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Is $f_X(1500)$ observed in the $B\to π(K)KK$ decays $ρ^0(1450)$?

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 $ρ^0(1450)$ reported recently by LHCb. Adopting the perturbative QCD approach, we determine the di-kaon distribution amplitudes with the $ρ^0(1450)$ resonance from the LHCb data for the quasi-two-body decays $B^{\pm}\to π^{\pm}ρ^0(1450)\toπ^{\pm}K^+K^-$. It is then shown that the $B^+ \to K^+K^+K^-$ decay spectrum around the invariant mass $M(K^+K^-)\sim 1.5~\rm GeV$ measured by BaBar can be well described by the resonant contribution from $ρ^0(1450)$. The broad structure in the $B^{+}\to K^{+} K_SK_S$ spectrum around the invariant mass $1.5~\rm GeV$ of a $K_SK_S$ pair, which $ρ^0(1450)$ 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 $B^{\pm}\to π^{\pm}ρ^0(1450)\toπ^{\pm}K^+K^-$, $B^{+}\to K^{+}ρ^0(1450)\to K^+K^+K^-$ and $B^{0}\to K^{0}ρ^0(1450)\to K^0K^+K^-$ 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.