Referee this paper: cern.ch/133382
by R.J. Crewther, Di P Vecchia, (show more)
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This 1979 paper by R.J. Crewther, P. Di Vecchia, G. Veneziano, and E. Witten estimates the instanton effects in low-energy QCD in leading order in chiral effective theory. The chiral lagrangian describing the pion-octet is called current algebra here, as a nod to Gell-Mann. The paper finds the leading order effects of a theta-angle on eta decays and on the neutron electric dipole moment, in the limit of small explicit symmetry breaking, so small up down masses, and small pion mass. It uses the bound on neutron electric dipole moment to bound the magnitude of $\theta$ away from the CP invariant value of 0. Independently, it calculates Gell-Mann Okubo style mass relations in the pion octet for $\theta=\pi$ to explicitly rule out the other CP symmetric value.