Vector Correlators in Lattice QCD: methods and applications

TL;DR

This paper explores lattice QCD methods for calculating the hadronic vacuum polarization, leveraging experimental data to improve predictions for (g-2)mu and electromagnetic coupling, and proposes strategies for more accurate and impactful computations.

Contribution

It introduces novel lattice techniques for calculating R(s) and the current correlator, and proposes using these calculations to determine lattice spacing and analyze finite-size effects.

Findings

Direct lattice calculation of R(s) in the threshold region using twisted boundary conditions.

Potential of the Euclidean current correlator to test experimental R(s) data for (g-2)mu.

Quantification and parametrization of finite-size effects from two-pion states.

Abstract

We discuss the calculation of the leading hadronic vacuum polarization in lattice QCD. Exploiting the excellent quality of the compiled experimental data for the e^+e^- --> hadrons cross-section, we predict the outcome of large-volume lattice calculations at the physical pion mass, and design computational strategies for the lattice to have an impact on important phenomenological quantities such as the leading hadronic contribution to (g-2)mu and the running of the electromagnetic coupling constant. First, the R(s) ratio can be calculated directly on the lattice in the threshold region, and we provide the formulae to do so with twisted boundary conditions. Second, the current correlator projected onto zero spatial momentum, in a Euclidean time interval where it can be calculated accurately, provides a potentially critical test of the experimental R(s) ratio in the region that is most relevant for (g-2)mu. This observation can also be turned around: the vector correlator at intermediate distances can be used to determine the lattice spacing in fm, and we make a concrete proposal in this direction. Finally, we quantify the finite-size effects on the current correlator coming from low-energy two-pion states and provide a general parametrization of the vacuum polarization on the torus.