Quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ in the perturbative QCD approach

Abstract

In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ with the two-pion distribution amplitude ${\Phi }_{\pi \pi }^{\mathrm{D}}$ by using the perturbative QCD factorization approach, where $P$ represents a light pseudoscalar meson $K,\pi ,\eta$ and ${\eta }^{\prime }$. The relativistic Breit-Wigner formula for the $D$-wave resonance $f_2(1270)$ is adopted to parameterize the timelike form factor $F_{\pi }$, which contains the final state interactions between the pions in the resonant regions. The consistency of theoretical results with data can be achieved by determining the Gegenbauer moments of the $D$-wave two-pion distribution amplitudes. The decay rates for the considered decay modes are generally in the order of $10^{-9}$ to $10^{-6}$. The integrated direct $CP$ asymmetries for the charged modes agree with the {\it BABAR} and Belle measurements. As a by-product, we extract the branching ratios of $B_{(s)}\to P{f}_2(1270)$ from the corresponding quasi-two-body decay modes, which still need experimental tests at the ongoing and forthcoming experiments.

15 pages,3 figures

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Cited by in corpus (19)

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• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
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• Resonant Contributions to Three-body $B\to KKK$ Decays in Perturbative QCD Approach
• Branching Fractions and CP Asymmetries of the Quasi-Two-Body Decays in $B_s\to K^0({\overline{K}}^0)K^{\pm }{\pi }^{\mp }$ within PQCD Approach
• Studies of the resonance components in the $B_s$ decays into charmonia plus kaon pair
• $S$, $P$ and $D$-wave resonance contributions to $B_{(s)}\to {\eta }_c(1S,2S)K\pi$ decays in the perturbative QCD approach
• Study of $B_{(s)}\to (\pi \pi )(K\pi )$ decays in the perturbative QCD approach
• $P$-wave contributions to $B_{(s)}\to \psi K\pi$ decays in perturbative QCD approach
• Study of the $B_s$ $\to$ $\varphi f_0(980)$ $\to$ $\varphi {\pi }^{+}{\pi }^{-}$ decay with perturbative QCD approach
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• Direct $CP$ violation of three bodies decay process from the resonance effect
• Study of the four-body decays $B_S^0\to \pi \pi \pi \pi$ in the perturbative QCD approach
• Resonances $\varphi (1020)$ and $\varphi (1680)$ contributions for the three-body decays $B^{+}\to D_s^{+}K\bar{K}$
• Exclusive semileptonic decays of $D$ and $D_s$ mesons into orbitally and radially excited states of strange and light mesons
• Quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$ in the perturbative QCD approach
• Charmless Quasi-two-body $B$ Decays in Perturbative QCD Approach: Taking $B\to K(\mathcal{R}\to )K^{+}{K}^{-}$ As Examples
• Study of quasi-two-body B^{0}\rightarrow T(ππ, K\bar{K},πη) decays in perturbative QCD approach
• Exclusive semileptonic $B$ decays to the ground and excited states of light mesons