CanθQCD=π?

Abstract

Recent work suggests that wormholes in spacetime may drive ${\theta }_{\mathrm{QCD}}$ to π, and it has been argued that this is not in conflict with any observations. We have therefore determined current-mass ratios of the light quarks in second-order chiral perturbation theory, with attention to the relative sign of the up-quark mass. We discuss an ambiguity which makes it impossible to determine the quark mass ratios from chiral-Lagrangian considerations alone. Using results from lattice QCD we resolve the ambiguity to obtain $m_u$/$m_d$=0.61±0.26, $m_s$/$m_d$=21±2, implying that ${\theta }_{\mathrm{QCD}=0\mathrm{}}$. .AE