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

TL;DR

This paper provides a model-independent analysis of $b o c \, \ell \, \nu$ form factors using lattice QCD, dispersion relations, and heavy-quark symmetries, predicting decay ratios and polarizations for future experimental tests.

Contribution

It introduces a novel, model-independent global analysis method for hadronic form factors in semileptonic decays, combining multiple theoretical tools for improved predictions.

Findings

Predicted $R(D_s^*)=0.20(3)$ and $R(J/\psi)=0.25(3)$.

Derived bounds on form factors from lattice QCD and dispersion relations.

Provided leading-order NRQCD relations for $B_c^+$ decay form factors.

Abstract

We present a model-independent global analysis of hadronic form factors for the semileptonic decays $b\rightarrow c\ell\nu$ 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 $R(D_s^*)=0.20(3)$ 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 $B_c^+ \rightarrow \{J/\psi , \eta_c \}$ form factors.