Search

Different from the previous treatment in a two-body framework, we introduce the dimeson distribution amplitudes (DAs) to describe the strong dynamics between the S-wave resonances $a_0(980, 1450)$ and the $K\bar K (\pi\eta)$ pair, where the Gegenbauer coefficient required is determined from the experimental data on the time-like form factors involved. The branching ratios and direct CP asymmetries of the decays $B \to a^{(\prime)}_0 h \to K\bar K(\pi\eta) h$, with $a_0=a_0(980)$, $a^{\prime}_0=a_0(1450)$ and $h$ referring to a pion or a kaon, are then calculated in the perturbative QCD (PQCD) approach. We find that the branching ratios of the corresponding quasi-two-body decays $B\to a^{(\prime)}_0 K$ obtained with the narrow width approximation are closer to those predicted in the QCD factorization (QCDF) approach compared to the previous PQCD calculations, no matter a three-body or a two-body framework is assumed. Furthermore, all our predictions for these $B\to a^{(\prime)}_0 K$ decays are below the current experimental upper limits except for those of decays $B^0\to a^{(\prime)-}_0K^+$, which are (slightly) larger than the upper limits. Under the narrow width approximation, the branching ratios of the decays $B^+\to a^{(\prime)+}_0\pi^0$, $B^0\to a^{(\prime)+}_0\pi^-$ and $B^0\to a^{(\prime)0}_0\pi^0$ are comparable to or agree well with the previous PQCD and the QCDF calculations. While for the decays $B^+\to a^{(\prime)0}_0\pi^+$ and $B^0\to a^{(\prime)-}_0\pi^+$, their branching ratios are predicted to be unexpectedly large, for example, the obtained branching ratio of decay $B^+\to a^0_0\pi^+$ is even higher than the current experimental upper limit., Comment: 22 pages, 2 figures

The semileptonic and nonleptonic decays of the b-flavor vector mesons $B^{*}_{u,d,s}$ and $B_{c}^{*}$ are investigated within the covariant light-front quark model (CLFQM). By calculating the form factors of the transitions $B_{u, d, s, c}^{*}\to P$ under the CLFQM, with $P$ denoting a pseudoscalar meson, i.e., $\pi, K, \eta_c(1S,2S), D_{(s)}, B_{(s)}$, we predict and discuss several physical observables, including the branching ratios, polarization fractions $f_{L}, f_{\|}$, and forward-backward asymmetries $A_{FB}$. The total widths of the single-photon radiative decay channels for these b-flavor vector mesons are estimated using their partial widths. In these considered decays, one can find that the semileptonic decays $B_{s}^{*0}\to D_{s}^{-}\ell^{\prime+}{\nu}_{\ell^\prime}$ and $B_{c}^{*+}\to B_{s}^{0}\ell^{\prime+}{\nu}_{\ell^\prime}, \eta_{c}\ell^{\prime+}{\nu}_{\ell^\prime}$, with $\ell^\prime$ being $e$ or $\tau$, and the nonleptonic channels $B_{c}^{*+}\to B^0_{s} \pi^{+}, B^0_{s} \rho^{+}$ have the largest branching ratios, which can reach up to the $10^{-7}$ order, and are most likely to be accessible at the future high-luminosity LHCb and Belle-II experiments., Comment: 30 pages, 4 figures,accepted for publication in Chin. Phys. C

Just like other heavy flavor mesons, the weak decays of $D^*_{(s)}$ mesons can also provide a platform to check the Standard Model (SM), explore new physics (NP) and understand the mechanisms of weak interactions. At present, the theoretical and experimental researches on $D^*_{(s)}$ mesons are relatively limited. In addition to the dominant electromagnetic decays, the $D^*_{(s)}$ weak decays should also be feasible to explore the $D^*_{(s)}$ mesons. In this paper, we use the covariant light-front quark model (CLFQM) to study the branching ratios of the semi-leptonic decays $D^*_{(s)}\to P\ell^{+}\nu_{\ell}$ and the non-leptonic decays $D^*_{(s)}\to PP, PV$ with $P=\pi, K, \eta^{(\prime)}, V=\rho, K^*, \phi$ and $\ell=e, \mu$, which are within the range $10^{-13}\sim 10^{-6}$. Among these decays, the channels $D_{s}^{*+}\to\eta \ell^{+}\nu_{\ell}$ and $D^{*+}_{s}\to \eta\rho^{+}$ possess the largest branching ratios, which can reach up to $10^{-6}$ order. These decays are most likely to be accessible at the future high-luminosity experiments. One can find that the branching ratios $\mathcal{B}r(D_{s}^{*+}\to\eta \ell^{+}\nu_{\ell})=1.46\times10^{-6}$ and $\mathcal{B}r(D_{s}^{*+}\to\eta \rho^{+})=1.04\times10^{-6}$ correspond to tens of thousands of events in the $e^+e^-$ collider experiments, such as the STCF, CEPC and FCC-ee, and tens of millions of events at the HL-LHC. In a word, it is feasible to study the $D^*_{(s)}$ meson weak decays in the future experiments. Furthermore, we also predict and discuss another two physical observations, that is, the longitudinal polarization fraction $f_{L}$ and the forward-backward asymmetry $A_{FB}$, for our considered decays., Comment: 23 pages, 4 figures. arXiv admin note: text overlap with arXiv:2311.04431

