Mixing between flavor singlets in lattice gauge theories coupled to matter fields in multiple representations

TL;DR

This paper presents a detailed numerical study of flavor-singlet mixing in a lattice gauge theory with multiple fermion representations, relevant for composite Higgs models and top partial compositeness.

Contribution

It introduces a novel lattice approach to measure masses and mixing angles of flavor-singlet states in theories with multiple fermion representations.

Findings

Effective measurement of masses and mixing angles despite noisy disconnected diagrams

Application of advanced smearing techniques and eigenvalue methods in lattice simulations

First extensive numerical analysis of flavor-singlet mixing in this class of theories

Abstract

We provide the first extensive, numerical study of the non-trivial problem of mixing between flavor-singlet composite states emerging in strongly coupled lattice field theories with matter field content consisting of fermions transforming in different representations of the gauge group. The theory of interest is the minimal candidate for a composite Higgs model that also accommodates a mechanism for top partial compositeness: the $Sp(4)$ gauge theory coupled to two (Dirac) fermions transforming as the fundamental and three as the two-index antisymmetric representation of the gauge group, respectively. We apply an admixture of APE and Wuppertal smearings, as well as the generalized eigenvalue problem approach, to two-point functions involving flavor-singlet mesons, for ensembles having time extent longer than the space extent. We demonstrate that, in the region of lattice parameter space accessible to this study, both masses and mixing angles can be measured effectively, despite the presence of (numerically noisy) contributions from disconnected diagrams.