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.

19 pages

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