In this work, we investigate the form factors of the transitions $B_{(s)} \to D_{0}^{\ast}(2300),D_{s0}^{\ast}(2317),$ $ D_{s1}(2460) $ and $ D_{s1}(2536)$ in the covariant light-front quark model (CLFQM), where these final states are considered as P-wave excited charmed mesons. In order to obtain the form factors for the physical transition processes, we need to extend these form factors from the space-like region to the time-like region. The $q^{2}$-dependence for each transition form factor is also plotted. Then, combined with those form factors, the branching ratios of the two-body nonleptonic decays $B_{(s)}\to D^*_{(s)0}(2300,2317)M, D_{s1}(2460,2536)M$ with $M$ being a light pseudoscalar (vector) meson or a charmed meson are calculated by considering the QCD radiative corrections to the hadronic matrix elements with the QCD factorization approach. Most of our predictions are comparable to the results given by other theoretical approaches and the present available data., Comment: 30 pages, 4 figures

In this paper, we investigate the quasi-two-body decays $B_c \to K_0^{*}(1430,1950) D_{(s)} \to K \pi D_{(s)}$ within the perterbative QCD (PQCD) framework. The S-wave two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the $K\pi$ pair, which involve the time-like form factors and the Gegenbauer polynomials. In the calculations, we adopt two kinds of parameterization schemes to describe the time-like form factors: One is the relativistic Breit-Wigner (RBW) formula, which is usually more siutable for the narrow resonances, and the other is the LASS line shape proposed by the LASS Collaboration, which includes both the resonant and nonresonant components. We find that the branching ratios and the direct CP violations for the decays $B_c \to K_0^{*}(1430) D_{(s)}$ obtained from those of the quasi-two-body decays $B_c \to K_0^{*}(1430) D_{(s)} \to K \pi D_{(s)}$ under the narrow width approximation (NWA) can be consistent well with the previous PQCD results calculated in the two-body framework by assuming that $K^*_0(1430)$ being the lowest lying $\bar q s$ state, which is so-called scenario II (SII). We conclude that the LASS parameterization is more siutable to describe the $K_0^{*}(1430)$ than the RBW formula, and the nonresonant components play an important role in the branching ratios of the decays $B_c \to K_0^{*}(1430) D_{(s)} \to K \pi D_{(s)}$. In view of the large difference between the decay width measurements for the $K_0^{*}(1950)$ given by BaBar and LASS collaborations, we calculate the branching ratios and the CP violations for the quasi-two-body decays $B_c \to K_0^{*}(1950) D_{(s)} \to K \pi D_{(s)}$ by using two values, $\Gamma_{K^*_0(1950)}=0.100\pm0.04$ GeV and $\Gamma_{K^*_0(1950)}=0.201\pm0.034$ GeV, besides the two kinds of parameterizations for the resonance $K^*_0(1950)$., Comment: 16 pages, 3 figures

In addition to the strong and electromagnetic decay modes, the $\psi(1S,2S)$ and $\eta_{c}(1S,2S)$ can also decay via the weak interaction. Such weak decays can be detected by the high-luminosity heavy-flavor experiments. At present, some of the semileptonic and nonleptonic $J/\Psi$ weak decays have been measured at BESIII. Researching for these charmonium weak decays to $D_{(s)}$ meson can provide a platform to check of the standard model (SM) and probe new physics (NP). So we investigate the semileptonic and nonleptonic weak decays of $\psi(1S,2S)$ and $\eta_{c}(1S,2S)$ to $D_{(s)}$ within the covariant light-front quark model (CLFQM). With form factors of the transitions $\psi(1S,2S)\to D_{(s)}$ and $\eta_{c}(1S,2S)\to D_{(s)}$ calculated under the CLFQM, we predict and discuss some physical observables, such as the branching ratios, the longitudinal polarizations $f_{L}$ and the forward-backward asymmetries $A_{FB}$. One can find that the Cabibbo-favored semi-leptonic decay channels $\psi(1S,2S)\to D_{s}^{-}\ell^{+}\nu_{\ell}$ with $\ell=e,\mu$ and the nonleptonic decay modes $\psi(1S,2S)\to D_{s}^{-}\rho^{+}$ have relatively large branching ratios of the order $\mathcal{O}(10^{-9})$, which are most likely to be accessible at the future high-luminosity experiments., Comment: 26 pages, 4 figures

In this work, we investigate the semileptonic decays of $B_{c}$ meson to $\eta_{c}(1S,2S,3S)$, $\psi(1S,2S,3S)$ and $X(3872)$ within the framework of covariant light-front quark model (CLFQM). We combine the helicity amplitudes via the corresponding form factors to obtain the branching ratios of the semileptonic decays $B_{c}\to \eta_{c}(1S, 2S, 3S)\ell\nu_{\ell}$, $B_{c}\to \psi(1S, 2S, 3S))\ell\nu_{\ell}$ and $B_{c}\to X(3872)\ell\nu_{\ell}$ with $\ell=e,\mu,\tau$. In view of the $R_{J/\Psi}$ anomaly released by the LHCb collaboration, it is necessary to calculate the ratios $R_X$ with $X=\psi(1S,2S,3S),\eta_c(1S,2S,3S),X(3872)$ systematically, which are helpful to check the lepton flavor universality (LFU). Furthermore, we also take into account another two physical observables, one is the longitudinal polarization fraction $f_{L}$ and the other is the forward-backward asymmetry $A_{FB}$, which can provide new clues to understand the $R_{J /\Psi}$ anomaly. Such theoretical predictions are necessary and interesting, which can be tested in the future LHCb experiments., Comment: 23 pages, 4 figures

