Comment on "Lattice determination of $Σ$-$Λ$ mixing"

A recent lattice QCD (LQCD) calculation of $Σ$-$Λ$ 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 $Σ$-$Λ$ mixing matrix element to known octet baryon mass differences and which has been used widely to evaluate charge symmetry breaking effects in $Λ$ hypernuclei. We show that the LQCD-calculated $Σ$-$Λ$ mixing matrix element and octet baryon masses satisfy the DvH mass formula, concluding thereby that a good LQCD evaluation of $Σ$-$Λ$ mixing requires an equally good reproduction of octet baryon mass differences which is yet to be demonstrated.

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