Probing for new physics in polarized $\Lambda_b$ decays at the $Z$

Polarized ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}\ensuremath{\gamma}$ decays at the Z pole are shown to be well suited for probing a large variety of new physics effects. A new observable is proposed, the angular asymmetry between the ${\ensuremath{\Lambda}}_{b}$ spin and photon momentum, which is sensitive to the relative strengths of the opposite chirality and standard model chirality $\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma}$ dipole operators. Comparison with the $\ensuremath{\Lambda}$ decay polarization asymmetry and with the ${\ensuremath{\Lambda}}_{b}$ polarization extracted from semileptonic decays allows important tests of the $V\ensuremath{-}A$ structure of the standard model. The modifications of the rates and angular asymmetries which arise at next-to-leading order are discussed. The measurements for ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}\ensuremath{\gamma}$ and the $\mathrm{CP}$ conjugate mode, with branching ratios of a few times ${10}^{\ensuremath{-}5},$ are shown to be sensitive to nonstandard sources of $\mathrm{CP}$ violation in the ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}\ensuremath{\gamma}$ matrix element. Form factor relations for heavy-to-light baryon decays are derived in the large energy limit, which are of general interest.