Matrix elements from moments of correlation functions

TL;DR

This paper introduces a method to compute matrix elements and their momentum-space derivatives from lattice correlation functions, enabling direct access to form factor slopes and charge radii in hadronic physics.

Contribution

The authors derive expressions relating momentum-space derivatives of matrix elements to coordinate-space moments, and demonstrate their application to calculate form factor slopes on the lattice.

Findings

Successfully computed the slope of the isovector form factor at various Q^2.

Provided a method to obtain the charge radius directly from lattice data.

Showed potential for broader applications in hadronic matrix element calculations.

Abstract

Momentum-space derivatives of matrix elements can be related to their coordinate-space moments through the Fourier transform. We derive these expressions as a function of momentum transfer $Q^2$ for asymptotic in/out states consisting of a single hadron. We calculate corrections to the finite volume moments by studying the spatial dependence of the lattice correlation functions. This method permits the computation of not only the values of matrix elements at momenta accessible on the lattice, but also the momentum-space derivatives, providing {\it a priori} information about the $Q^2$ dependence of form factors. As a specific application we use the method, at a single lattice spacing and with unphysically heavy quarks, to directly obtain the slope of the isovector form factor at various $Q^2$, whence the isovector charge radius. The method has potential application in the calculation of any hadronic matrix element with momentum transfer, including those relevant to hadronic weak decays.