The S-wave resonance contributions in the $B_s^0$ decays into $\psi (2S,3S)$ plus pion pair

Abstract

The three-body decays $B_s^0\to \psi (2S,3S){\pi }^{+}{\pi }^{-}$ are studied based on the perturbative QCD approach. With the help of the nonperturbative two-pion distribution amplitudes, the analysis is simplified into the quasi-two-body processes. Besides the traditional factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order vertex corrections are also included to cancel the scale dependence. The $f_0(980)$, $f_0(1500)$ resonance contributions as well as the nonresonant contributions are taken into account using the presently known $\pi \pi$ time-like scalar form factor for the $s\bar{s}$ component. It is found that the predicted $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$ decay spectra in the pion pair invariant mass shows a similar behavior as the experiment. The calculated S-wave contributions to the branching ratio of $B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-}$ is $6.0\times 10^{-5}$, which is in agreement with the LHCb data $\mathcal{B}(B_s^0\to \psi (2S){\pi }^{+}{\pi }^{-})=(7.2\pm 1.2)\times 10^{-5}$ within errors. The estimate of $\mathcal{B}(B_s^0\to \psi (3S){\pi }^{+}{\pi }^{-})$ can reach the order of $10^{-5}$, pending for the corresponding measurements.

7 pages, 3 figures, 2 tables

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• Charmless Three-body Decays of B Mesons
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• Analysis of the resonant components in B0->J/ψpi+pi-
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• Measurement of the CP-violating phase $\beta$ in $B^0\to J/\psi {\pi }^{+}{\pi }^{-}$ decays and limits on penguin effects
• The $B_c\to \psi (2S)\pi$, ${\eta }_c(2S)\pi$ decays in the perturbative QCD approach
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• $CP$ violation for $B_c^{+}\to D_{(s)}^{+}{\pi }^{+}{\pi }^{-}$ in Perturbative QCD

Cited by in corpus (7)

• Quasi-two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))\to D\pi \pi$ in the perturbative QCD factorization approach
• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• Quasi-two-body decays $B\to {\eta }_c(1S,2S)[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD approach
• Quasi-two-body decays $B\to D{K}^{\ast }(892)\to DK\pi$ in the perturbative QCD approach
• Branching ratios, $CP$ asymmetries and polarizations of $B\to \psi (2S)V$ decays
• Quasi-two-body decays $B_c\to D_{(s)}[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD factorization approach
• Three body radiative decay $B_s\to \varphi {\bar{K}}^0\gamma$ in the PQCD approach