Bounds on the Light Quark Masses: the scalar channel revisited

TL;DR

This paper derives lower bounds on the sum of up and down quark masses using dispersion relations, scalar spectral functions, and perturbative QCD, suggesting these bounds are higher than recent lattice QCD estimates.

Contribution

It revisits the bounds on light quark masses through a theoretical approach combining dispersion relations and QCD, providing potentially higher lower bounds than previous lattice results.

Findings

Lower bounds on m_u + m_d are higher than recent lattice QCD estimates.

The approach combines long-distance spectral function properties with short-distance perturbative QCD.

Results suggest a reevaluation of light quark mass estimates may be necessary.

Abstract

We evaluate lower bounds on the sum of the up and down quark masses. The bounds follow from the constraints provided by the dispersion relation obeyed by the two--point function of the scalar current density when combined with properties of the scalar spectral function at long--distances and perturbative QCD at short--distances. Our results point to values of $m_u+m_d$ somewhat higher than those reported recently in the literature using lattice QCD simulations.