Search

The $CP$ violation (CPV) in the baryon system has not yet been definitively established. We demonstrate that individual partial-wave CPV in the $\Lambda_b\to p\pi^-,pK^-$ decays can exceed $10\%$, but the destruction between different partial waves results in small net direct CPV as observed in current experiments. There is thus high possibility of identifying CPV in $b$-baryon decays through measurements of partial-wave CPV. The above observation is supported by the first full QCD calculation of two-body hadronic $\Lambda_b$ baryon decays with controllable uncertainties in the perturbative QCD formalism., Comment: 5 pages, 2 figures,4 tables

The scalars $f_0$ closest to 1.5 GeV contain the mesons $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, and the latter two ones are usually viewed as the potential candidates for the scalar glueballs. In this work, by including the important contributions from the vertex corrections, we study the decays $B^0 \to J/\psi f_0$ within the improved perturbative QCD approach and analyze the possible scalar glueball hunting. Together with the two mixing models, namely, $f_0(1500) (f_0(1710))$ being the primary scalar glueball in model I (II), and two classification scenarios, namely, $f_0$ being the $q\bar q$ excited (ground) states in scenario 1 (2), the branching fractions associated with their ratios for $B^0 \to J/\psi f_0$ are evaluated comprehensively. The predictions with still large uncertainties in the considered two mixing models are roughly consistent with currently limited data, which indicates that both more rich data and more precise predictions are urgently demanded to figure out the scalar glueball clearly in the future. Moreover, several interesting ratios between the branching fractions of $B^0 \to J/\psi f_0(\to \pi^+ \pi^-/K^+ K^-)$ and $B^0 \to J/\psi \rho^0/\phi (\to \pi^+ \pi^-/ K^+ K^-)$ that could help us to understand the nature of scalar $f_0$ are defined and predicted theoretically. These ratios should be examined in future experiments., Comment: 28 pages, 3 figures, 6 tables; revised version according to referee's comments; contents improved and references added

Within the nonrelativistic QCD (NRQCD) framework, we complete the three-loop calculations of the NRQCD renormalization constants and the matching coefficients, for the heavy flavor-changing temporal vector, spatial-spatial tensor, spatial-temporal axial-tensor currents, which are coupled to the $P$-wave $c\bar b$ mesons. We further study the ten decay constants for the $c\bar b$ mesons ($B_c,B_c^*,B_{c0}^*,B_{c1}$) coupled with the ten heavy flavor-changing currents involving (pseudo-)scalar, (axial-)vector and (axial-)tensor up to the next-to-next-to-next-to-leading order (N$^3$LO) of $\alpha_s$. We obtain the six ratios of decay constants by approximating them to the corresponding ratios of matching coefficients. We find the N$^3$LO QCD corrections to the six ratios of decay constants have good convergence and weak scale-dependence. We finally predict the hierarchical relationship among the ten decay constants for the $c\bar b$ mesons coupled with the ten currents.

We present the three-loop calculations of the nonrelativistic QCD (NRQCD) current renormalization constants and corresponding anomalous dimensions, and the matching coefficients for the spatial-temporal tensor and spatial-spatial axial-tensor currents with two different heavy quark masses. We obtain the convergent decay constant ratio up to the next-to-next-to-next-to-leading order (N$^3$LO) for the $S$-wave vector meson $B_c^*$ involving the tensor and axial-tensor currents. We obtain the three-loop finite ($\epsilon^0$) term in the ratio of the QCD heavy flavor-changing tensor current renormalization constant in the on-shell ($\mathrm{OS}$) scheme to that in the modified-minimal-subtraction ($\mathrm{\overline{MS}}$) scheme, which is helpful to obtain the three-loop matching coefficients for all heavy flavor-changing (axial-)tensor currents.

