Quark disconnected diagrams in chiral perturbation theory - the scalar form factor

TL;DR

This paper computes the scalar pion form factor contributions from different Wick contractions using chiral perturbation theory, revealing correlations and the significance of disconnected diagrams for lattice QCD data analysis.

Contribution

It provides model-independent next-to-leading order expressions for Wick contractions in the scalar pion form factor, aiding lattice data extrapolation and understanding of disconnected contributions.

Findings

Disconnected contributions are suppressed in the form factor but significant in the scalar radius.

Correlations among contractions are expressed via low-energy constants.

Results facilitate lattice QCD data analysis for scalar form factors.

Abstract

Expressions for the Wick contractions contributing to the scalar pion form-factor were computed model-independently in chiral perturbation theory at next-to-leading order. The results reveal correlations amongst the different contractions in terms of low-energy constants and allow for extrapolating lattice data for individual Wick contractions. The quark disconnected contribution to the real part of the form factor turns out to be suppressed with respect to the quark connected one. The corresponding contribution to the scalar radius has the same size as the connected contribution and can therefore not be neglected.