On the decay mode ${\mathrm{\Lambda }}_b\to X_s\gamma$

We study the inclusive $H_b\to X_s\gamma$ decay with $H_b$ a beauty baryon, in particular ${\mathrm{\Lambda }}_b$, employing an expansion in the heavy quark mass at $O(m_b^{-3})$ at leading order in ${\alpha }_s$, keeping the dependence on the hadron spin. For a polarized baryon we compute the distribution ${\displaystyle \frac{d^2\mathrm{\Gamma }}{dyd\cos {\theta }_P}}$, with $y=2E_{\gamma }\mathrm{/}{m}_b$, $E_{\gamma }$ the photon energy and ${\theta }_P$ the angle between the baryon spin vector and the photon momentum in the $H_b$ rest-frame. We discuss the correlation between the baryon and photon polarization, and show that effects of physics beyond the Standard Model can modify the photon polarization asymmetry. We also discuss a method to treat the singular terms in the photon energy spectrum obtained by the OPE.