Precision Model-Independent Bounds from Global Analysis of $b\to c\ell \nu$ Form Factors

Abstract

We present a model-independent global analysis of hadronic form factors for the semileptonic decays $b\to c\ell \nu$ that exploits lattice-QCD data, dispersion relations, and heavy-quark symmetries. The analysis yields predictions for the relevant form factors, within quantifiable bounds. These form factors are used to compute the semileptonic ratios $R(H_c)$ and various decay-product polarizations. In particular, we find $R(D_s^{\ast })=0.20(3)$ and $R(J/\psi )=0.25(3)$, predictions that can be compared to results of upcoming LHCb measurements. In developing this treatment, we obtain leading-order NRQCD results for the nonzero-recoil relations between the $B_c^{+}\to \{J/\psi ,{\eta }_c\}$ form factors.

Comments: 13 pages, 8 figures