Form Factor Counting and HQET Matching for New Physics in $Lambda_b to Lambda_c^*l u$

We calculate the $Lambda_b to Lambda_c^*(2595) l u$ and $Lambda_b to Lambda_c^*(2625) l u$ form factors and decay rates for all possible $b to c l bar u$ four-Fermi interactions in and beyond the Standard Model (SM), including nonzero charged lepton masses and terms up to order $mathcal{O}(alpha_s, 1/m_{c,b})$ in the heavy quark effective theory (HQET). We point out a subtlety involving the overcompleteness of the representation of the spin-parity $1/2^+ to 3/2^-$ antisymmetric tensor form factors, relevant also to other higher excited-state transitions, and present a general method for the counting of the physical form factors for any hadronic transition matrix element and their matching onto HQET. We perform a preliminary fit of a simple HQET-based parametrization of the $Lambda_b to Lambda_c^*$ form factors at $mathcal{O}(alpha_s, 1/m_{c,b})$ to an existing quark model, providing preliminary predictions for the lepton universality ratios $R(Lambda_c^*)$ beyond the SM. Finally, we examine the putative incompatibility of recent lattice QCD results with expectations from the heavy-quark expansion and available experimental data.