In this work we study the quasi-two-body decays $B_c \to \ K^{*} h \to K \pi h (h = D, D_s, K, \pi, \eta, \eta')$ in the perturbative QCD (PQCD) approach. The two-meson distribution amplitudes (DAs) $\Phi^{\text{P-wave}}_{K\pi}$ are introduced to describe the final state interactions of the K \pi pair, which involve the time-like form factors F_{K\pi}(s) parameterized by the relativistic Breit-Wigner function and the Gegenbauer polynomials. We calculate the branching ratios for these quasi-two-body decays, from which one can obtain the branching raios for the corresponding two-body decays under the narrow width approximation relation. We find that $B^+_c\to K^{*+}D^0$ and $B^+_c\to K^{*0}D^+$ have the largest branching ratios, which can reach up to $10^{-6}$, while the branching ratios for other two-body decays are very small and only about $10^{-8}\sim10^{-7}$. As we expected that the branching ratios of the pure annihilation decays are usually small, while in our considered such type of decays, the channel $B_c^+ \to \bar K^{*0}K^{+}$ has the largest branching ratio, which is near $10^{-6}$. These results are consistent with the previously PQCD calculations obtained in the two-body framework, which can be tested by the future LHCb experiments. For the decays $B_c^+ \to K^{*+} D^{0}\to K^{0}\pi^+D^{0} , B_c^+ \to K^{*0}D^{+}\to K^{+}\pi^-D^{+}$ and $B_c^+ \to \bar K^{*0}D_s^{+}\to K^{-}\pi^+D_s^{+}$, we calculate their direct CP violations and find that $A_{CP}(B_c^+ \to K^{*+}D^{0}\to K^{0}\pi^+D^{0})=(-14.6_{-1.12}^{+9.19})\%$ is the largest one, which is possible measured by the present LHCb experiments. For the pure annihilation type decays, there is no CP violations because only the tree operators are involved. Furthermore, we also give the differential distributions of the branching ratios and the direct CP violations for the decays $B_c\to K^* D_{(s)}\to K \pi D_{(s)}$., Comment: 15 pages, 3 figures, 2 tables

In this work, we investigate the quasi-two-body decays $B_c\to D^*h\to D\pi h$ with $h = (K^0,\pi^0,\eta,\eta^{\prime})$ using the perturbative QCD(PQCD) approach. The description of final state interactions between the $D\pi$ pair is achieved through the two-meson distribution amplitudes(DAs), which are normalized to the time-like form factor. The PQCD predictions on the branching ratios of the quasi-two-body decays $B_c\to D^*h\to D\pi h$ show an obvious hierarchy: $Br(B_{c}^+ \to D^{*+} K^{0}\to D^0\pi^+K^{0})=({5.22}_{-0.74}^{+0.86})\times{10}^{-6}, Br(B_{c}^+ \to D^{*+} \pi^{0}\to D^0\pi^+\pi^{0})=(0.93\pm0.26)\times{10}^{-7}, Br(B_{c}^+ \to D^{*+} \eta\to D^0\pi^+\eta) =({2.83}_{-0.52}^{+0.59})\times{10}^{-8}$ and $Br(B_{c}^+ \to D^{*+} \eta^\prime\to D^0\pi^+\eta^\prime)=({1.89}_{-0.36}^{+0.40})\times{10}^{-8}$. From the invariant mass $m_{D\pi}$-dependence of the decay spectrum for each channel, one can find that the branching fraction is concentrated in a narrow region around the $D^{*}$ pole mass. So one can obtain the branching ratios for the corresponding two-body decays $B_c\to D^{*+}h$ under the narrow width approximation. We find that the branching ratios of the decays $B_c\to D^{*+}h$ are consistent well with the previous PQCD calculations within errors. These predictions will be tested by the future experiments., Comment: 12 pages, 3 figures, accepted for publication in Chin. Phys. C

In this work, we investigate the form factors of $B_c$ decays into $J/\Psi, \psi(2S,3S)$, $\eta_c, \eta_c(2S,3S), \chi_{c0}, \chi_{c1}, h_c$ and $X(3872)$ mesons in the covariant light-front quark model (CLFQM). For the purpose of the branching ratio calculation, the form factors of $B_c\to D^{(*)}, D^{(*)}_s$ transitions are also included. In order to obtain the form factors for the physical transition processes, we need extend these form factors from the space-like region to the time-like region. The $q^2$-dependence for each transition form factor is also plotted. Then, under the factorization method, we calculate the branching ratios of 80 $B_c$ decay channels with a charmonium involved in each mode. Most of our predictions are comparable with the results given by most of other approaches. As to the decays with the radially excited state S-wave charmonia, such as $\psi(2S,3S)$ and $\eta_c(2S,3S)$, involved, there are two sets of parameters for their light-front wave functions, corresponding to scenario I (SI) and scenario II (SII), are adopted to calculate the branching ratios. Comparing with the future experimental data, one can discriminate which parameters are more favored., Comment: 38 pages, 11 figures, 17 tables. Comments are welcome

We study the decays $B_{c,u,d}\to X(3872)P$ in the perturbative QCD (PQCD) approach, where the puzzling resonance $X(3872)$ is involved and $P$ represents a light pseudoscalar meson $K$ and $\pi$. Assuming the $X(3872)$ as a $1^{++}$ charmonium state, we find the following results: (a) The branching ratios for the decays $B^+_c\to X(3872)\pi^+$ and $B^+_c\to X(3872) K^+$ agree with the results predicted by the covariant light-front approach within errors, but are larger than those given by the generalized factorization approach; (b) The branching ratio for the decay $B^+\to X(3872)K^+$ is predicted as $(3.8^{+1.1}_{-1.0})\times10^{-4}$, which is smaller than the previous PQCD calculation result, but still slightly larger than the upper limits set by Belle and BaBar. So we suggest that the decays $B^{0,+}\to X(3872)K^{0,+}$ should be precisely measured by the running LHCb and Belle II experiments, which is very helpful to probe the inner structure of the $X(3872)$; (c) Compared with the decays $B_{u,d}\to X(3872)K$, the decays $B_{u,d}\to X(3872)\pi$ have much smaller branching ratios, which drop to as low as $10^{-6}$; (d) The direct CP violations for these considered decays are very small, only $10^{-3}\sim 10^{-2}$, because the penguin contributions are loop suppressed compared with the tree contributions. Testing the results for the branching ratios and the CP violations including the implicit $SU(3)$ and isospin symmetries in these decays by experiments is helpful to probe the nature of the $X(3872)$., Comment: 11 pages, 2 figures

