Ratios of the light quark masses: Cubic curve vs ellipse

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 $m_u/m_d=0.455(8)$.

arXiv comment8 pages, 2 figuras, 2 tables, Version accepted for publication in Phys. Rev. D

References in corpus (26)

• FLAG Review 2021
• Ab initio calculation of the neutron-proton mass difference
• The ratios of the light quark masses
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Virtual Photons in Chiral Perturbation Theory
• Nambu Jona-Lasinio Like Models and the Low Energy Effective Action of QCD
• Light Meson Physics from Maximally Twisted Mass Lattice QCD
• Electromagnetic Splittings and Light Quark Masses in Lattice QCD
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• Lattice QCD at the physical point: light quark masses
• Dispersive analysis of the decay eta -> 3 pi
• Electromagnetic Corrections for Pions and Kaons : Masses and Polarizabilities
• Final State Interactions and Khuri-Treiman Equations in $\eta \to 3\pi$ decays
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Bounds on the light quark masses
• Violations of Dashen's Theorem
• Electromagnetic corrections in the anomaly sector
• Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions
• Up and down quark masses and corrections to Dashen's theorem from lattice QCD and quenched QED
• SU(2) chiral perturbation theory low-energy constants from 2+1 flavor staggered lattice simulations
• The decay $\eta \to 3\pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$
• Extended chiral Khuri-Treiman formalism for $\eta \to 3\pi$ and the role of the $a_0(980)$, $f_0(980)$ resonances
• Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons
• Lattice computation of the electromagnetic contributions to kaon and pion masses
• Proper-time method for unequal masses
• $1/N_c$ Nambu -- Jona-Lasinio model: Electrically charged and strange pseudoscalars