# Excited-state effects in nucleon structure on the lattice using hybrid interpolators

## TL;DR

This paper investigates hybrid interpolators with gluonic excitations in lattice QCD to reduce excited-state effects in nucleon structure calculations, finding mixed success depending on the observable.

## Contribution

It introduces a cost-effective variational approach using hybrid interpolators to mitigate excited-state contamination in lattice QCD nucleon studies.

## Key findings

- Reduces excited-state effects in two-point correlators.
- Suppresses some matrix element excited-state contributions.
- Enhancement of effects observed for certain observables.

## Abstract

It would be very useful to find a way of reducing excited-state effects in lattice QCD calculations of nucleon structure that has a low computational cost. We explore the use of hybrid interpolators, which contain a nontrivial gluonic excitation, in a variational basis together with the standard interpolator with tuned smearing width. Using the clover discretization of the field strength tensor, a calculation using a fixed linear combination of standard and hybrid interpolators can be done using the same number of quark propagators as a standard calculation, making this a cost-effective option. We find that such an interpolator, optimized by solving a generalized eigenvalue problem, reduces excited-state contributions in two-point correlators. However, the effect in three-point correlators, which are needed for computing nucleon matrix elements, is mixed: for some matrix elements such as the tensor charge, excited-state effects are suppressed, whereas for others such as the axial charge, they are enhanced. The results illustrate that the variational method is not guaranteed to reduce the net contribution from excited states except in its asymptotic regime, and suggest that it may be important to use a large basis of interpolators capable of isolating all of the relevant low-lying states.