Goldstone Boson Scattering with a Light Composite Scalar

TL;DR

This study investigates how a light scalar resonance influences Goldstone boson scattering in a nearly conformal gauge theory, using lattice simulations and effective field theory to analyze low-energy interactions.

Contribution

It provides the first nonperturbative lattice analysis of Goldstone boson scattering in SU(3) with eight flavors, incorporating a light scalar via dilaton EFT.

Findings

EFT accurately describes lattice scattering data within expected correction sizes.

The light scalar significantly affects the scattering phase shifts.

Results support the relevance of a light scalar in near-conformal gauge theories.

Abstract

The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studies) on Goldstone boson scattering, employing a dilaton effective field theory (EFT) at the tree level. The EFT gives a good description of the scattering data, insofar as the magnitude of deviations between EFT and lattice data are no larger than the expected size of next-to-leading order corrections in the EFT.