Is $f_X(1500)$ observed in the $B\to \pi (K)KK$ decays ${\rho }^0(1450)$?

Abstract

We suggest that the uncertain state $f_X(1500)$ observed by Belle and BaBar more than a decade ago, which has been viewed as a single scalar or a combination of several even spin resonances, is the vector ${\rho }^0(1450)$ reported recently by LHCb. Adopting the perturbative QCD approach, we determine the di-kaon distribution amplitudes with the ${\rho }^0(1450)$ resonance from the LHCb data for the quasi-two-body decays $B^{\pm }\to {\pi }^{\pm }{\rho }^0(1450)\to {\pi }^{\pm }{K}^{+}{K}^{-}$. It is then shown that the $B^{+}\to K^{+}{K}^{+}{K}^{-}$ decay spectrum around the invariant mass $M(K^{+}{K}^{-})\sim 1.5\mathrm{GeV}$ measured by BaBar can be well described by the resonant contribution from ${\rho }^0(1450)$. The broad structure in the $B^{+}\to K^{+}{K}_S{K}_S$ spectrum around the invariant mass $1.5\mathrm{GeV}$ of a $K_S{K}_S$ pair, which ${\rho }^0(1450)$ cannot decay into because of Bose-Einstein statistics, can be accounted for by a nonresonant $S$-wave contribution alone. The branching fractions and/or the direct $CP$ asymmetries of the $B^{\pm }\to {\pi }^{\pm }{\rho }^0(1450)\to {\pi }^{\pm }{K}^{+}{K}^{-}$, $B^{+}\to K^{+}{\rho }^0(1450)\to K^{+}{K}^{+}{K}^{-}$ and $B^0\to K^0{\rho }^0(1450)\to K^0{K}^{+}{K}^{-}$ modes are predicted, which can be tested at the ongoing LHCb and Belle-II experiments. We encourage experimental colleagues to scrutinize our postulation by analyzing relevant data with higher precision.

7 Pages, 3 Figures. Accepted by PRD

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Cited by in corpus (9)

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• Contributions for the kaon pair from $\rho (770)$, $\omega (782)$ and their excited states in the $B\to K\bar{K}h$ decays
• Global determination of two-meson distribution amplitudes from three-body $B$ decays in the perturbative QCD approach
• Quasi-two-body $B_{(s)}\to V\pi \pi$ Decays with Resonance $f_0(980)$ in PQCD Approach
• Resonances $\rho (1450{)}^{+}$ and $\rho (1700{)}^{+}$ in $B\to DKK$ decays
• Data-based analysis of Forward-Backward Asymmetry in $B^{\pm }\to K^{\pm }{K}^{\mp }{K}^{\pm }$
• Study of the four-body decays $B_S^0\to \pi \pi \pi \pi$ in the perturbative QCD approach
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays