Dispersion relations and Lattice QCD pinpoint the $\sigma$ meson

Lattice QCD is the model-independent, theoretical approach to study low-energy strong interactions. We can study unstable particles, known as resonances, using modeled reaction amplitudes describing lattice QCD spectra. These amplitudes satisfy only a subset of the mathematical requirements, unitarity, but fail to implement crossing symmetry and analyticity. This is a problem when extrapolating amplitudes far from the data region, e.g. in the case of resonances like the $\sigma$, leading to large systematic uncertainties in the pole position. In these works carried out by Arkaitz Rodas (ODU, co-PI), Jo Dudek (JLab/W&M, co-PI), and Robert Edwards (JLab, co-PI), we show how dispersion relations implement the additional constraints to reduce the allowed combination of parameterizations describing previously lattice-determined $\pi\pi$ partial waves. As a result, the $\sigma$ pole position is determined with minimal systematic uncertainty. Combining these with previous results, we provide a determination of the $\sigma$ particle’s fundamental parameters for four values of the pion mass.

Papers: Phys. Rev. D 109 (2024), 034513; Phys. Rev. D 108 (2023), 034513