Unitarity Bounds and Basis Transformations in SMEFT: An Analysis of Warsaw and SILH Bases

TL;DR

This paper calculates and compares unitarity bounds for dimension-six operators in SMEFT within Warsaw and SILH bases, demonstrating how bounds transform under basis changes using the equivalence theorem.

Contribution

It provides explicit analytical unitarity bounds in both bases and clarifies how these bounds transform under basis changes using a coupled channel analysis.

Findings

Unitarity bounds can be transformed between bases using the equivalence theorem.

Explicit bounds are calculated for both Warsaw and SILH bases.

Transformation rules depend on the operator subsets involved in the basis change.

Abstract

The equivalence between the Warsaw and SILH bases in Standard Model Effective Field Theory is well established, with transformation rules connecting the two via equations of motion and field redefinitions. This study presents an explicit calculation of the analytical unitarity bounds-defined as the marginal limit of the parameter space-for dimension-six operators within both the Warsaw and SILH bases. We employ a coupled channel analysis to scrutinize scattering processes involving vector bosons and fermions. We conduct a comprehensive investigation into the transformation of unitarity bounds under changes in the operator basis. Our findings demonstrate that the transformation rules, as implicated by the equivalence theorem, can be directly applied to convert unitarity bounds from one basis to another, provided that the operators involved in the transformation rules do not belong to the same subset defined by a block in the coupled channel matrix.