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 $\Gamma_{a_0(1950) \to KK/\pi\eta}$.
Highlights
It is known that the scalar mesons with the masses below and near 1 GeV, say the isoscalar mesons σ=f0ð500Þ and f0ð980Þ, the isovector a0ð980Þ and the isodoublet κ, form a SUð3Þ flavor nonet
Several channels are suggested for the forthcoming experimental measurements to reveal the multiparticle configurations of a0, such as the channel B0 → a−0 ð980Þ1⁄2→ π−ηπþ with the largest predicted branching fraction, the channels B0 → aÆ0 ð1450Þ1⁄2→ KÆK 0; πÆηπ∓ whose branching fractions obtained in the second scenario is about three times larger in magnitude than that obtained in the first scenario, and the channels Bþ → aþ0 ð1950Þ1⁄2KþK 0=πþηK0 whose branching fractions are linearly dependent on the partial width Γa0ð1950Þ→KK=πη
Motivated by the discrepancy between the experimental measurements of three-body B → a0ð980Þ1⁄2→ πηK decays and the theoretical predictions of two-body B → a0ð980ÞK decays, we study the contributions from a0 in the threebody B → 1⁄2πηð1⁄2KK Þh decays in the framework of the perturbative QCD (PQCD) approach, where the width effects of the intermediated isovector scalar mesons a0 are demonstrated in detail
Summary
It is known that the scalar mesons with the masses below and near 1 GeV, say the isoscalar mesons σ=f0ð500Þ and f0ð980Þ, the isovector a0ð980Þ and the isodoublet κ, form a SUð3Þ flavor nonet. The case becomes different in the weak decays like B → f0ð980Þlν with large recoiling, where the conventional qqassignment can be expected to be dominated in the energetic f0ð980Þ since the possibility to form a tetraquark state is power suppressed compared to the state of the quark pair [13]; the final state interaction (FSI) is weak too This argument encounters a challenge from the PQCD calculation of B → a0ð980ÞK decays [14], where the theoretical predictions of branching fractions are much larger than that of the measured upper limits. Revealing the sizeable effects from width and background (20%–30%) to the conventional treatment in the single narrow-width approximation for the LCSRs prediction of the B → ρ transition form factors This result is confirmed by the other independent LCSRs with dipion distribution amplitudes (DAs) where the hadronic dipion state has a small invariant mass and simultaneously a large recoil [26,27]. The PQCD predictions on Bs decays are presented in the Appendix A, and the factorization formulas of the related quasi-two-body decay amplitudes are listed in Appendix B
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