Running vacuum model in a non-flat universe

We investigate observational constraints on the running vacuum model (RVM) of \begin{document}$\Lambda=3\nu (H^{2}+K/a^2)+c_0$\end{document} in a spatially curved universe, where \begin{document}$\nu$\end{document} is the model parameter, \begin{document}$K$\end{document} corresponds to the spatial curvature constant, \begin{document}$a$\end{document} represents the scalar factor, and \begin{document}$c_{0}$\end{document} is a constant defined by the boundary conditions. We study the CMB power spectra with several sets of \begin{document}$\nu$\end{document} and \begin{document}$K$\end{document} in the RVM. By fitting the cosmological data, we find that the best fitted \begin{document}$\chi^2$\end{document} value for RVM is slightly smaller than that of \begin{document}$\Lambda$\end{document}CDM in the non-flat universe, along with the constraints of \begin{document}$\nu\leqslant O(10^{-4})$\end{document} (68% C.L.) and \begin{document}$|\Omega_K=-K/(aH)^2|\leqslant O(10^{-2})$\end{document} (95% C.L.). In particular, our results favor the open universe in both \begin{document}$\Lambda$\end{document}CDM and RVM. In addition, we show that the cosmological constraints of \begin{document}$\Sigma m_{\nu}=0.256^{+0.224}_{-0.234}$\end{document} (RVM) and \begin{document}$\Sigma m_{\nu}=0.257^{+0.219}_{-0.234}$\end{document} (\begin{document}$\Lambda$\end{document}CDM) at 95% C.L. for the neutrino mass sum are relaxed in both models in the spatially curved universe.     

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model,with a free parameter a to reflect the competition between the "direct" channel and the "exchange" channel,is employed to study the QCD phase structure at finite iso spin chemical potential μ_I,finite bary on chemical potential μ_B and finite temperature T,and especially to study the location of the QCD critical point.Our results show that in order to match the corresponding lattice results of iso spin density and energy density,the contributions of the "exchange" channel need to be considered in the framework of the NJL model,and a weighting factor α=0.5 should be taken.It is also found that for fixed isospin chemical potentials,the lower temperature of the phase transition is obtained with increasing a in the T-μ_I plane,and the largest difference of the phase transition temperature with different a's appears at μ_I~1.5 mπ.At μ_I=0 the temperature of the QCD critical end point(CEP) decreases with increasing a,while the critical baryon chemical potential increases.At high isospin chemical potential(μ_I=500 MeV),the temperature of the QCD tricritical point(TCP) increases with increasing a,and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as μ_B increases.At low density,the critical temperature of the QCD phase transition with different a's rapidly increases with μ_I at the beginning,and then increases smoothly around μ_I 300 MeV.In the high baryon density region,the increase of the iso spin chemical potential will raise the critical baryon chemical potential of the phase transition.     

Calculations of the α-decay properties of Z = 120, 122, 124, 126 isotopes

The \begin{document}$\alpha$\end{document}-decay properties of even-Z nuclei with Z = 120, 122, 124, 126 are predicted. We employ the generalized liquid drop model (GLDM), Royer's formula, and universal decay law (UDL) to calculate the \begin{document}$\alpha$\end{document}-decay half-lives. By comparing the theoretical calculations with the experimental data of known nuclei from Fl to Og, we confirm that all the employed methods can reproduce the \begin{document}$\alpha$\end{document}-decay half-lives well. The preformation factor \begin{document}$P_{\alpha}$\end{document} and \begin{document}$\alpha$\end{document}-decay energy \begin{document}$Q_{\alpha}$\end{document} show that \begin{document}$^{298,304,314,316,324,326,338,348}$\end{document}120, \begin{document}$^{304,306,318,324,328,338}$\end{document}122, and \begin{document}$^{328,332,340,344}$\end{document}124 might be stable. The \begin{document}$\alpha$\end{document}-decay half-lives show a peak at Z = 120, N = 184, and the peak vanishes when Z = 122, 124, 126. Based on detailed analysis of the competition between \begin{document}$\alpha$\end{document}-decay and spontaneous fission, we predict that nuclei nearby N = 184 undergo \begin{document}$\alpha$\end{document}-decay. The decay modes of \begin{document}$^{287-339}$\end{document}120, \begin{document}$^{294-339}$\end{document}122, \begin{document}$^{300-339}$\end{document}124, and \begin{document}$^{306-339}$\end{document}126 are also presented.     

