Flavor SU(3) analysis of the charmless semileptonic $B\to PV{\ell }^{+}{\nu }_{\ell }$ decays

Abstract

All charmless $B\to PV{\ell }^{+}{\nu }_{\ell }$ ($P$ denotes the light pseudoscalar meson and $V$ denotes the vector meson) decays have not been experimentally observed to date, but some of them might be measured in the near future. The charmless $B\to PV{\ell }^{+}{\nu }_{\ell }$ decays with the axial-vector ($A$) resonance states, the tensor ($T$) resonance states and the excited vector ($V_{E,D}$) resonance states are studied based on flavor SU(3) analysis in this work, where $V_E$ contains $\{\rho (1450),K^{\ast }(1410),\omega (1420),\varphi (1680)\}$ with quantum numbers $n^{2S+1}{L}_J=2^3{S}_1$ and $V_D$ contains $\{\rho (1700),K^{\ast }(1680),\omega (1650),\varphi (2170)\}$ with quantum numbers $n^{2S+1}{L}_J=1^3{D}_1$. The hadronic amplitudes of the $B\to A/T{\ell }^{+}{\nu }_{\ell }$ decays are related by the nonperturbative parameters, and the branching ratio predictions of $B\to A/T/V_{E,D}{\ell }^{+}{\nu }_{\ell }$ are obtained, and then the branching ratios of the $B\to A(A\to PV){\ell }^{+}{\nu }_{\ell }$, $B\to T(T\to PV){\ell }^{+}{\nu }_{\ell }$, $B\to V_E(V_E\to PV){\ell }^{+}{\nu }_{\ell }$ and $B\to V_D(V_D\to PV){\ell }^{+}{\nu }_{\ell }$ are obtained by the narrow width approximation or further considering the width effects. We find that most branching ratios of the $B\to A{\ell }^{+}{\nu }_{\ell }$ decays and many branching ratios of the $B\to A(A\to PV){\ell }^{+}{\nu }_{\ell }$ decays are on the order of $\mathcal{O}(10^{-4}-10^{-3})$, and all branching ratios with the tensor resonance states and the excited vector resonance states are small. Our results could be tested in the future BelleII and LHCb experiments.

Comments: 19 pages