Connected, Disconnected and Strange Quark Contributions to HVP

TL;DR

This paper calculates vector two-point functions in Chiral Perturbation Theory to estimate the ratio of disconnected to connected contributions, including strange quark effects, and finds the ratio to be small and negative.

Contribution

It extends previous estimates of the disconnected to connected ratio to two-loop order in ChPT, providing a more accurate and comprehensive analysis.

Findings

The ratio of disconnected to connected contributions is approximately -0.1.

Higher order corrections slightly modify the earlier one-loop estimate.

The strange quark contributions are quantitatively assessed.

Abstract

We calculate all neutral vector two-point functions in Chiral Perturbation Theory (ChPT) to two-loop order and use these to estimate the ratio of disconnected to connected contributions as well as contributions involving the strange quark. We extend the ratio of $-1/10$ derived earlier in two flavour ChPT at one-loop order to a large part of the higher order contributions and discuss corrections to it. Our final estimate of the ratio disconnected to connected is negative and a few % in magnitude.