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Note on new interesting baryon channels to measure the photon polarization in b -> s gamma

At LHC a large number of b-flavored baryons will be produced. In this note we propose new baryon modes to determine the photon helicity of the penguin transition $b \to s γ$. The decay $Λ_b \to Λγ$ has the drawback that the $Λ$, being neutral and long-lived, will escape detection most of the time. To overcome this difficulty, transitions of the type $Λ_b \to Λ^{*} γ$ have been proposed, where $Λ^{*}$ denotes an excited state decaying strongly within the detector into the clean mode $p K^-$. The doublet $Ξ_b$, that decays weakly, has a number of good features. The charged baryon $Ξ_b^-$ will decay into the mode $Ξ^- γ$, where the ground state hyperon $Ξ^-$, although it will decay most of the time outside the detector, can be detected because it is charged. We consider also the decay of $Ξ_b$ into $Ξ^{*} γ$, where a higher mass state $Ξ^{*}$ can decay strongly within the detector. We point out that the initial transverse polarization of $Ξ_b$ has to be known in all cases. To determine this parameter through the transition $Ξ_b \to J/Ψ Ξ$, we distinguish between different cases, and underline that in some situations one needs {\it theoretical input} on the asymmetry parameter $α_{Ξ_b}$ of the primary decay. {\it A fortiori} the same considerations apply to the case of the $Λ_b$.