In this work we study the quasi-two-body decays $B\to K^*\gamma\to K\pi\gamma$ in the perturbative QCD (PQCD) approach. The two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the $K\pi$ pair, which involve the time-like form factors and the Gegenbauer polynomials. We calculate the CP averaged branching ratios for the decays $B_{(s)}\to K^*\gamma\to K\pi\gamma$. Our results are in agreement with the new update data measured by Belle II, which suggests these quasi-two-body decays are more appropriate to be analyzed in three-body framework than in the two-body one. We also predict the direct CP-violation asymmetries for the considered decay modes and find that $A_{CP}(B_{u,d}\to K^*\gamma\to K\pi\gamma)$ is small and less than $1\%$ in magnitude, while $A_{CP}(B_{s}\to K^*\gamma\to K\pi\gamma)$ is larger and can arrive at a few percent. Our predictions can be tested by the future B meson experiments., Comment: 10 pages, 6 figures

We study the quasi-two-body $D\to TP$ decays and the three-body $D$ decays proceeding through intermediate tensor resonances, where $T$ and $P$ denote tensor and pseudoscalar mesons, respectively. We employ $D\to T$ transition form factors based upon light-cone sum rules and the covariant light-front quark model to evaluate the decay rates, with the former giving a better agreement with current data. Though the tree amplitudes with the emitted meson being a tensor meson vanish under factorization approximation, contributions proportional to the tensor decay constant $f_T$ can be produced from vertex and hard spectator-scattering corrections. We also investigate the finite-width effects of the tensor mesons and find that, contrary to three-body $B$ decays, the tensor-mediated $D$ decays are more seriously affected and the narrow width approximation has to be corrected. More experimental data are required in order to extract information topological amplitudes associated with quasi-two-body $D\to TP$ decays. Among the data, the $D^+\to f_2\pi^+$ and $D^+\to \bar K_2^{*0}\pi^+$ branching fractions are not self consistent and further clarification is called for., Comment: 18 pages

We study the quasi-two-body $D\to SP$ decays and the three-body $D$ decays proceeding through intermediate scalar resonances, where $S$ and $P$ denote scalar and pseudoscalar mesons, respectively. Our main results are: (i) Certain external and internal $W$-emission diagrams with the emitted meson being a scalar meson are na{\"i}vely expected to vanish, but they actually receive contributions from vertex and hard spectator-scattering corrections beyond the factorization approximation. (ii) For light scalars with masses below or close to 1~GeV, it is more sensible to study three-body decays directly and compare with experiment as the two-body branching fractions are either unavailable or subject to large finite-width effects of the scalar meson. (iii) We consider the two-quark (scheme I) and four-quark (scheme II) descriptions of the light scalar mesons, and find the latter generally in better agreement with experiment. This is in line with recent BESIII measurements of semileptonic charm decays that prefer the tetraquark description of light scalars produced in charmed meson decays. (iv) The topological amplitude approach fails here as the $D\to SP$ decay branching fractions cannot be reliably inferred from the measurements of three-body decays, mainly because the decay rates cannot be factorized into the topological amplitude squared and the phase space factor. (v) The predicted rates for $D^0\to f_0 P, a_0 P$ are generally smaller than experimental data by one order of magnitude, presumably implying the significance of $W$-exchange amplitudes. (vi) The $W$-annihilation amplitude is found to be very sizable in the $SP$ sector with $|A/T|_{SP}\sim 1/2$, contrary to its suppression in the $PP$ sector with $|A/T|_{PP}\sim 0.18$., Comment: 30 pages, 2 figures, references and discussions added, version accepted by PRD

We probe the inner structure of the meson $D^*_{s0}(2317)$ through the decays of $B_{(s)}$ to two charmed mesons within pQCD approach. Assuming $D^*_{s0}(2317)$ as a scalar meson with $\bar cs$ structure, we find that the predictions for the branching ratios of the decays $B^+\to D^{*+}_{s0}(2317)\bar D^{(*)0}, B^0\to D^{*+}_{s0}(2317)D^{(*)-}$ can explain data within errors. The branching ratios for the decays $B_s\to D^{*+}_{s0}(2317)D_s^{(*)+}$ are estimated to reach up to $10^{-3}$ order, which can be observed by the present LHCb and SuperKEKB experiments. In this work, the decay constant of the meson $D^*_{s0}(2317)$ is an input parameter. Unfortunately, its value has been studied by many references but with large uncertainties. Our calculation shows that a smaller decay constant of the meson $D^*_{s0}(2317)$ is supported by compared with the present data, say $55\sim70$ MeV. We also calculate the ratios $R_1=\frac{Br(B^+\to D^{*+}_{s0}(2317)\bar D^0)}{Br(B^+\to D^{*+}_{s0}(2317)\bar D^{*0})})$ and $R_2=\frac{Br(B^0\to D^{*+}_{s0}(2317)D^-)}{Br(B^0\to D^{*+}_{s0}(2317)D^{*-})}$, which are valuable to determine the inner structure of $D^*_{s0}(2317)$ by compared with the experimental results. Our predictions for the ratios $R_{1,2}$ are consistent with the present data within errors.We expect that these two ratios can be well measured by the future experiments through improving the measurement accuracy for the decays $B^+\to D^{*+}_{s0}(2317)\bar D^{*0}$ and $B^0\to D^{*+}_{s0}(2317)D^{*-}$., Comment: 19 pages, 2 figures

