Expanding the Interpolator Basis in the Variational Method to Explicitly Account for Backward Running States

TL;DR

This paper introduces a method to explicitly include backward running states in the variational approach of lattice QCD, enhancing signal clarity by expanding the interpolator basis and using linear combinations, demonstrated on a near-physical pion mass lattice.

Contribution

It presents a novel approach to account for backward states in the variational method by expanding the interpolator basis and employing the Time-Shift Trick, improving signal extraction.

Findings

Backward states can be explicitly modeled and removed.

Expanding the basis improves the signal quality.

Method demonstrated on a $64^4$ lattice near physical pion mass.

Abstract

In this paper, I show that backward (in time) running states can be explicitly accounted for by expanding the interpolator basis in the variational method in lattice QCD. The backward running states can then be removed by choosing an appropriate linear combination of interpolators, which improves the signal significantly. The proof of principle, which also makes use of the Time-Shift Trick (Generalized Pencil-of-Functions method), will be delivered at an example on a $64^4$ lattice close to the physical pion mass.