QCD sum rules for hyperon-nucleon interactions

Abstract

We investigate the hyperon-nucleon interactions in the QCD sum rule starting from the nucleon matrix element of the hyperon correlation function. Through the dispersion relation, the correlation function in the operator product expansion (OPE) is related with its integral over the physical energy region. The dispersion integral around the hyperon-nucleon $(YN)$ threshold is identified as a measure of the interaction strength in the $YN$ channel. The Wilson coefficients of the OPE for the hyperon correlation function are calculated. The obtained sum rules relate $YN$ interaction strengths to the nucleon matrix elements of the quark-gluon composite operators, which include strange quark operators as well as up and down quark operators. It is found that the $YN$ interaction strengths are smaller than the $NN$ interaction strength since the nucleon matrix elements of strange quark operators are smaller than those of up and down quark operators. Among $YN$ channels $\ensuremath{\Lambda}N$ channel has stronger interaction than $\ensuremath{\Sigma}N$ and $\ensuremath{\Xi}N$ channels. It is also found that the interaction strength is greater in the ${\ensuremath{\Sigma}}^{+}p\phantom{\rule{0.3em}{0ex}}({\ensuremath{\Xi}}^{0}p)$ channel than in the ${\ensuremath{\Sigma}}^{\ensuremath{-}}p\phantom{\rule{0.3em}{0ex}}({\ensuremath{\Xi}}^{\ensuremath{-}}p)$ channel since the nucleon matrix elements of up quark operators are greater than those of down quark operators. The spin-dependent part is much smaller than the spin-independent part in the $YN$ and $NN$ channels. The results of the sum rules are compared with those of the phenomenological meson-exchange models.