Probing isovector scalar mesons in the charmless three-body $B$ decays

Abstract

We propose to study the multiparticle configurations of isovector scalar mesons, saying $a_0(980)$ and $a_0(1450)$, in the charmless three-body $B$ decays by considering the width effects. Two scenarios of $a_0$ configurations are assumed, in which the first one take $a_0(980)$ as the lowest-lying $q\bar{q}$ state and $a_0(1450)$ as the first radial excited state, the second one take $a_0(1450)$ as the lowest-lying $q\bar{q}$ state and $a_0(1950)$ as the first radial excited state while $a_0(980)$ is not a $q\bar{q}$ state. Within these two scenarios, we do the PQCD calculation for the quasi-two-body $B\to a_0\left[\to K\bar{K}/\pi \eta \right]h$ decays and extract the corresponding branching fractions of two-body $B\to a_{0}h$ decays under the narrow width approximation. Our predictions show that the first scenario of $a_0(980)$ configuration can not be excluded by the available measurements in $B$ decays, the contributions from $a_0(1450)$ to the branching fractions in most channels are comparable in the first and second scenarios. Several channels are suggested for the forthcoming experimental measurements to reveal the multiparticle configurations of $a_0$, such as the channel $B^0\to a_0^{-}(980)\left[\to {\pi }^{-}\eta \right]{\pi }^{+}$ with the largest predicted branching fraction, the channels $B^0\to a_0^{\pm }(1450)\left[\to K^{\pm }{\bar{K}}^0,{\pi }^{\pm }\eta \right]{\pi }^{\mp }$ whose branching fractions obtained in the second scenario is about three times larger in magnitude than that obtained in the first scenario, and also the channels $B^{+}\to a_0^{+}(1950)\left[K^{+}{\bar{K}}^0/{\pi }^{+}\eta \right]K^0$ whose branching fractions are linear dependent on the partial width ${\Gamma }_{a_0(1950)\to KK/\pi \eta }$.

Comments: 29pages, 4 figures and 7 tables, minor revision, typos corrected, references updated