Within the framework of non-relativistic QCD (NRQCD) factorization, we compute the matching coefficients between full Quantum Chromodynamics (QCD) and NRQCD for the heavy flavor-changing vector, axial-vector, scalar and pseudo-scalar currents up to next-to-next-to-next-to-leading order (N$^3$LO). We accomplish the analytical expressions for the three-loop renormalization constants and the corresponding anomalous dimensions for all of the four NRQCD currents with two different heavy flavors. The three-loop QCD corrections to the matching coefficients turn out to be significantly larger than lower order corrections. By employing the scale relation, we obtain the N$^3$LO corrections to the wave functions at the origin for the vector $B_c^*$ meson and the pseudo-scalar $B_c$ meson from the known result for the equal-mass heavy quarkonium in potential NRQCD (pNRQCD). We find large cancellations at the third order between the matching coefficients and the wave functions at the origin, and obtain the convergent decay constants of $B^*_{c}$ and $B_{c}$ up to N$^3$LO. We present the complete perturbative QCD predictions for the decay constants, leptonic decay widths, and branching ratios of the beauty-charmed mesons., Comment: arXiv admin note: text overlap with arXiv:2301.00220

We show the three-loop calculation of the matching coefficients $\mathcal{C}_J$ for the four heavy flavor-changing currents in nonrelativistic Quantum Chromodynamics effective theory and confirm the surprising observation of the nonconvergence behaviors of the matching coefficients for beauty-charm mesons. We demonstrate that the higher-order correction to the wave function at origin can solve the nonconvergence problem. By employing the scaling relation, we simultaneously obtain the decay constants for beauty-charm mesons up to the three-loop accuracy and the hyperfine mass splitting in agreement with the experimental data. The perturbative predictions for the leptonic decays of the beauty-charm mesons shall provide a guide in ongoing and future precision heavy flavor experiments., Comment: The content of this paper arXiv:2303.02692 substantially overlaps with that of the paper arXiv:2303.07220, the latter of which has already been published in the JHEP journal (JHEP 05 (2023) 189)

Within the framework of perturbative QCD factorization, we investigate the nonfactorizable contributions to these factorization-forbidden Quasi-two-body decays $B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-)$ with $ h=\pi, K$. We compare our predicted branching ratios for the $B_{(s)}\rightarrow K\chi_{c0}\rightarrow K\pi^+\pi^-(K^+K^-)$ decay with available experiment data as well as predictions by other theoretical studies. The branching ratios of these decays are consistent with data and other theoretical predictions. In the Cabibbo-suppressed decays $B_{(s)}\rightarrow h\chi_{c0}\rightarrow h\pi^+\pi^-(K^+K^-)$ with $h=\bar{K}^0,\pi$, however, the values of the branching ratios are the order of $10^{-7}$ and $10^{-8}$. The ratio $R_{\chi_{c0}}$ between the decay $B^+\rightarrow \pi^+\chi_{c0}\rightarrow \pi^+\pi^+\pi^-$ and $B^+\rightarrow K^+\chi_{c0}\rightarrow K^+\pi^+\pi^-$ and the distribution of branching ratios for different decay modes in invariant mass are considered in this work., Comment: 8 pages, 2 figures, accepted for publication in Chin. Phys. C

We compute the matching coefficient between the quantum chromodynamics (QCD) and the non-relativistic QCD ( NRQCD) for the flavor-changing scalar current involving the heavy charm and bottom quark, up to the three-loop order within the NRQCD factorization. For the first time, we obtain the analytical expressions for the three-loop renormalization constant $\tilde{Z}_s(x,R_f)$ and the corresponding anomalous dimension $\tilde{\gamma}_s(x,R_f)$ for the NRQCD scalar current with the two heavy bottom and charm quark. We present the precise numerical results for those relevant coefficients $(C_{FF}(x_0), \cdots, C_{FBB}(x_0))$ with an accuracy of about thirty digits. The three-loop QCD correction turns out to be significantly large. The obtained matching coefficient $C_s(\mu_f,\mu,m_b,m_c)$ is helpful to analyze the threshold behaviours when two different heavy quarks are close to each other and form the double heavy $B_c$ mesons., Comment: The projector is updated

