Using analytic continuation for the hadronic vacuum polarization computation

TL;DR

This paper explores the use of analytic continuation to compute the hadronic vacuum polarization function in different momentum regions, with applications to the Adler function and muon magnetic moment.

Contribution

It demonstrates the feasibility of analytic continuation for hadronic calculations and discusses potential further applications in particle physics.

Findings

Successful application to Adler function

Effective computation of muon anomalous magnetic moment

Positive outlook for future use of the method

Abstract

We present two examples of applications of the analytic continuation method for computing the hadronic vacuum polarization function in space- and time-like momentum regions. These examples are the Adler function and the leading order hadronic contribution to the muon anomalous magnetic moment. We comment on the feasibility of the analytic continuation method and provide an outlook for possible further applications.