Quasi-four-body semileptonic decay ${\bar{B}}^0\to a_0(1450{)}^{+}(\to {\pi }^{+}\eta ){\ell }^{-}{\bar{\nu }}_{\ell }$ within $a_0(1450)$-resonance leading-twist LCDA under QCDSR

Abstract

The finite width of broad scalar resonances should be taken into account when relating semileptonic $B$-meson transitions to experimentally reconstructable multihadron final states. The quasi-four-body semileptonic decays ${\bar{B}}^0\to a_0(1450{)}^{+}(\to \pi \eta ){\ell }^{-}{\bar{\nu }}_{\ell }$ with $\ell =(e,\mu ,\tau )$ provide a platform for investigating the scalar $a_0(1450{)}^{+}$-resonance as the lowest-Fock-state quark-antiquark component. We calculate the first five odd $\xi$-moments of $a_0(1450)$-resonance twist-2 light-cone distribution amplitude (LCDA) using QCDSR within the background-field theory, including vacuum condensates up to dimension six. Based on these moments, two twist-2 LCDA schemes are constructed: a light-cone harmonic oscillator model (S1), whose free parameters are fitted to the first five odd moments, and a truncated Gegenbauer expansion (S2) retaining only $a_{1,3}(\mu )$. The ${\bar{B}}^0\to a_0(1450{)}^{+}$ transition form factors are then calculated using light-cone sum rules. At large recoil region, we present the TFFs with different scheme. The finite-width effect of $a_0(1450)$-resonance is further incorporated through a two-channel Flatté parametrization including the $\pi \eta$ and $K\bar{K}$ channels. The $\pi \eta$ invariant-mass distribution exhibits a pronounced resonance peak around $s\simeq m_{a_0(1450)}^2$. The spectra of the electron and muon channels are nearly identical, while the $\tau$-channel is significantly suppressed because the larger lepton mass reduces the available phase space. After integration over the full quasi-four-body phase space, the branching fractions are given. We expect that these results will provide useful guidance for future experimental and theoretical studies of ${\bar{B}}^0\to a_0(1450{)}^{+}(\to \pi \eta ){\ell }^{-}{\bar{\nu }}_{\ell }$ decay and help improve our understanding of the internal structure of $a_0(1450)$.

arXiv comment10 pages, 5 figures