We present the next-to-next-to-leading order (NNLO) QCD corrections to the decay constants for both the pseudoscalar and vector beauty-charmed mesons $B_{c}$ and $B^*_{c}$ in nonrelativistic QCD effective theory. Explicit NNLO calculation verified that the $B_c$ decay constant from pseudoscalar current is identical with the $B_c$ decay constant from axial-vector current. The NNLO result for the vector decay constant of $B^*_{c}$ meson is novel. Combined with the latest extraction of nonrelativistic QCD long-distance matrix elements of $B_c$ meson, we give the branching ratios of leptonic decays of $B_{c}$ and $B^*_{c}$ mesons. In addition, the novel anomalous dimension for the flavor-changing heavy quark vector current in nonrelativistic QCD effective theory are helpful to investigate the threshold behaviours of two different heavy quarks., Comment: 9 pages, 7 figures, 6 tables; the inputting values of LDMEs are changed with new references and then the phenomenological results are also updated; some comments added; several typos corrected

The perturbative QCD (PQCD) approach based on $k_T$ factorization has made a great achievement for the QCD calculation of the hadronic B decays. Regulating the endpoint divergence by the transverse momentum of quarks in the propagators, one can do the perturbation calculation for kinds of diagrams including the annihilation type diagrams. In this paper, we review the current status of PQCD factorization calculation of two-body charmless $B\to PP, PV, VV$ decays up to the next-to-leading order (NLO) QCD corrections. two new power suppressed terms in decaying amplitudes are also taken into account. By using the universal input (non-perturbative) parameters, we collected the branching ratios and ${\bf CP}$ asymmetry parameters for all the charmless two body $B$ decays, calculated in the PQCD approach up to the NLO, including some power suppressed terms in decaying amplitudes. The results are compared with the ones from QCD factorization approach, soft-collinear effective theory approach and the current experimental measurements. For most considered B meson decays, the PQCD results for branching ratios agree well with other approaches and the experimental data. The PQCD predictions for the ${\bf CP}$ asymmetry parameters for many of the decay channels do not agree with other approaches, but have a better agreement with the experimental data. The longstanding $K \pi $ puzzle about the pattern of the direct CP asymmetries of the penguin-dominated $B \to K \pi $ decays can be understood after the inclusion of the NLO contributions in PQCD. The NLO corrections and power suppressed terms play an important role in the color suppressed and pure annihilation type $B$ decay modes. These rare decays are more sensitive to different types of corrections, providing opportunity to examine the factorization approach with the more precise experimental measurements., Comment: 52 pages, 4 figures, 11 tables

We present a next-to-leading order (NLO) QCD corrections to $B_c\to \eta_c$ and $B_c\to J/\psi$ tensor form factors within nonrelativistic QCD (NRQCD) framework. The full analytical results for $B_c$ to S-wave charmonium tensor form factors are obtained. We also studied the asymptotic behaviours of tensor form factors in hierarchy heavy quark limit, i.e. $m_b\to\infty,~ m_c\to\infty, ~\mathrm{and }~m_c/m_b\to0$. A compact expression for tensor form factors are given analytically in the hierarchy heavy quark limit. The relation among different form factors is also analyzed especially at large momentum recoil point. The numerical results for the $B_c$ to charmonium tensor form factors in all the physical region are given in the end., Comment: comments: 9 pages, 9 figures; some typos corrected, references added; to be published in PRD

In this work, we make a detailed analysis on the penguin-dominant processes $B_{(s)}^0 \to \phi\phi \to (K^+K^-)(K^+K^-)$ in the perturbative QCD (PQCD) approach. In addition to the dominant $P$-wave resonance, the scalar background $f_0(980) \to K^+K^-$ is also accounted for. We improve the Gegenbauer moments in $KK$ two-meson distribution amplitudes by fitting the PQCD factorization formulas to measured branching ratios of three-body and four-body $B$ decays. We extract the branching ratios of two-body $B_{(s)}^0 \to \phi\phi$ decays from the corresponding four-body decay modes and calculate the relevant polarization fractions together with two relative phases $\phi_{\parallel,\perp}$, which are consistent with the previous theoretical predictions. The PQCD predictions for the "true" triple product asymmetries (TPAs) are zero which are expected in the standard model due to the vanishing weak phase difference, and support the current data reported by the CDF and LHCb Collaborations. A large "fake" TPA $\mathcal{A}_\text{T-fake}^1=30.4\%$ of the decay $B^0_s \to \phi\phi \to (K^+K^-)(K^+K^-)$ is predicted for the first time, which indicates the presence of the significant final-state interactions. The TPAs of the rare decay channel $B^0 \to \phi\phi\to (K^+K^-)(K^+K^-)$ are also predicted and can be tested in the near future., Comment: 21 pages,2 figures,7 tables;some numerical results updated. arXiv admin note: text overlap with arXiv:2107.10684

