A Stochastic Method for Semileptonic Form Factor Calculations on the Lattice

TL;DR

This paper introduces a stochastic propagator method as an alternative to the traditional sequential propagator in lattice QCD calculations of semileptonic form factors, aiming to improve efficiency and data collection.

Contribution

The paper presents a stochastic propagator technique that allows simultaneous access to multiple momentum and sink smearing combinations with fewer inversions, compared to the traditional method.

Findings

The stochastic method yields more correlators at fixed cost, reducing statistical errors at some kinematic points.

Stochastic noise is significant but can be managed with additional inversions.

The method's computational cost is comparable to the sequential method, with potential efficiency gains.

Abstract

We investigate an alternative to the Sequential Propagator Method used in Lattice QCD calculations of semileptonic form factors. We replace the sequential propagator with a stochastic propagator so that, in principle, all momentum and sink smearing combinations are available with only a single spin-color inversion. Practically, the stochastic noise is significant and must be reduced at the cost of more inversions. We study the behavior of the stochastic noise and compare the computational costs of this stochastic technique and the Sequential Propagator Method. We also present preliminary semileptonic form factor results using the stochastic technique on N_f=2 configurations with a non-perturbatively improved Sheikoleslami-Wohlert action generated by the QCDSF collaboration. At a fixed cost, measured in terms of the number of heavy-quark inversions, the method provides more correlators for the extraction of the form factors at various q^2's than the Sequential Propagator Method. These additional correlators reduce the total statistical errors of certain kinematic points, although the stochastic error is still comparable to the gauge error at other points.