Constructing massive on-shell contact terms

TL;DR

This paper systematically derives independent four-point contact terms for massive particles using a novel on-shell formalism, facilitating future amplitude computations in theories like the electroweak sector.

Contribution

It introduces a comprehensive method for constructing massive contact terms using little-group-covariant spinor formalism, including relations to massless amplitudes and applications to the standard model.

Findings

Derived independent four-point contact terms for massive particles.

Listed three-point amplitudes up to spin-3 for massive states.

Specialized results to the electroweak sector of the standard model.

Abstract

The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent four-point contact terms involving massive scalars, spin-1/2 fermions, and vectors. Independent three-point amplitudes are also listed for massive particles up to spin-3. We make extensive use of the simple relations between massless and massive amplitudes in this formalism. Our general results are specialized to the (broken-phase) particle content of the electroweak sector of the standard model. The (anti)symmetrization among identical particles is then accounted for. This work opens the way for the on-shell computation of massive four-point amplitudes.