Revisiting the pion's scalar form factor in chiral perturbation theory

TL;DR

This paper calculates the pion's scalar form factor, including quark-disconnected contributions, in chiral perturbation theory at next-to-leading order, highlighting their importance for accurate lattice QCD simulations.

Contribution

It provides the first detailed NLO analysis of both connected and disconnected contributions to the pion's scalar form factor in two and three flavor chiral perturbation theory.

Findings

Disconnected contributions significantly affect the scalar radius.

Neglecting disconnected diagrams can lead to systematic errors in lattice QCD.

The methodology can be applied to other QCD observables.

Abstract

The quark-connected and the quark-disconnected Wick contractions contributing to the pion's scalar form factor are computed in the two and in the three flavour chiral effective theory at next-to-leading order. While the quark-disconnected contribution to the form factor itself turns out to be power-counting suppressed its contribution to the scalar radius is of the same order of magnitude as the one of the quark-connected contribution. This result underlines that neglecting quark-disconnected contributions in simulations of lattice QCD can cause significant systematic effects. The technique used to derive these predictions can be applied to a large class of observables relevant for QCD-phenomenology.