Progress on pseudoscalar flavour-singlets in Sp(4) with mixed fermion representations

TL;DR

This study investigates the spectrum of pseudoscalar flavour-singlet mesons in an Sp(4) gauge theory with mixed fermion representations, relevant for composite Higgs models, revealing light states and their mixing behavior.

Contribution

First measurement of pseudoscalar flavour-singlet meson masses and mixing in an Sp(4) gauge theory with mixed fermions, informing composite Higgs model building.

Findings

Two light pseudoscalar flavour-singlet states identified.

One state is a Nambu-Goldstone boson, the other acquires mass from the axial anomaly.

Mixing effects are small at moderate fermion masses.

Abstract

We measure the masses of the pseudoscalar flavour-singlet meson states in the $Sp(4)$ gauge theory coupled to two Dirac fermions transforming in the fundamental representation and three Dirac fermions in the antisymmetric representation. This theory provides a compelling ultraviolet completion for the minimal composite Higgs model implementing also partial compositeness for the top quark. The spectrum contains two, comparatively light, pseudoscalar flavour-singlet states, which mix with one another. One of them is a Nambu-Goldstone boson (in the massless limit), whereas the other receives a mass from the $U(1)_A$ axial anomaly. We demonstrate how to measure the mixing between these two states. For moderately heavy fermion masses, we find that the two wave functions are dominated by one of the fermion representations, mixing effects being small.