Inclusive rare $\Lambda_b$ decays to photon

Inclusive $H_b \to X_s \, \gamma$ decays, with $H_b$ a beauty baryon, are treated exploiting an expansion up to the third order in the inverse of the $b$ quark mass $m_b$ and to LO in $\alpha_s$, keeping the dependence on the hadron spin. Double distribution $\frac{d^2\Gamma}{dy \, d \cos \theta_P}$ is computed for polarized baryons, with $y = 2 \, E_\gamma / m_b$, $E_\gamma$ the photon energy and $\theta_P$ the angle between the baryon spin vector and the photon momentum in the $H_b$ rest-frame. Modifications to the photon polarization asymmetry can probe effects of physics beyond the Standard Model. A systematic method to treat the singular terms in the photon energy spectrum obtained by the OPE is proposed.