Controlling unwanted exponentials in lattice calculations of radiative leptonic decays

TL;DR

This paper compares methods to control systematic errors from unwanted exponentials and excited states in lattice QCD calculations of radiative leptonic decays, improving accuracy in form factor determination.

Contribution

It introduces and compares 3d and 4d sequential propagator methods, and a hybrid approach, to better control systematic uncertainties in lattice QCD calculations.

Findings

3d sequential propagator better controls intermediate state errors.

4d sequential propagator more effectively manages excited state errors.

Hybrid approach improves overall systematic error control.

Abstract

Two important sources of systematic errors in lattice QCD calculations of radiative leptonic decays are unwanted exponentials in the sum over intermediate states and unwanted excited states created by the meson interpolating field. Performing the calculation using a 3d sequential propagator allows for better control over the systematic uncertainties from intermediate states, while using a 4d sequential propagator allows for better control over the systematic uncertainties from excited states. We calculate form factors using both methods and compare how reliably each controls these systematic errors. We also employ a hybrid approach involving global fits to data from both methods.