Data-based analysis of Forward-Backward Asymmetry in $B^{\pm }\to K^{\pm }{K}^{\mp }{K}^{\pm }$

Abstract

An analysis of the Forward-Backward Asymmetry (FBA) in the decay $B^{\pm }\to K^{\pm }{K}^{\mp }{K}^{\pm }$ is carried out based on the LHCb data. It is found that the large FBA observed for the invariant mass of the $K^{+}{K}^{-}$ pair around 1.5 GeV can be explained by the interference of the amplitudes between the resonances with even and odd spins, where the former can be the spin-0 $f_0(1500)$ resonance plus a non-resonance $s$-wave, while the latter is a spin-1 resonance which is probably ${\rho }^0(1450)$. The analysis shows the existence of the decay channel $B^{\pm }\to {\rho }^0(1450)K^{\pm }$, with $CP$ asymmetry of $A_{CP}(B^{\pm }\to {\rho }^0(1450)K^{\pm })=(-3.4\pm 3.0)\%$. This is in contradiction with the conclusion of BaBar in Phys. Rev. D 85, 112010, according to which the analysis showed no signal of the spin-1 resonance ${\rho }^0(1450)$. We suggest our experimental colleagues to perform a closer analysis to this channel. We also suggest to perform the measurements of the FBAs (as well as the FB-$CP$As) in other three-body decay channels of beauty and charmed mesons, as it is helpful for resonance analysis.

Comments: 14 pages, 5 figures, 3 tables