  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 $b \to s \gamma$. The decay $\Lambda_b \to \Lambda \gamma$ has the
drawback that the $\Lambda$, being neutral and long-lived, will escape
detection most of the time. To overcome this difficulty, transitions of the
type $\Lambda_b \to \Lambda^{*} \gamma$ have been proposed, where $\Lambda^{*}$
denotes an excited state decaying strongly within the detector into the clean
mode $p K^-$. The doublet $\Xi_b$, that decays weakly, has a number of good
features. The charged baryon $\Xi_b^-$ will decay into the mode $\Xi^- \gamma$,
where the ground state hyperon $\Xi^-$, although it will decay most of the time
outside the detector, can be detected because it is charged. We consider also
the decay of $\Xi_b$ into $\Xi^{*} \gamma$, where a higher mass state $\Xi^{*}$
can decay strongly within the detector. We point out that the initial
transverse polarization of $\Xi_b$ has to be known in all cases. To determine
this parameter through the transition $\Xi_b \to J/\Psi\ \Xi$, we distinguish
between different cases, and underline that in some situations one needs {\it
theoretical input} on the asymmetry parameter $\alpha_{\Xi_b}$ of the primary
decay. {\it A fortiori} the same considerations apply to the case of the
$\Lambda_b$.
