Ratios of the light quark masses: Cubic curve vs ellipse

TL;DR

This paper derives bounds on light quark mass ratios by fitting meson mass data to an algebraic cubic curve, refining previous estimates with additional lattice simulation constraints.

Contribution

It introduces a new algebraic cubic curve model for quark mass ratios based on meson mass fits and lattice data constraints.

Findings

Refined ratio m_u/m_d = 0.455(8)

Derived bounds on light quark masses

Compared cubic curve and ellipse models

Abstract

The bounds on the light quark masses are obtained by fitting the squares of pseudoscalar meson masses $m_\pi^2$ and $m_K^2$ to second order in $1/N_c$ expansion. The result is an algebraic cubic curve whose coefficients are the known Weinberg values for the quark mass ratios $m_u/m_d$ and $m_s/m_d$. Additional restrictions arise when using the ratio $m_s/m_{ud}=27.23(10)$ quoted by FLAG for lattice simulations with four quark flavors. This provides a tight constraint on the ratio $m_u/m_d = 0.455(8)$.