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Register a new userDetermining Sigma - Lambda mixing
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SU2 isospin breaking effects in baryon octet (and decuplet) masses are due to a combination of up and down quark mass differences and electromagnetic effects. These mass differences are small. Between the Sigma and Lambda the mass splitting is much larger, but this is mostly due to their different wavefunctions. However there is now also mixing between these states. We determine the QCD mixing matrix and hence find the mixing angle and mass splitting.
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Isospin breaking effects in baryon octet (and decuplet) masses are due to a combination of up and down quark mass differences and electromagnetic effects and lead to small mass splittings. Between the Sigma and Lambda this mass splitting is much larger, this being mostly due to their different wavefunctions. However when isospin is broken, there is a mixing between between these states. We describe the formalism necessary to determine the QCD mixing matrix and hence find the mixing angle and mass splitting between the Sigma and Lambda particles due to QCD effects.
Mixing in the $Sigma^0$-$Lambda^0$ system is a direct consequence of broken isospin symmetry and is a measure of both isospin-symmetry breaking as well as general SU(3)-flavour symmetry breaking. In this work we present a new scheme for calculating the extent of $Sigma^0$-$Lambda^0$ mixing using simulations in lattice QCD+QED and perform several extrapolations that compare well with various past determinations. Our scheme allows us to easily contrast the QCD-only mixing case with the full QCD+QED mixing.
In this Reply, we respond to the above Comment. Our computation [Phys. Rev. D 91 (2015) 074512] only took into account pure QCD effects, arising from quark mass differences, so it is not surprising that there are discrepancies in isospin splittings and in the Sigma - Lambda mixing angle. We expect that these discrepancies will be smaller in a full calculation incorporating QED effects.
Properties of hypernuclei are studied in the context of a chiral Lagrangian which successfully describes ordinary nuclei. Lambda-Sigma^0 mixing arises from nondiagonal vertices in flavor space induced by the vector mesons and by the electromagnetic field. The set of Dirac equations for the coupled hyperon system is discussed. Results are presented for energy spectra and electromagnetic properties of hyperons in the nuclear environment. Simple estimates suggest that flavor mixing can lead to sizable changes in the lifetimes of Lambda hypernuclei.
We analyze the mixing between $Sigma^0$ and $Lambda^0$ based on the baryon masses. We distinguish the contributions from QCD and QED in the baryon mass splittings. We find that the mixing angle between $Sigma^0$ and $Lambda^0$ is $(2.07pm 0.03)times 10^{-2} $, which leads to the decay branching fraction and up-down asymmetry of $Lambda_c^+ to Sigma^0 e^+ u_e$ to be ${cal B}(Lambda_c^+ to Sigma^0 e^+ u_e)=(1.5pm 0.2)times 10^{-5}$ and $alpha(Lambda_c^+ to Sigma^0 e^+ u_e)=-0.86pm 0.04$, respectively. Moreover, we obtain that $Delta {cal B}equiv {cal B}(Lambda_c^+to Sigma^0 pi^+) - {cal B}(Lambda_c^+to Sigma^+pi^0)=(3.8pm 0.5)times 10^{-4}$ and $Delta alpha equivalpha(Lambda_c^+to Sigma^0 pi^+) -alpha(Lambda_c^+to Sigma^+pi^0)=(-1.6pm 0.7)times10^{-2}$, which should vanish without the mixing.
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