On the extraction of zero momentum form factors on the lattice

TL;DR

The paper introduces a lattice method to extract zero momentum transfer form factors directly from correlation functions by expanding in external momenta, avoiding model-dependent extrapolations.

Contribution

It presents a novel approach to determine Lorentz-invariant form factors at zero momentum transfer directly from lattice correlation functions.

Findings

Validated the method with axial current correlators.

Applied to semileptonic decay form factors.

Used for hadronic vacuum polarization in muon g-2 calculations.

Abstract

We propose a method to expand correlation functions with respect to the spatial components of external momenta. From the coefficients of the expansion it is possible to extract Lorentz-invariant form factors at zero spatial momentum transfer avoiding model dependent extrapolations. These objects can be profitably calculated on the lattice. We have explicitly checked the validity of the proposed procedure by considering two-point correlators with insertions of the axial current, the form factors of the semileptonic decay of pseudoscalar mesons, and the hadronic vacuum polarization tensor entering, for example, the lattice calculation of the anomalous magnetic moment of the muon.