Isospin Symmetry Breaking in the Quark Condensates, $<\bar{d}d>/=<\bar{u}u>$, as Estimated from QCD Sum Rules

Abstract

Isospin symmetry breaking in the quark condensates, $<\bar{d}d>/=<\bar{u}u>$, 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 $\frac{1}{2}(m_{{\Sigma }^{-}}+m_{{\Sigma }^0})-m_{{\Sigma }^{+}}$ in order to obtain a reasonable estimate on such isospin symmetry breaking parameter $\gamma$ defined as $(<\bar{d}d>-<\bar{u}u>)/<\bar{u}u>$. 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 $\frac{1}{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.

Comments: 10 pages, 2 figures, Latex