Penguin-dominated $B\to \varphi K_1(1270)$ and $\varphi K_1(1400)$ decays in the perturbative QCD approach

Abstract

We investigate the CP-averaged branching ratios, the polarization fractions, the relative phases, and the CP-violating asymmetries of the penguin-dominated $B\to \varphi K_1(1270)$ and $\varphi K_1(1400)$ decays in the perturbative QCD(pQCD) approach, where $K_1(1270)$ and $K_1(1400)$ are believed to be the mixtures of two distinct types of axial-vector $K_{1A}{(}^3{P}_1)$ and $K_{1B}{(}^1{P}_1)$ states with different behavior, however, their mixing angle ${\theta }_{K_1}$ is still a hot and controversial topic presently. By numerical evaluations with two different mixing angles ${\theta }_{K_1}\sim 33^{\circ }$ and $58^{\circ }$ and phenomenological analysis, we find that: (a) the pQCD predictions for the branching ratio, the longitudinal polarization fraction and the direct CP violation of $B^{\pm }\to \varphi K_1(1270{)}^{\pm }$ decay with the smaller angle $33^{\circ }$ are in good agreement with the currently available data; (b) though the central values significantly exceed the available upper limit, both pQCD predictions of $Br(B^{\pm }\to \varphi K_1(1400{)}^{\pm })$ with two different mixing angles are consistent with that obtained in QCD factorization and with the preliminary data in 2$\sigma$ errors. These results and other relevant predictions for the considered decays will be further tested by the LHCb and the forthcoming Super-B experiments; (c) the weak annihilation contributions can play an important role in $B\to \varphi K_1(1270)$ and $\varphi K_1(1400)$ decays; (d) these pQCD predictions combined with the future precision measurements can examine the reliability of the factorization approach employed here, but also explore the complicated QCD dynamics and mixing angle ${\theta }_{K_1}$ of the axial-vector $K_1(1270)$ and $K_1(1400)$ system.

arXiv comment19 pages, 1 figure; context enlarged with detailed calculations and corresponding discussions, references added, and the main conclusions remain unchanged; Accepted for publication in Phys.Rev.D

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• $B_{d,s}^0\to f_1{f}_1$ decays with $f_1(1285)-f_1(1420)$ mixing in the perturbative QCD approach
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