Patterns of flavour symmetry breaking in hadron matrix elements involving u, d and s quarks

TL;DR

This paper explores how flavour symmetry breaking affects octet baryon matrix elements involving u, d, and s quarks, using a flavour expansion approach constrained along a specific mass trajectory, with implications for lattice QCD calculations.

Contribution

It develops a constrained flavour expansion formalism for baryon matrix elements considering SU(3) breaking, including higher-order terms and connections to lattice QCD correlators.

Findings

Expansion constrained along a constant singlet quark mass trajectory.

Higher orders do not add further constraints on expansion parameters.

Numerical lattice results for vector form factors demonstrate the method.

Abstract

By considering a flavour expansion about the SU(3)-flavour symmetric point, we investigate how flavour-blindness constrains octet baryon matrix elements after SU(3) is broken by the mass difference between quarks. Similarly to hadron masses we find the expansions to be constrained along a mass trajectory where the singlet quark mass is held constant, which provides invaluable insight into the mechanism of flavour symmetry breaking and proves beneficial for extrapolations to the physical point. Expansions are given up to third order in the expansion parameters. Considering higher orders would give no further constraints on the expansion parameters. The relation of the expansion coefficients to the quark-line-connected and quark-line disconnected terms in the 3-point correlation functions is also given. As we consider Wilson clover-like fermions, the addition of improvement coefficients is also discussed and shown to be included in the formalism developed here. As an example of the method we investigate this numerically via a lattice calculation of the flavour-conserving matrix elements of the vector first class form factors.