QCD isospin breaking<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>χ</mml:mi></mml:math>PT low-energy constants from the instanton vacuum
Аннотация
In the framework of the instanton vacuum model we evaluate the chiral perturbation theory low-energy constants ${h}_{3}$, ${l}_{7}$. We found that in the instanton vacuum model the constant ${l}_{7}$ is very sensitive to the shape of the instanton and the instanton vacuum parameters. We evaluated the constant ${l}_{7}$ for two different zero-mode profiles and as a function of the average instanton size $\ensuremath{\rho}$ and interinstanton distance $R$. Our result agrees with an old ``order of magnitude'' estimate of this constant from Gasser and Leutwyler [Ann. Phys. (N.Y.) 158, 142 (1984).]. The obtained value of ${l}_{7}$ implies that the pure QCD contribution to the pion mass difference is small, $\ensuremath{\sim}1%$ of the observed experimental value.