Angular distribution of $\Lambda_b^0\to pK^-\ell^+\ell^-$ decays comprising $\Lambda$ resonances with spin up to $\leq5/2$

This paper describes the angular distribution of $\Lambda_b^0\to \Lambda(\to pK^-)\ell^+\ell^-$ decays. A full expression is given for the case of multiple interfering spin-states with spin $\leq \tfrac{5}{2}$. This distribution is relevant for future measurements of $\Lambda_b^0\to pK^-\ell^+\ell^-$ decays, where different states cannot easily be separated based on their mass alone. New observables arise when considering spin-$\tfrac{5}{2}$ states as well as interference between states. An exploration of their behaviour for a variety of beyond the Standard Model scenarios shows that some of these observables exhibit interesting sensitivity to the Wilson coefficients involved in $b\to s\ell^+\ell^-$ transitions. Others are insensitive to the Wilson coefficients and can be used to verify the description of $\Lambda_b^0\to \Lambda$ form-factors. A basis of weighting functions that can be used to determine all of the angular observables described in this paper in a moment analysis of the experimental data is also provided.