The $Λ_b\toΛ^\ast(1520)(\to N\!\bar{K})\ell^+\ell^-$ decay at low-recoil in HQET

Abstract: In this paper we discuss the Standard Model and new physics sensitivity of the $$\Lambda_b\to\Lambda^{\ast(1520)(\to} N!\bar{K})\ell<sup>+\ell<sup>-$$ decay at low-recoil, where $\ell<sup>\pm$ are massive leptons and $N!\bar{K}={pK^-, n\bar{K}⁰ }$. We provide a full angular distribution with a set of operators that includes the Standard Model operators and their chirality flipped counterparts, and new scalar and pseudo-scalar operators. The resulting angular distribution allows us to construct observables that we study in the Standard Model and in model-independent new physics scenarios. To reduce the hadronic effects emanating from the $\Lambda_b\to\Lambda<sup>\ast(1520)$ transition form factors, we exploit the Heavy Quark Effective theory framework valid at low $\Lambda<sup>\ast(1520)$ recoil, \emph{i.e.,} large dilepton invariant mass squared $q^2\sim \mathcal{O}(m_b<sup>2)$. Working to the leading order in $1/m_b$ and including $\mathcal{O}(\alpha_s)$ corrections, we compute the `improved Isgur-Wise relations' between the form factors. The relations correlate the form factors and thereby allow the description of this decay at the low-recoil region with a smaller number of independent form factors.