The axial-vector mesons $f_1(1285)$ and $f_1(1420)$ are particularly viewed as the mixtures of flavor states $f_n$ and $f_s$ with mixing angle $\varphi$. In order to determine this angle, we study the $B_{d,s}^0\to J/\psi f_1(1285,1420)$ and $B_{d,s}^0\to \eta_c f_1(1285,1420)$ decays in perturbative QCD (PQCD) approach, including the effects of vertex corrections, nonfactorizable diagrams and penguin operators. Not only the branching fractions, but also the direct $CP$ asymmetries and the polarization fractions are calculated. It is found that the branching fractions of these decays are large enough to be measured in the running LHCb and Belle-II experiments. Moreover, in comparison with the observed ${\cal B}(B_{d,s}^0 \to J/\psi f_1(1285))$, $B_s^0 \to (J/\psi, \eta_c) f_1(1420)$ decays have large branching fractions, which could be measured promisingly through $f_1(1420) \to K_S^0 K^\pm \pi^\mp$ in experiments. We also propose several ratios that could be used to further constrain the absolute value of the mixing angle $\varphi$, but its sign cannot be determined yet in these decays. The direct CP asymmetries of these decays indicate the penguin pollution in the $B_d^0 \to (J/\psi, \eta_c) f_1$ decays cannot be neglected. We acknowledge that there are large theoretical uncertainties arising from the distribution amplitudes of axial-vector mesons and charmonium states, and more precise nonperturbative parameters are called. The comparisons between our results and future experimental data would help us to understand the nature of $f_1$ states and to test the PQCD approach., Comment: 18 pages, 3 figures, journal version, published in EPJC

We reanalyze the $\Lambda_b\to p$ transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a $\Lambda_b$ baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist $\Lambda_b$ baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 $\Lambda_b$ baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays $\Lambda_b\to p\ell\bar{\nu}_\ell$ and the hadronic decay $\Lambda_b\to p\pi$ are also close to the data. It implies that the $b$ quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of $B$ meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach., Comment: 37 pages, 7 figures, version to be published in Eur.Phys.J.C

In this work, we provide estimates of the branching ratios, direct $CP$ asymmetries and triple product asymmetries in $B_{(s)} \to (\pi\pi)(K\pi)$ decays in the perturbative QCD approach, where the $\pi\pi$ and $K\pi$ invariant mass spectra are dominated by the vector resonances $\rho(770)$ and $K^*(892)$, respectively. Some scalar backgrounds, such as $f_0(500,980) \to \pi\pi$ and $K^*_0(1430) \to K\pi$ are also accounted for. The $\rho(700)$ is parametrized by the Gounaris-Sakurai function. The relativistic Breit-Wigner formula for the $f_0(500)$ and Flatt\'e model for the $f_0(980)$ are adopted to parameterize the time-like scalar form factors $F_S(\omega^2)$. We also use the D.V. Bugg model to parameterize the $f_0(500)$ and compare the relevant theoretical predictions from different models. While in the region of $K\pi$ invariant mass, the $K^*_0(1430)$ is described with the LASS lineshape and the $K^*(892)$ is modeled by the Breit-Wigner function. We find that the decay rates for the considered decay modes agree with currently available data within errors. As a by-product, we extract the branching ratios of two-body decays $B_{(s)} \to \rho(770)K^*(892)$ from the corresponding four-body decay modes and calculate the relevant polarization fractions. Our prediction of longitudinal polarization fraction for $B^0\to \rho(770)^0 K^*(892)^0$ decay deviates a lot from the recent LHCb measurement, which should be resolved. It is shown that the direct $CP$ asymmetries are large due to the sizable interference between the tree and penguin contributions, but they are small for the tree-dominant or penguin-dominant processes. The PQCD predictions for the triple product asymmetries are small which are expected in the standard model, and consistent with the current data reported by the LHCb Collaboration.Our results can be tested by the future precise data from the LHCb and Belle II experiments., Comment: 29 pages, 2 figures

