Moments from Momentum Derivatives in Lattice QCD

TL;DR

This paper introduces a momentum-derivative approach in lattice QCD that avoids divergences and allows for separate determination of even and odd moments, demonstrated on nucleon transversity moments.

Contribution

It presents a novel momentum-space method for extracting moments in lattice QCD that circumvents power divergences and enables separate analysis of even and odd moments.

Findings

Successfully determined the first three moments beyond gT in nucleon transversity.

Demonstrated the method's ability to avoid power divergent mixings.

Showed that moments can be extracted order by order to all orders.

Abstract

We show that the traditional moments approach in lattice QCD, based on operator product expansion (OPE), can be realized in a way that utilizes derivatives in momentum rather than in distance. This also avoids power divergent mixings, and thus allows to extract moments order by order, to all orders in principle. Moreover, by exploiting the symmetry of lattice matrix elements,we can determine the even and odd moments separately. As a demonstrative example, we determine the first three moments beyond the tensor charge gT of the isovector quark transversity distribution in the nucleon.