Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons

TL;DR

This paper employs on-shell methods to compute tree-level EFT amplitudes involving scalars and vectors coupled to gluons, avoiding explicit operator references and revealing the structure of EFT operators through kinematic polynomials.

Contribution

It introduces an on-shell approach to calculate EFT amplitudes directly, linking the number of operators to polynomial structures in Mandelstam invariants without referencing specific operators.

Findings

Calculated key amplitudes relevant for LHC processes

Derived massless-$Z'$ amplitudes from massive ones

Showed decomposition of massive amplitudes into massless components

Abstract

We use on-shell methods to calculate tree-level effective field theory (EFT) amplitudes, with no reference to the EFT operators. Lorentz symmetry, unitarity and Bose statistics determine the allowed kinematical structures. As a by-product, the number of independent EFT operators simply follows from the set of polynomials in the Mandelstam invariants, subject to kinematical constraints. We demonstrate this approach by calculating several amplitudes with a massive, SM-singlet, scalar ($h$) or vector ($Z^\prime$) particle coupled to gluons. Specifically, we calculate $hggg$, $hhgg$ and $Z^\prime ggg$ amplitudes, which are relevant for the LHC production and three-gluon decays of the massive particle. We then use the results to derive the massless-$Z^\prime$ amplitudes, and show how the massive amplitudes decompose into the massless-vector plus scalar amplitudes. Amplitudes with the gluons replaced by photons are straightforwardly obtained from the above.