Counting and building operators in theories with hidden symmetries and application to HEFT

TL;DR

This paper develops new methods for counting operators in Higgs Effective Field Theory (HEFT) considering hidden symmetries, providing explicit formulas and computational tools to facilitate EFT operator basis construction.

Contribution

It introduces a new counting formula for HEFT operators incorporating full gauge symmetry and connects different symmetry frameworks explicitly.

Findings

Derived a new operator counting formula for HEFT.

Connected CCWZ and linear frames in symmetry analysis.

Provided Mathematica code for operator enumeration.

Abstract

Identifying a full basis of operators to a given order is key to the generality of Effective Field Theory (EFT) and is by now a problem of known solution in terms of the Hilbert series. The present work is concerned with hidden symmetry in general and Higgs EFT in particular and {\it(i)} connects the counting formula presented in [1] in the CCWZ formulation with the linear frame and makes this connection explicit in HEFT {\it (ii)} outlines the differences in perturbation theory in each frame {\it (iii)} presents a new counting formula with measure in the full $SU(3)\times SU(2)\times U(1)$ group for HEFT and {\it (iv)} provides a Mathematica code that produces the number of operators at the user-specified order in HEFT.