Controlling excited-state contributions with distillation in lattice QCD calculations of nucleon isovector charges gSu−d , gAu−d , gTu−d

Colin Egerer,Frank Winter,David Richards

doi:10.1103/physrevd.99.034506

Abstract

We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges $g_S^{u-d}$, $g_A^{u-d}$, and $g_T^{u-d}$. We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited-states compared to use of a single, local interpolating operator. The additional benefit arising through the use of the variational method in the distillation approach is less dramatic, but nevertheless significant given that it requires no additional Dirac inversions.

Highlights

The past decade has seen tremendous improvement in the ability of Lattice QCD (LQCD) calculations to provide results that can confront experiment
Lattice computations of some key quantities remain at odds with experimental determinations, including the momentum fraction carried by partons in the nucleon, and, notably, the axial-vector charge, guA−d, of the nucleon. These discrepancies are often attributed to finite-volume effects, and to the contribution of excited states to ground-state matrix elements
The calculation of the axial-vector charge has been a particular focus within the lattice community, and a dedicated effort to resolve these discrepancies has demonstrated success [1], using a method to control excited states inspired by the Feynman-Hellman theorem

Summary

Introduction

The past decade has seen tremendous improvement in the ability of Lattice QCD (LQCD) calculations to provide results that can confront experiment. Lattice computations of some key quantities remain at odds with experimental determinations, including the momentum fraction carried by partons in the nucleon, and, notably, the axial-vector charge, guA−d, of the nucleon. These discrepancies are often attributed to finite-volume effects, and to the contribution of excited states to ground-state matrix elements. The calculation of the axial-vector charge has been a particular focus within the lattice community, and a dedicated effort to resolve these discrepancies has demonstrated success [1], using a method to control excited states inspired by the Feynman-Hellman theorem. “distillation” [2], and the variational method for the case of the nucleon charges guA−d, guS−d and guT−d.

Methods

Results

Conclusion