Isospin Symmetry Breaking in the Quark Condensates, $< \bar dd>\not= < \bar uu>$, as Estimated from QCD Sum Rules

Abstract

Isospin symmetry breaking in the quark condensates, $< \bar dd> \not= < \bar uu>$, is a fundamental parameter in both the QCD sum rule studies and the chiral perturbation theory. In this article, we apply the QCD sum rule method to treat the hyperon mass difference ${1\over 2}(m_{\Sigma^-}+m_{\Sigma^0})-m_{\Sigma^+}$ in order to obtain a reasonable estimate on such isospin symmetry breaking parameter $\gamma$ defined as $(< \bar dd>-< \bar uu>)/ < \bar uu>$. Note that the electromagnetic contributions to the particular mass difference are expected to cancel almost completely. Using the light-quark mass difference $m_d-m_u=4\pm 1$ MeV and the experimental data ${1\over 2}(m_{\Sigma^-}+m_{\Sigma^0})-m_{\Sigma^+}$$=5.62\pm 0.13$ MeV, we obtain $\gamma= -0.011\pm 0.001$, a value which is slightly larger than the commonly adopted value and is of smaller uncertainty.