After the discovery of the double-charm baryon $\Xi_{cc}^{++}$ by LHCb, one of the most important topics is to search for the bottom-charm baryons which contain a $b$ quark, a $c$ quark and a light quark. In this work, we study the two-body non-leptonic weak decays of a bottom-charm baryon into a spin-$1/2$ bottomed baryon and a light pseudoscalar meson with the short-distance contributions calculated under the factorization hypothesis and the long-distance contributions considering the final-state-interaction effects. The branching fractions of all fifty-seven decay channels are estimated. The results indicate that $\Xi_{bc}^+\to\Xi_b^0\pi^+$, $\Xi_{bc}^{0}\to\Xi_{b}^{-}\pi^+$ and $\Omega_{bc}^0\to\Omega_b^-\pi^+$ decay modes have relatively large decay rates and thus could be used to experimentally search for the bottom-charm baryons. The topological diagrams and the SU(3) symmetry of bottom-charm baryon decays are discussed., Comment: 25 pages, 3 figures, 8 tables. Version for publication in EPJC

The doubly charmed baryon $\Xi_{cc}^{++}$ was recently observed by LHCb via the decay processes of $\Xi_{cc}^{++}\to \Lambda_c^+ K^-\pi^+\pi^+$ and $\Xi_c^+\pi^+$. These discovery channels were successfully predicted in the framework that the short-distance contributions are calculated under the factorization hypothesis and the long-distance contributions are estimated using the rescattering mechanism for the final-state-interaction effects. In this paper, we illustrate the above framework in details by systematic studies on the two-body baryonic decays $\mathcal{B}_{cc}\to\mathcal{B}_{c}P$ involving the doubly charmed baryons $\mathcal{B}_{cc}=(\Xi_{cc}^{++} , \Xi_{cc}^+,\Omega_{cc}^+)$, the singly charmed baryons $\mathcal{B}_{c}=(\mathcal{B}_{\bar{3}}, \mathcal{B}_{6})$ and the light pseudoscalar mesons $P=(\pi,K,\eta_{1,8})$., Comment: 31 pages, 4 figures, 9 tables. Version published in Chinese Physics C

In this paper, we studied systematically the semileptonic decays $B_s \to \phi l^+ l^-$ with $l^-=(e^-,\mu^-,\tau^-)$ by using the perturbative QCD (PQCD) and the "PQCD+Lattice" factorization approach, respectively. We first evaluated all relevant form factors $F_i(q^2)$ in the low $q^2$ region using the PQCD approach, and we also took the available lattice QCD results at the high-$q^2$ region as additional input to improve the extrapolation of $F_i(q^2)$ from the low-$q^2$ region to the endpoint $q^2_{max}$. We then calculated the branching ratios and many other physical observables: $A_{FB}^{l}$, $F_L^{\phi}$, $S_{3,4,7}$, $A_{5,6,8,9}$ and the clean angular observables $P_{1,2,3} $ and $P^{\prime}_{4,5,6,8}$.From our studies, we find the following points: (a) the PQCD and "PQCD+Lattice" predictions of ${\cal B}( B_s \to \phi \mu^+ \mu^-)$ are about $7\times 10^{-7}$, which agree well with the LHCb measured values and the QCD sum rule prediction within still large errors; (b) we defined and calculated the ratios of the branching ratios $R_\phi^{e\mu}$ and $R_\phi^{\mu\tau}$; (c) the PQCD and "PQCD+Lattice" predictions of the longitudinal polarization $F_L$, the CP averaged angular coefficients $S_{3,4,7} $ and the CP asymmetry angular coefficients $A_{5,6,8,9}$, agree with the LHCb measurements in all considered bins within the still large experimental errors; and (d) for those currently still unknown observables $R_\phi^{e\mu}, R_\phi^{\mu\tau}, A_{FB}^{l}, P_{1,2,3}$ and $P^{\prime}_{4,5,6,8}$, we suggest LHCb and Belle-II Collaboration to measure them in their experiments., Comment: 32 pages, 4 figures and 12 tables. Some new corrections to the text. arXiv admin note: text overlap with arXiv:2003.12226