We extend the threshold resummation of the large logarithms $\ln x$ which appear in factorization formulas for exclusive $B$ meson decays, $x$ being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with $x\sim 0$ stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the $B\to K\pi$ decays under the NLL resummation, and find that it induces 20-25\% variation of the direct CP asymmetries compared to those from the LL resummation. Our way to avoid the Landau singularity in the inverse Mellin transformation causes little theoretical uncertainty., Comment: 12 pages,4 figures

In this work, we use pQCD approach to calculate 20 $B_{(s)}\to D^*_{s0}(2317)P(V)$ two body decays by assuming $D^*_{s0}(2317)$ as a $\bar cs$ scalar meson, where $P(V)$ denotes a pseudoscalar (vector) meson. These $B_{(s)}$ decays can serve as an ideal platform to probe the valuable information on the inner structure of the charmed-strange meson $D^*_{s0}(2317)$, and to explore the dynamics of strong interactions and signals of new physics. These considered decays can be divided into two types: the CKM favored decays and the CKM suppressed decays. The former are induced by $b\to c$ transition, whose branching ratios are larger than $10^{-5}$. The branching fraction of the decay $\bar B^0_s\to D^{*+}_{s0}(2317)\rho^{-}$ is the largest and reaches about $1.8\times 10^{-3}$, while the branching ratios for the decay $\bar B^0_s\to D^{*+}_{s0}(2317)K^{*-}$ and other two pure annihilation decays $\bar B^0\to D^{*+}_{s0}(2317)K^-, D^{*+}_{s0}(2317)K^{*-}$ are only at $10^{-5}$ order. Our predictions are consistent well with the results given by the light cone sum rules approach. These decays are most likely to be measured at the running LHCb and the forthcoming SuperKEKB. The latter are induced by $b\to u$ transition, among of which the channel $\bar B^0\to D^{*-}(2317)\rho^+$ has the largest branching fraction, reaching up to $10^{-5}$ order. Again the pure annihilation decays $B^-\to D^{*-}_{s0}(2317)\phi, \bar B^0\to D^{*-}_{s0}(2317)K^+(K^{*+}), B^-\to D^{*-}_{s0}(2317)K^0(K^{*0})$, have the smallest branching ratios, which drop to as low as $10^{-10}\sim10^{-8}$., Comment: 15 pages, 1 figure

We study the three body radiative decay $B_s\to \phi \bar K^0 \gamma$ by introducing the $\phi K$ pair distribution amplitudes (DAs) in the perturbative QCD approach. This nonperturbative inputs, the two meson DAs, is very important to simplify the calculations. Besides the dominant electromagnetic penguin operator $O_{7\gamma}$, the subleading contributions from chromomagnetic penguin operator $O_{8g}$, quark-loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay $B_s\to \phi \bar K^0 \gamma$ is about $(9.26^{+1.79+3.12+0.64}_{-1.61-3.86-0.49})\times10^{-8}$, which is much smaller compared with that for the decay $B^0\to \phi K^0\gamma$. It is mainly because that the former decay induces by $b\to d\gamma$ with small CKM matrix element being proportional to $\lambda^3$. The prediction for the direct CP asymmetry is $A^{dir}_{CP}(B_s\to \phi \bar K^0 \gamma)=(-4.1^{+0.4+1.7+0.2}_{-0.6-1.2-0.1})\%$, which is well consistent with the result from the U-spin symmetry approach. we also predict the $B_s \to\phi \bar K^0\gamma$ decay spectrum, which exhibits a maximu at the $\phi K$ invariant masss around 1.95 GeV., Comment: 17 pages,6 figures, Accepted for publication in EPJC

Two body $B$ meson decays involving the radially excited meson $\psi(2S)/\eta_c(2S)$ in the final states are studied by using the perturbative QCD (pQCD) approach. We find that: (a) The branching ratios for the decays involving $K$ meson are predicted as $Br(B^+\to\psi(2S)K^+)=(5.37^{+1.85}_{-2.22})\times10^{-4}, Br(B^0\to\psi(2S)K^0)=(4.98^{+1.71}_{-2.06})\times10^{-4}, Br(B^+\to\eta_c(2S)K^+)=(3.54^{+3.18}_{-3.09})\times10^{-4}$, which are consistent well with the present data when including the next-to-leading-order (NLO) effects. Here the NLO effects are from the vertex corrections and the NLO Wilson coefficients. The large errors in the decay $B^+\to\eta_c(2S)K^+$ are mainly induced by using the decay constant $f_{\eta_c(2S)}=0.243^{+0.079}_{-0.111}$ GeV with large uncertainties. (b) While there seems to be some room left for other higher order corrections or the non-perturbative long distance contributions in the decays involving $\pi$ meson, $Br(B^+\to\psi(2S)\pi^+)=(1.17^{+0.42}_{-0.50})\times10^{-5}, Br(B^0\to\psi(2S)\pi^0)=0.54^{+0.20}_{-0.23}\times10^{-5}$, which are smaller than the present data. The results for other decays can be tested at the running LHCb and forthcoming Super-B experiments. (c) There is no obvious evidence of the direct CP violation being seen in the decays $B\to \psi(2S)\pi(K), \eta_c(2S)\pi(K)$ in the present experiments, which is supported by our calculations. If a few percent value is confirmed in the future , it would indicate new physics definitely., Comment: 11 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.00524

