Scalar and axial vector matrix elements of proton in quenched QCD: Calculation of both connected and disconnected contributions

Abstract

$\pi$-$N$ $\sigma$ term and proton axial vector matrix elements are calculated including disconnected contributions with a variant wall source method using the Wilson quark action at $\beta=5.7$ in quenched QCD. For the $\sigma$ term, we find $\sigma_{disc}/\sigma_{conn}=2.35(46)$ and $\sigma=44(6)$MeV--60(9)MeV. The fraction of proton spin carried by quarks is $\Delta\Sigma=\Delta{u}+\Delta{d}+\Delta{s}=+0.638(54)-0.347(46)-0.109(30)= +0.18(10)$.