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

TL;DR

This paper calculates scalar and axial vector matrix elements of the proton in quenched QCD, including both connected and disconnected contributions, providing insights into the sigma term and proton spin structure.

Contribution

It introduces a method to compute both connected and disconnected contributions to proton matrix elements using a variant wall source in quenched QCD.

Findings

The sigma term is estimated as 44-60 MeV.

The quark spin contribution to the proton is approximately 0.18.

Disconnected contributions are significant in the calculations.

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 $\Delta\Sigma=\Delta{u}+\Delta{d}+\Delta{s}=+0.638(54)-0.347(46)-0.109(30)= +0.18(10)$.