We studied the B meson decays $B\to J/\Psi K_1(1270,1400)$ in the pQCD approach beyond the leading order. With the vertex corrections and the NLO Wilson coefficients included, the branching ratios of the considered decays are $Br(B^+\to J/\Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}\times10^{-3}, Br(B^+\to J/\Psi K_1(1400)^+)=7.03^{+2.70}_{-2.52}\times10^{-4}$, and $Br(B^0\to J/\Psi K_1(1270)^0)=(1.63^{+0.60}_{-0.64})\times10^{-3}$ with the mixing angle $\theta_{K_1}=33^\circ$, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that $\theta_{K_1}\sim33^\circ$ is much more favored than $58^{\circ}$. Furthermore, we also give the predictions for the polarization fractions, direct CP violations from the different polarization components, the relative phase angles for the considered decays with the mixing angle $\theta_{K_1}=33^\circ$ and $58^\circ$, respectively. The direct CP violations of the two charged decays $B^+\to J/\Psi K_1(1270,1400)^+$ are very small $(10^{-4}\sim10^{-5})$, because there is no weak phase until up to $\mathcal{O}(\lambda^4)$ with the Wolfenstein parameter $\lambda=0.22537$. These results can be tested at the running LHCb and forthcoming Super-B experiments., Comment: 14 pages,3 figures,to appear in EPJC

Direct CP violation in charmless three-body hadronic decays of $B$ mesons is studied within the framework of a simple model based on the factorization approach. Three-body decays of heavy mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated and penguin-dominated three-body decays arise from the $b\to u$ tree transition and $b\to s$ penguin transition, respectively. The former can be evaluated in the framework of heavy meson chiral perturbation theory with some modification, while the latter is governed by the matrix element of the scalar density $\langle M_1M_2|\bar q_1 q_2|0\rangle$. Strong phases in this work reside in effective Wilson coefficients, propagators of resonances and the matrix element of scalar density. In order to accommodate the branching fraction and CP asymmetries observed in $B^-\to K^-\pi^+\pi^-$, the matrix element $\langle K\pi|\bar sq|0\rangle$ should have an additional strong phase, which might arise from some sort of power corrections such as final-state interactions. We calculate inclusive and regional CP asymmetries and find that nonresonant CP violation is usually much larger than the resonant one and that the interference effect is generally quite significant. If nonresonant contributions are turned off in the $K^+K^-K^-$ mode, the predicted CP asymmetries due to resonances will be wrong in sign when confronted with experiment. In our study of $B^-\to \pi^-\pi^+\pi^-$, we find that ${\cal A}_{C\!P}(\rho^0\pi^-)$ should be positive in order to account for CP asymmetries observed in this decay. However, all theories predict a large and negative CP violation in $B^-\to \rho^0\pi^-$. Measurements of CP-asymmetry Dalitz distributions put very stringent constraints on the theoretical models. We check the magnitude and the sign of violation in some (large) invariant mass regions to test our model., Comment: 32 pages, 3 figures

Through analyzing the $B_{(s)}$ charmed decays $B^{0}\to \bar D_{0}f_0(980)$ and $B_{s}\to \bar D_{0}f_0(980)$ within the framework of the PQCD factorization approach and comparing with the current data, we find that there are two possible regions for the $f_0(980)-f_0(500)$ mixing angle $\theta$: one is centered at $34^\circ\sim38^\circ$ and the other is falls into $142^\circ\sim154^\circ$. The former can overlap mostly with one of allowed angle regions extracted from the decay $B^{0}\to \bar D_{0}f_0(500)$. The branching fractions of $B_s$ decay modes are less sensitive to the mixing angle compared with those of B decay modes. Especially, for the decay $B_{s}\to D^0 f_0(980)$, its branching fraction changes only slightly between $(1.2\sim1.8)\times10^{-7}$ when the mixing angle $\theta$ runs from $0^\circ$ to $180^\circ$. All of our results support the picture that the $f_0(980)$ is dominated by two quark component in the B decay dynamic mechanism. Furthermore, the $s\bar s$ component is more important than the $q\bar q=(u\bar u+d\bar d)/\sqrt{2}$ component. This point is different from $f_0(500)/\sigma$. Last but not least, our picture is not in conflict with the popular four-quark explanation., Comment: 15 pages, 4 figures

Within the framework of the perturbative QCD approach, we study the two-body charmless decays $B\to K_1(1270)(K_1(1400))\pi(K)$. We find the following results: (i) The decays $\bar B^0\to K_1(1270)^+\pi^-, K_1(1400)^+\pi^-$ are incompatible with the present experimental data. There exists a similar situation for the decays $\bar B^0\to a_1(1260)^+K^-, b_1(1235)^+K^-$, which are usually considered that the nonperturbative contributions are needed to explain the data. But the difference is that the nonperturbative contributions seem to play opposite roles in these two groups of decays.(ii) The pure annihilation type decays $\bar B^0\to K_1^{\pm}(1270)K^{\mp}, K_1^{\pm}(1400)K^{\mp}$ are good channels to test whether an approach can be used to calculate correctly the strength of the penguin-annihilation amplitudes. Their branching ratios are predicted at $10^{-7}$ order, which are larger than the QCDF results. (iii) The dependence of the direct CP-violating asymmetries of these decays on the mixing angle $\theta_{K_1}$ are also considered., Comment: 18 pages, 4 figures

