Form Factor Counting and HQET Matching for New Physics in ${\Lambda }_b\to {\Lambda }_c^{\ast }l\nu$

Abstract

We calculate the ${\Lambda }_b\to {\Lambda }_c^{\ast }(2595)l\nu$ and ${\Lambda }_b\to {\Lambda }_c^{\ast }(2625)l\nu$ form factors and decay rates for all possible $b\to cl\bar{\nu }$ 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 ${\Lambda }_b\to {\Lambda }_c^{\ast }$ form factors at $\mathcal{O}({\alpha }_s,1/m_{c,b})$ to an existing quark model, providing preliminary predictions for the lepton universality ratios $R({\Lambda }_c^{\ast })$ beyond the SM. Finally, we examine the possible incompatibility of recent lattice QCD results with expectations from the heavy-quark expansion and available experimental data.

Comments: 17 pages, 3 figures, published version