Chiral limit of QCD

TL;DR

This paper analyzes quenched chiral perturbation theory in QCD, examining how singular terms from the η' meson affect various quantities and highlighting limitations in current extrapolation methods for light quark masses.

Contribution

It provides a detailed analysis of quenched chiral perturbation theory effects and discusses the breakdown of standard extrapolation formulas for light quarks in quenched QCD.

Findings

Standard expressions break down for m_q < m_s/2 in quenched data

Singular η' contributions affect the calculation of nucleon axial charge

Limitations in current methods for determining light quark masses from lattice QCD

Abstract

This talk contains an analysis of quenched chiral perturbation theory and its consequences. The chiral behavior of a number of quantities such as the pion mass $m_\pi^2$, the Bernard-Golterman ratios $R$ and $\chi$, the masses of nucleons, and the kaon B-parameter are examined to see if the singular terms induced by the additional Goldstone boson,$\eta'$, are visible in present data. The overall conclusion (different from what I presented at the lattice meeting) of this analysis is that, with some caveats on the extra terms induced by $\eta'$ loops, the standard expressions break down when extrapolating the quenched data with $m_q < m_s/2$ to physical light quarks. I then show that due to the single and double poles in the quenched $\eta'$, the axial charge of the proton cannot be calculated using the Adler-Bell-Jackiw anomaly condition. I conclude with a review of the status of the calculation of light quark masses from lattice QCD.