Hadronic charmless B decays to scalar mesons are studied within the framework of QCD factorization (QCDF). Considering two different scenarios for scalar mesons above 1 GeV, we find that the data favor the scenario in which the scalars $a_0(1450)$ and $K_0^*(1430)$ are the lowest lying $q\bar q$ bound states. This in turn implies a preferred four-quark nature for light scalars below 1 GeV. Assuming $K_0^*(1430)$ being a lowest lying $q\bar s$ state, we show that the data of $B\to K_0^*(1430)\eta^{(')}$ and $B\to K_0^*(1430)(\rho,\omega,\phi)$ can be accommodated in QCDF without introducing power corrections induced from penguin annihilation, while the predicted $B^-\to \ov K_0^{*0}(1430)\pi^-$ and $\ov B^0\to K_0^{*-}(1430)\pi^+$ are too small compared to experiment. In principle, the data of $K_0^*(1430)\pi$ modes can be explained if penguin-annihilation induced power corrections are taken into account. However, this will destroy the agreement between theory and experiment for $B\to K_0^*(1430)(\eta^{(')},\rho,\omega,\phi)$. Contrary to the pseudoscalar meson sector where $B\to K\eta'$ has the largest rate in 2-body decays of the $B$ meson, we show that $Br(B\to K_0^*\eta')<\B(B\to K_0^*\eta)$. The decay $\ov B^0\to a_0(980)^+K^-$ is found to have a rate much smaller than that of $\ov B^0\to a_0(980)^+\pi^-$ in QCDF, while it is the other way around in pQCD. Experimental measurements of these two modes will help discriminate between these two different approaches. Assuming 2-quark bound states for $f_0(980)$ and $f_0(500)$, the observed large rates of $f_0(980)K$ and $f_0(980)K^*$ modes can be explained in QCDF with the $f_0(980)\!-\!f_0(500)$ mixing angle $\theta$ in the vicinity of $20^\circ$., Comment: 25 pages, 3 figures

Within the framework of perturbative QCD approach, we study the charmless two-body decays into final states involving one axial-vector (A), $a_1(1260)$ or $b_1(1235)$, and one vector (V), namely $\rho(\omega,\phi)$. Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) Except the decays $\bar B^0\to a^{0}_1\rho^0(\omega)$, other tree-dominated decays $B\to a_1\rho(\omega)$ have larger branching ratios, at the order of $10^{-5}$. (b)Except the decays $\bar B\to b^+_1\rho^-$ and $B^-\to b^0_1\rho^-$, other $B\to b_1\rho(\omega)$ decays have smaller branching ratios, at the order of $10^{-6}$. (c) The decays $B\to a_1(b_1) \phi$ are highly suppressed and have very small branching ratios, at the order of $10^{-9}$. (d) For the decays $\bar B^0 \to a_1^0\rho^0$ and $B^-\to b_1^-\rho^0$, their two transverse polarizations are larger than their longitudinal polarizations, which are about 43.3% and 44.9%, respectively. (d) The two transverse polarizations have near values in the decays $B\to a_1\rho(\omega)$, while have large differences in some of $B\to b_1\rho(\omega)$ decays. (e) For the decays $B^-\to a^{0}_1\rho^-, b^{0}_1\rho^-$ and $\bar B^0\to b^{0}_1\rho^0, b^{0}_1\omega$, where the transverse polarization fractions range from 4.7 to 7.5%, we calculate their direct CP-violating asymmetries with neglecting the transverse polarizations and find that those for two charged decays have smaller values, which are about 11.8% and -3.7%, respectively., Comment: 15pages, 4 figures

Within the framework of perturbative QCD approach, we study the charmless two-body decays $B_s \to a_1(1260)(b_1(1235))P(V)$ ($P, V$ represent the light pseudo-scalar and vector mesons, respectively.). Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) The decays $\bar B^0_s\to a^{-}_1K^{+}(K^{*+})$ have the contributions from the factorization emission diagrams with a large Wilson coefficient $C_2+C_1/3$ (order of 1), so they have the largest branching ratios and arrive at $10^{-5}$ order. While for the decays $\bar B^0_s\to a^{0}_1 K^{0}(K^{*0})$, the Wilson coefficient is $C_1+C_2/3$ in tree level and color suppressed, so their branching ratios are small and fall in the order of $10^{-7}\sim10^{-8}$. For the decays $\bar B^0_s\to b_1K(K^*)$, all of their branching ratios are of order few times $10^{-6}$. (b) For the pure annihilation type decays $\bar B^0_s\to a_1(b_1)\rho$ except the decays $\bar B^0_s\to a_1\pi$ having large branching ratios of order few times $10^{-6}$, the most other decays have the branching ratios of $10^{-7}$ order. The branching ratios of the decays $\bar B^0_s\to a^0_1(b^0_1)\omega$ are the smallest and fall in the order of $10^{-8}\sim10^{-9}$. (c)The branching ratios and the direct CP-asymmetries of decays $\bar B^0_s\to a^0_1(b_1^0)\eta^{(\prime)}$ are very sensitive to take different Gegenbauer moments for $\eta^{(\prime)}$. (d) Except for the decays $\bar B^0_s\to a^{0}_1 K^{*0}, a^{0}_1\omega, b^{0}_1\omega$, the longitudinal polarization fractions of other $\bar B^0_s\to a_1(b_1)V$ decays are very large and more than 90%. (e) Compared with decays $\bar B^0_s\to a_1(b_1)P$, most of $\bar B^0_s\to a_1(b_1)V$ decays have smaller direct CP asymmetries., Comment: 17 pages, 5 figures

