A new representation of the Adler function for lattice QCD

TL;DR

This paper introduces a novel lattice QCD representation for the Adler function, enabling continuous virtuality access and analyzing finite-size effects, with a focus on flavor structure and disconnected diagram contributions.

Contribution

It presents a new representation of the Adler function for lattice QCD that allows continuous virtuality access regardless of flavor structure, and provides a theoretical analysis of finite-size effects and flavor contributions.

Findings

The new representation enables continuous access to the Adler function across virtualities.

Finite-size effects are analyzed using operator product expansion and spectral representation.

Disconnection diagram contributions are independently confirmed.

Abstract

We address several aspects of lattice QCD calculations of the hadronic vacuum polarization and the associated Adler function. We implement a representation derived previously which allows one to access these phenomenologically important functions for a continuous set of virtualities, irrespective of the flavor structure of the current. Secondly we present a theoretical analysis of the finite-size effects on our particular representation of the Adler function, based on the operator product expansion at large momenta and on the spectral representation of the Euclidean correlator at small momenta. Finally, an analysis of the flavor structure of the electromagnetic current correlator is performed, where a recent theoretical estimate of the Wick-disconnected diagram contributions is rederived independently and confirmed.