A Non-linear Representation of General Scalar Extensions of the Standard Model for HEFT Matching

TL;DR

This paper introduces a non-linear $U$ representation to simplify the matching process between HEFT and general scalar extensions of the Standard Model, providing a unified framework for various models.

Contribution

It presents a novel non-linear $U$ representation for scalar multiplets, enabling straightforward HEFT matching with general scalar extensions of the Standard Model.

Findings

Complete matching between HEFT and real triplet extension demonstrated.

U representation formulated for general scalar extensions.

Simplifies the process of model matching in Higgs Effective Field Theory.

Abstract

We introduce a non-linear representation of ultraviolet~(UV) complete model, $U$ representation, under which matching HEFT to general scalar extensions of the standard model is straightforward. The main idea is to express a scalar multiplet in its linear form rotated by $U$ matrices, where $U$ matrix is exponential form of Goldstones based on Pauli matrices and meanwhile is a special $SU(2)_L$ rotation. All together the doublet is expressed in $U$ matrix multiplying a doublet column or bidoublet matrix, which is composed of physical Higgs. We show a complete matching between HEFT and real triplet extension. Meanwhile, under tensor notation, we give $U$ representation for general scalar extensions.