In the two-quark model supposition for $K_0^{*}(1430)$, the branching ratios and the direct CP-violating asymmetries for decays $\bar B_s^0\to K^{*0}_0(1430)\pi^0, K^{*+}_0(1430)\pi^-$ are studied by employing the perturbative QCD factorization approach. We find that although these two decays are both tree-dominated, the ratio of their penguin to tree contributions are very different: there is only a few percent for the decay $\bar B_s^0\to K^{*+}_0(1430)\pi^-$, while about 37% in scenario I, even 51% in scenario II for the decay $\bar B_s^0\to K^{*0}_0(1430)\pi^0$. It results that these two decays have very different values in the branching ratios and the direct CP asymmetries. The branching ratio of the decay $\bar B_s^0\to K^{*+}_0(1430)\pi^-$ is at the order of $10^{-5}$, and its direct CP asymmetry is about (20-30)%. While for the decay $\bar B_s^0\to K^{*0}_0(1430)\pi^0$, its direct CP-violating asymmetry is very large and about 90%, but it is difficult to measure it, because the branching ratio for this channel is small and only $10^{-7}$ order., Comment: 8pages, 2figures

Within the framework of perturbative QCD approach, we study the charmless two-body decays $B\to a_1(1260)K^*, b_1(1235)K^*$. Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) Our predictions for the branching ratios are consistent well with the QCDF results within errors, but much larger than the naive factorization approach calculation values. (b) We predict that the anomalous polarizations occurring in the decays $B\to \phi K^*, \rho K^*$ also happen in the decays $B\to a_1K^*$, while do not happen in the decays $B\to b_1K^*$. Here the contributions from the annihilation diagrams play an important role to explain the lager transverse polarizations in the decays $B\to a_1K^*$, while they are not sensitive to the polarizations in decays $B\to b_1K^*$. (c) Our predictions for the direct CP-asymmetries agree well with the QCDF results within errors. The decays $\bar B^0\to b^{+}_1K^{*-}, B^-\to b^{0}_1K^{*-}$ have larger direct CP-asymmetries, which could be measured by the present LHCb experiments., Comment: 12pages, 1figures. arXiv admin note: substantial text overlap with arXiv:1203.5913, arXiv:1203.5918

In the two-quark model supposition for the meson $a_0(1450)$, which can be viewed as either the first excited state (scenario I) or the lowest lying state (scenario II), the branching ratios and the direct CP-violating asymmetries for decays $B^-\to a^{0}_0(1450)K^{*-}, a^{-}_0(1450)K^{*0}$ and $\bar B^0\to a^{+}_0(1450)K^{*-}, a^{0}_0(1450)\bar K^{*0}$ are studied by employing the perturbative QCD factorization approach. We find the following results: (a) For the decays $B^-\to a^{-}_0(1450)K^{*0}, \bar B^0\to a^{+}_0(1450)K^{*-}, a^{0}_0(1450)\bar K^{*0}$, their branching ratios in scenario II are larger than those in scenario I about one order. So it is easy for the experiments to differentiate between the scenario I and II for the meson $a_0(1450)$. (b)For the decay $B^-\to a^{0}_0(1450)K^{*-}$, due to not receiving the enhancement from the $K^*-$emission factorizable diagrams, its penguin operator contributions are the smallest in scenario II, which makes its branching ratio drop into the order of $10^{-6}$. Even so, its branching ratio in scenario II is still larger than that in scenario I about 2.5 times. (c) Even though our predictions are much larger than those from the QCD factorization results, they are still consistent with each other within the large theoretical errors from the annihilation diagrams. (d) We predict the direct CP- violating asymmetry of the decay $B^-\to a^{-}_0(1450)K^{*0}$ is small and only a few percent., Comment: 15 Pages, 5 Figures

In the two-quark model supposition for $K_0^{*}(1430)$, which can be viewed as either the first excited state (scenario I) or the lowest lying state (scenario II), the branching ratios and the direct CP-violating asymmetries for decays $\bar B_s^0\to K^{*0}_0(1430)\phi, K^{*0}_0(1430)\omega, K^{*0}_0(1430)\rho^0, K^{*+}_0(1430)\rho^-$ are studied by employing the perturbative QCD factorization approach. We find the following results: (a) Enhanced by the color allowed tree amplitude with large Wilson coefficients $a_1=C_2+C_1/3$, the branching ratio of $\bar B_s^0\to K^{*+}_0(1430)\rho^-$ is much larger than those of the other three decays and arrives at $(3.4^{+0.8}_{-0.7})\times 10^{-5}$ in scenario I, even $10^{-4}$ order in scenario II, and its direct CP violating asymmetry is the smallest, around 10%, so this channel might be measurable in the current LHC-b experiments, where a large number (about $10^{12}$) of $B$ mesons will be produced per year. This high statistics will make the measurement possible. (b) For the decay modes $\bar B^0_s\to K^{*0}_0(1430)\omega, K^{*0}_0(1430)\rho^0$, their direct CP-violating asymmetries are large, but it might be difficult to measure them, because their branching ratios are small and less than (or near) $10^{-6}$ in both scenarios. For example, in scenario I, these values are ${\cal B}(\bar B_s^0\to K^*_0(1430)\omega)=(8.2^{+1.8}_{-1.7})\times 10^{-7}, {\cal B}(\bar B_s^0\to K^*_0(1430)\rho^0)=(9.9^{+2.1}_{-2.0})\times 10^{-7}, \acp^{dir}(\bar B^0_s\to K^{*0}_0(1430)\omega)=-24.1^{+2.8}_{-2.5}, \acp^{dir}(\bar B^0_s\to K^{*0}_0(1430)\rho^0)=26.6^{+2.5}_{-2.5}.$ (c) For the decay $\bar B^0_s\to K^*_0(1430)\phi$, the predicted branching ratios are also small and a few times $10^{-7}$ in both scenarios; there is no tree contribution at the leading order, so its direct CP-violating asymmetry is naturally zero., Comment: 15 Pages, 4 figures