Comment on "Lattice determination of $\Sigma$-$\Lambda$ mixing"

TL;DR

This paper discusses the discrepancy between lattice QCD calculations and the Dalitz-von Hippel mass formula regarding $\Sigma$-$\Lambda$ mixing, emphasizing the importance of accurately reproducing octet baryon masses for reliable results.

Contribution

It highlights that lattice QCD results align with the Dalitz-von Hippel mass formula only when octet baryon masses are accurately reproduced, questioning the current lattice calculations' reliability.

Findings

LQCD results satisfy the Dalitz-von Hippel mass formula when baryon masses are correctly reproduced.

Current LQCD calculations of $\Sigma$-$\Lambda$ mixing are inconsistent with the mass formula due to baryon mass discrepancies.

Accurate reproduction of octet baryon masses is crucial for reliable lattice QCD evaluations of $\Sigma$-$\Lambda$ mixing.

Abstract

A recent lattice QCD (LQCD) calculation of $\Sigma$-$\Lambda$ mixing by the QCDSF-UKQCD Collaboration [Phys. Rev. D 91, 074512 (2015)] finds a mixing angle about half of that found from the Dalitz-von Hippel (DvH) flavor SU(3) mass formula which relates the $\Sigma$-$\Lambda$ mixing matrix element to known octet baryon mass differences and which has been used widely to evaluate charge symmetry breaking effects in $\Lambda$ hypernuclei. We show that the LQCD-calculated $\Sigma$-$\Lambda$ mixing matrix element and octet baryon masses satisfy the DvH mass formula, concluding thereby that a good LQCD evaluation of $\Sigma$-$\Lambda$ mixing requires an equally good reproduction of octet baryon mass differences which is yet to be demonstrated.