Comment on "Lattice determination 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.