Estimates of the isospin-violating ${\Lambda }_b\to {\Sigma }^0\varphi ,{\Sigma }^{0}J/\psi$ decays and the $\Sigma -\Lambda$ mixing

Abstract

We analyse the two purely isospin-violating decays ${\Lambda }_b\to {\Sigma }^0\varphi$ and ${\Lambda }_b\to {\Sigma }^{0}J/\psi$, proceed merely via the exchange topologies, in the framework of perturbative QCD approach. Assuming ${\Sigma }^0$ baryon belongs to the idealized isospin triplet with quark components of $usd$, the branching ratios of the two decay modes are predicted to be tiny, of the order $10^{-8}-10^{-9}$, leading to a difficulty in observing them. We then extend our study to include the $\Sigma -\Lambda$ mixing.It is found that the mixing has significant effect on the ${\Lambda }_b\to \Sigma$ decays, especially it can greatly increase the rate of the $J/\psi$ process, by as much as two orders of magnitude, yield $10^{-7}$, which should be searchable in the future. We also estimate a set of asymmetry observables with and without the mixing effect, which will be tested in coming experiments.

Comments: 23 pages, 1 figure, 10 tables;