Quark disconnected diagrams in chiral perturbation theory

TL;DR

This paper develops a method to separate and analyze quark-disconnected and connected contributions to hadronic correlation functions using partially quenched chiral perturbation theory, with applications to lattice QCD.

Contribution

It provides a novel framework to derive independent correlators for disconnected and connected diagrams and offers parameter-free predictions for certain contributions at NLO.

Findings

Derived expressions for disconnected and connected correlators in chiral effective theory.

Provided parameter-free NLO predictions for disconnected contributions in specific QCD theories.

Suggested use of twisted boundary conditions to enhance lattice QCD calculations.

Abstract

We show how quark-disconnected and quark-connected contributions to hadronic n-point functions can be written as independent correlators for which one can derive expressions in partially quenched chiral effective theory. As an example we apply the idea to the case of the hadronic vacuum polarisation. In particular, we consider the cases of the Nf = 2 theory without and with a partially quenched strange quark and also the Nf = 2 + 1 theory. In the latter two cases a parameter-free prediction for the disconnected contribution at NLO in the effective theory is given. Finally we show how twisted boundary conditions can then be used in lattice QCD to improve the q^2 resolution in the connected contributions even when flavour singlet operators are considered.