Study of semileptonic $B\to DP\ell^+\nu_\ell$ decays based on the SU(3) flavor symmetry

TL;DR

This paper uses SU(3) flavor symmetry to relate and predict branching ratios of various semileptonic B meson decays involving D mesons and leptons, including many for the first time, aiding future experimental tests.

Contribution

It introduces a method to relate decay amplitudes via SU(3) symmetry and predicts branching ratios for unmeasured decay modes using constrained nonperturbative coefficients.

Findings

Predicted many branching ratios for the first time.

Identified decay modes receiving only non-resonant contributions.

Determined decay modes with combined resonant and non-resonant contributions.

Abstract

Decays $B\to DP\ell^+\nu_\ell~(\ell=e,\mu,\tau)$ with the non-resonance, the charmed vector resonances, the charmed scalar resonances and the charmed tensor resonances are calculated by using the SU(3) flavor symmetry. Firstly, the decay amplitudes of different modes are related by the SU(3) flavor symmetry. Then, relevant experiential data are used to constrain nonperturbative coefficients in the non-resonant and various resonant $B\to DP\ell^+\nu_\ell$ decays. Finally, using the constrained nonperturbative coefficients, the branching ratios of not-yet-measured $B\to D^*P\ell^+\nu_\ell$ decays with the non-resonant and various charmed resonant contributions are predicted. Many branching ratios are predicted for the first time. We find that $B\to D\eta'\ell^+\nu_\ell, B_s\to D_s\eta'\ell^+\nu_\ell$ decays only receive the non-resonant contributions, $B\to D_sK\ell^+\nu_\ell$, $B_s\to DK\ell^+\nu_\ell$, $B\to D\eta\ell^+\nu_\ell$ and $B_s\to D_s\eta\ell^+\nu_\ell$ decays receive both non-resonant and charmed tensor resonant contributions, $B^+\to D^-\pi^+\ell^+\nu_\ell$ decays receive the non-resonant, the charmed scalar resonant and the charmed tensor resonant contributions, and other $B\to D\pi\ell^+\nu_\ell$ decays receive all four kinds of contributions. These results can be used to test the SU(3) flavor symmetry approach in the four-body semileptonic decays by the future LHCb and Belle-II experiments.