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

Abstract

In 2017, LHCb collaboration reported their first observation of the rare decays $B_s\to \varphi (f_0(980)$ $/f_2(1270)\to ){\pi }^{+}{\pi }^{-}$ and the evidence of $B^0\to \varphi (f_0(980)/f_2(1270)\to ){\pi }^{+}{\pi }^{-}$. Motivated by this, we study these quasi-two-body decays in the perturbative QCD approach. The branching fractions, $CP$ asymmetries and the polarization fractions are calculated. We find that within the appropriate two-meson wave functions, the calculated branching fractions are in agreement with the measurements of LHCb. Based on the narrow-width approximation, We also calculate the branching fractions of the quasi-two-body $B_{d,s}\to \varphi (f_0(980)/f_2(1270)\to ){\pi }^0{\pi }^0$ and $B_{d,s}\to \varphi (f_2(1270)\to )K^{+}{K}^{-}$, and hope the predictions to be tested in the ongoing LHCb and Belle II experiments. Moreover, the processes $B_{d,s}\to \varphi f_2(1270)$ are also analyzed under this approximation. We note that the $CP$ asymmetries of these decays are very small, because these decays are either penguin dominant or pure penguin processes.

21 Pages, 1 figure

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Cited by in corpus (2)

• Form factors of $P\to T$ transition within the light-front quark models
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