Lorentz Constraints on Massive Three-Point Amplitudes

TL;DR

This paper investigates how Lorentz symmetry constrains three-point amplitudes involving massive particles, deriving their generic form and identifying conditions that fix their structure, especially in the UV limit.

Contribution

It extends known massless amplitude constraints to cases with massive particles, providing a generic form and fixing conditions for three-point amplitudes under Lorentz symmetry.

Findings

The generic functional form of massive three-point amplitudes is derived.

Constants in the amplitude relate to coupling constants, fixed in certain limits.

A universal form of the amplitude is identified in a specific Lorentz frame.

Abstract

Using the helicity-spinor language we explore the non-perturbative constraints that Lorentz symmetry imposes on three-point amplitudes where the asymptotic states can be massive. As it is well known, in the case of only massless states the three-point amplitude is fixed up to a coupling constant by these constraints plus some physical requirements. We find that a similar statement can be made when some of the particles have mass. We derive the generic functional form of the three-point amplitude by virtue of Lorentz symmetry, which displays several functional structures accompanied by arbitrary constants. These constants can be related to the coupling constants of the theory, but in an unambiguous fashion only in the case of one massive particle. Constraints on these constants are obtained by imposing that in the UV limit the massive amplitude matches the massless one. In particular, there is a certain Lorentz frame, which corresponds to projecting all the massive momenta along the same null momentum, where the three-point massive amplitude is fully fixed, and has a universal form.