Branching ratios, CPCP asymmetries and polarizations of B→ψ(2S)VB\rightarrow \psi(2S) V decays

We analyzed the nonleptonic decays $B/B_s\to \psi(2S) V$ with $V=(\rho, \omega, K^{*}, \phi)$ by employing the perturbative QCD (PQCD) factorization approach. Here the branching ratios, the $CP$ asymmetries and the complete set of polarization observables are investigated systematically. Besides the traditional contributions from the factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order (NLO) vertex corrections could also provide considerable contributions. The PQCD predictions for the branching ratios of the $B_{(s)}\to \psi(2S)K^{*}, \psi(2S) \phi$ decays are consistent with the measured values within errors. As for $B\to \psi(2S) \rho, \psi(2S) \omega$ decays, the branching ratios can reach the order of $10^{-5}$ and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct $CP$ asymmetries of the considered decays are very small. Thus the observation of any large direct $CP$ asymmetry for these decays will be a signal for new physics. The mixing induced $CP$ asymmetries in the neutral modes are very close to $\sin 2\beta_{(s)}$, which suggests that these channels can give a cross-check on the measurement of the Cabbibo-Kobayashi-Maskawa (CKM) angle $\beta$ and $\beta_s$. We found that the longitudinal polarization fractions $f_0$ are suppressed to $\sim 50\%$ due to the large nonfactorizable contributions. The magnitudes and phases of the two transverse amplitudes $\mathcal {A}_{\parallel}$ and $\mathcal {A}_{\perp}$ are roughly equal, which is an indication for the approximate light quark helicity conservation in these decays. The overall polarization observables of $B\to \psi(2S) K^{*0}$ and $B_s\to \psi(2S) \phi$ channels are also in good agreement with the experimental measurements as reported by LHCb and BaBar. Other results can also be tested by the LHCb and Belle-II experiments.Comment: 14 pages, 1 figure, 6 table

Quasi-two-body decays B→ηc(1S,2S) [ρ(770),ρ(1450),ρ(1700)→] ππB \to \eta_c {(1S ,2S)}\;[\rho(770),\rho(1450),\rho(1700) \to ]\; \pi\pi in the perturbative QCD approach

In this paper, we calculated the branching ratios of the quasi-two-body decays $B \to \eta_c (1S ,2S)$ $[\rho(770), \rho(1450),\rho(1700)\to ] \pi\pi$ by employing the perturbative QCD (PQCD) approach. The contributions from the $P$-wave resonances $\rho(770)$, $\rho(1450)$ and $\rho(1700)$ were taken into account. The two-pion distribution amplitude $\Phi_{\pi\pi}^{\rm P}$ is parameterized by the vector current time-like form factor $F_{\pi}$ to study the considered decay modes. We found that (a) the PQCD predictions for the branching ratios of the considered quasi-two-body decays are in the order of $10^{-7} \sim 10^{-6}$, while the two-body decay rates ${\cal B}(B \to \eta_c{(1S,2S)} (\rho(1450),\rho(1700)))$ are extracted from those for the corresponding quasi-two-body decays; (b) the whole pattern of the pion form factor-squared $|F_\pi|^2$ measured by the BABAR Collaboration could be understood based on our theoretical results; (c) the general expectation based on the similarity between $B \to \eta_c \pi\pi$ and $B \to J/\psi \pi\pi$ decays are confirmed: $R_2(\eta_c)\approx 0.45$ is consistent with the measured $R_2(J/\psi)\approx 0.56\pm 0.09$ within errors; and (d) new ratios $R_3(\eta_c(1S))$ and $R_4(\eta_c(2S))$ among the branching ratios of the considered decay modes are defined and could be tested by future experiments.Comment: 10 pages, 3 figure

Quasi-two-body decays B→DK∗(892)→DKπB \to D K^*(892) \to D K \pi in the perturbative QCD approach

We study the quasi-two-body decays $B\to D K^*(892) \to D K\pi$ by employing the perturbative QCD approach. The two-meson distribution amplitudes \Phi_{K\pi}^{\text{P-wave}} are adopted to describe the final state interactions of the kaon-pion pair in the resonance region. The resonance line shape for the $P$-wave $K\pi$ component $K^*(892)$ in the time-like form factor $F_{K\pi}(s)$ is parameterized by the relativistic Breit-Wigner function. For most considered decay modes, the theoretical predictions for their branching ratios are consistent with currently available experimental measurements within errors. We also disscuss some ratios of the branching fractions of the concerned decay processes. More precise data from LHCb and Belle-II are expected to test our predictions.Comment: 10 pages, 3 figures and 2 tables.To be published in EPJ

The NLO contributions to the scalar pion form factors and the O(αs2){\cal O}(\alpha_s^2) annihilation corrections to the B→ππB\to \pi\pi decays

In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decrease to LO result in the considered $Q^2$ region; (b) the NLO time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ describes the ${\cal O}(\alpha_s^2)$ contribution to the factorizable annihilation diagrams of the considered $B \to \pi\pi$ decays, i.e. the NLO annihilation correction; (c) the NLO part of the form factor $F'^{(1)}_{\rm a,I}$ is very small in size, and is almost independent with the variation of cutoff scale $\mu_0$, but this form factor has a large strong phase around $-55^\circ$ and may play an important role in producing large CP violation for $B\to \pi\pi$ decays; and (d) for $B^0 \to \pi^+\pi^-$ and $\pi^0\pi^0$ decays, the newly known NLO annihilation correction can produce only a very small enhancement to their branching ratios, less than $3\%$ in magnitude, and therefore we could not interpret the well-known $\pi\pi$-puzzle by the inclusion of this NLO correction to the factorizable annihilation diagrams.Comment: 26 pages, 12 figures, 1 Table; Minor correction

4-Chloro­phenyl 2-oxo-2H-chromene-3-carboxyl­ate

In title compound, C16H9ClO4, the coumarin ring system is approximately planar [maximum deviation = 0.056 (1) Å] and is oriented with respect to the benzene ring at an angle of 22.60 (7)°. Inter­molecular C—H⋯O hydrogen bonding is present in the crystal