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

Abstract

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