Soft Matters, or the Recursions with Massive Spinors

TL;DR

This paper develops recursion relations for scattering amplitudes involving massive particles of any spin, combining BCFW shifts with soft limits, leading to new insights and practical tools for calculating complex scattering processes.

Contribution

It introduces a novel two-parameter shift method for massive particles, reformulates soft theorems for massive amplitudes, and provides new results on non-minimal interactions and amplitude representations.

Findings

Reformulated soft theorems applicable to massive particles

Derived recursion relations using combined BCFW and soft limits

Provided a new representation of Compton scattering amplitudes

Abstract

We discuss recursion relations for scattering amplitudes with massive particles of any spin. They are derived via a two-parameter shift of momenta, combining a BCFW-type spinor shift with the soft limit of a massless particle involved in the process. The technical innovation is that spinors corresponding to massive momenta are also shifted. Our recursions lead to a reformulation of the soft theorems. The well-known Weinberg's soft factors are recovered and, in addition, the subleading factors appear reshaped such that they are directly applicable to massive amplitudes in the modern on-shell language. Moreover, we obtain new results in the context of non-minimal interactions of massive matter with photons and gravitons. These soft theorems are employed for practical calculations of Compton and higher-point scattering. As a by-product, we introduce a convenient representation of the Compton scattering amplitude for any mass and spin.