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.

arXiv comment7 Pages, 3 Figures. Accepted by PRD

References in corpus (34)

• Weak Decays Beyond Leading Logarithms
• Charmless non-leptonic B_s decays to PP, PV and VV final states in the pQCD approach
• Dalitz analysis of the three-body charmless decays B+=>K+Pi+Pi- and B+=>K+K+K-
• Dalitz-plot analysis of the decays B+/- --> K+/- pi-/+ pi+/-
• Next-to-leading-order corrections to $B\to \pi$ form factors in $k_T$ factorization
• Modeling the Pion and Kaon Form Factors in the Timelike Region
• Charmless Three-body Decays of B Mesons
• Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+
• Three-Body Non-Leptonic B Decays and QCD Factorization
• Three-body nonleptonic B decays in perturbative QCD
• Study of three-body charmless B decays
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• Dalitz Plot Analysis of B+- --> pi+-pi+-pi-+ Decays
• Dalitz plot analysis of the decay B+- -> K+-K+-K-+
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Direct CP asymmetries of three-body $B$ decays in perturbative QCD
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Symmetry relations in charmless B->PPP decays
• $B$-meson light-cone distribution amplitude from the Euclidean quantity
• Laura++ : a Dalitz plot fitter
• Vector-pseudoscalar two-meson distribution amplitudes in three-body $B$ meson decays
• Amplitude analysis of $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays
• Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach
• Observation of the Decay B+ --> K+K-pi+
• Measurements of CP-Violating Asymmetries in the Decay B0-->K+K-K0
• B decays into light scalar particles and glueball
• Resonant Contributions to Three-body $B\to KKK$ Decays in Perturbative QCD Approach
• Quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ in the perturbative QCD approach
• Amplitude analysis and measurement of the time-dependent CP asymmetry of $B^0\to K_0^S{K}_0^S{K}_0^S$ decays
• Will the subprocesses $\rho (770,1450{)}^0\to K^{+}{K}^{-}$ contribute large branching fractions for $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays?
• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• Subleading power corrections to $B\to \gamma l\nu$ decay in PQCD approach
• Strong evidence of $\rho (1250)$ from a unitary multichannel reanalysis of elastic scattering data with crossing-symmetry constraints

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• Study of Quasi-two-body $B_{(s)}\to \varphi (f_0(980)/f_2(1270)\to )\pi \pi$ Decays in Perturbative QCD Approach
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• 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