which are useful for the calculation of massless hexagon amplitudes is given.