Research on convergence of the nuclear matrix elements for 2νββ decays

In this work, the characteristics of \begin{document}$2\nu\beta\beta$\end{document} decays for six nuclei (\begin{document}$^{36}$\end{document}Ar, \begin{document}$^{46}$\end{document}Ca, \begin{document}$^{48}$\end{document}Ca, \begin{document}$^{50}$\end{document}Cr, \begin{document}$^{70}$\end{document}Zn, and \begin{document}$^{136}$\end{document}Xe) in a mass range from \begin{document}$A = 36$\end{document} to \begin{document}$A = 136$\end{document} are studied within the nuclear shell model (NSM) framework. Calculations are presented for the half-lives, nuclear matrix elements (NMEs), phase space factors (\begin{document}$G_{2\nu}$\end{document}), and convergence of the NMEs. The theoretical results agree well with the experimental data. In addition, we predict the half-lives of \begin{document}$2\nu\beta\beta$\end{document} decays for four nuclei. We focus on the convergence of the NMEs by analyzing the number of contributing intermediate \begin{document}$1^{+}$\end{document} states (\begin{document}$N_{\rm{C}}$\end{document}) for the nuclei of interest. We assume that \begin{document}$N_{\rm{C}}$\end{document} is safely determined when the accumulated NMEs saturate 99.7% of the final calculated magnitude. From the calculations of the involved nuclei, we discover a connection between \begin{document}$N_{\rm{C}}$\end{document} and the total number of intermediate \begin{document}$1^{+}$\end{document} states (\begin{document}$N_{\rm{T}}$\end{document}). According to the least squares fit, we conclude that the correlation is \begin{document}$N_{\rm{C}}=\left( 10.8\pm 1.2\right) \times N_{\rm{T}}^{\left( 0.29\pm 0.02\right)}$\end{document}.     

Bayesian inference on isospin splitting of nucleon effective mass from giant resonances in ~(208)Pb

From a Bayesian analysis of the electric dipole polarizability,the constrained energy of isovector giant dipole resonance,the peak energy of isocalar giant quadrupole resonance,and the constrained energy of isocalar giant monopole resonance in ~(208)Pb,we extract the iso scalar and isovector effective masses in nuclear matter at saturation density p_0 as m_(s,0)~*/m=0.87_(-0.04)~(+0.04) and m_(v,0)~*/m=0.78_(-0.05)~(+0.06),respectively,at 90% confidence level.The constraints obtained on m_(s,0)~* and m_(v,0)~* lead to a positive iso spin splitting of nucleon effective mass in asymmetric nuclear matter of iso spin asymmetry δ at p_0 as m_(n-p)~*/m=(0.20_(-0.14)~(+0.15))δ.In addition,the symmetry energy at the subsaturation density p~*=0.05 fm~(-3) is determined to be E_(sym)(p~*)=16.7±1.3 MeV at 90% confidence level.     

Production of bottomonium-like Z_b states in e-h and ultraperipheral h-h collisions

The photoproduction of the bottomonium-like states Z_b(10610) and Z_b(10650) via γ p scattering is studied within an effective Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of Z_b states via the t-channel with π exchange. The numerical results show that the values of the total cross-sections of Z_b(10610) and Z_b(10650) can reach 0.09 nb and 0.02 nb, respectively,near the center-of-mass energy of 22 GeV. Experimental measurements and studies of the photoproduction of Z_b states near the energy region around W ■ 22 GeV are suggested. Moreover, with the help of eSTARlight and STARlight programs, we have obtained the cross-sections and numbers of events for Z_b(10610) production in electron-ion collisions(EIC) and ultraperipheral collisions(UPCs). The results show that a considerable number of Z_b(10610)events can be produced in the relevant experiments on EICs and UPCs. We have also calculated the rates and kinematic distributions for γp → Z_bn in ep and pA collisions via EICs and UPCs. The results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments in searching for bottomonium-like Z_b states.     

Systematic study of the α decay preformation factors of the nuclei around the Z = 82, N = 126 shell closures within the generalized liquid drop model

In this study, we systematically investigate the \begin{document}$\alpha$\end{document} decay preformation factors, \begin{document}$P_{\alpha}$\end{document} , and the \begin{document}$\alpha$\end{document} decay half-lives of 152 nuclei around Z = 82, N = 126 closed shells based on the generalized liquid drop model (GLDM) with \begin{document}$P_{\alpha}$\end{document} being extracted from the ratio of the calculated \begin{document}$\alpha$\end{document} decay half-life to the experimental one. The results show that there is a remarkable linear relationship between \begin{document}$P_{\alpha}$\end{document} and the product of valance protons (holes) \begin{document}$N_p$\end{document} and valance neutrons (holes) \begin{document}$N_n$\end{document} . At the same time, we extract the \begin{document}$\alpha$\end{document} decay preformation factor values of the even–even nuclei around the Z = 82, N = 126 closed shells from the study of Sun \begin{document}${et\ al.}$\end{document} [J. Phys. G: Nucl. Part. Phys., 45: 075106 (2018)], in which the \begin{document}$\alpha$\end{document} decay was calculated by two different microscopic formulas. We find that the \begin{document}$\alpha$\end{document} decay preformation factors are also related to \begin{document}$N_pN_n$\end{document} . Combining with our previous studies [Sun \begin{document}${et\ al.}$\end{document} , Phys. Rev. C, 94: 024338 (2016); Deng \begin{document}${et\ al.}$\end{document} , ibid. 96: 024318 (2017); Deng \begin{document}${et\ al.}$\end{document} , ibid. 97: 044322 (2018)] and that of Seif \begin{document}${et\ al.,}$\end{document} [Phys. Rev. C, 84: 064608 (2011)], we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent. This may be caused by the effect of the valence protons (holes) and valence neutrons (holes) around the shell closures. Finally, using the formula obtained by fitting the \begin{document}$\alpha$\end{document} decay preformation factor data calculated by the GLDM, we calculate the \begin{document}$\alpha$\end{document} decay half-lives of these nuclei. The calculated results agree with the experimental data well.     

Analysis of the strong decays of Pc(4312) as a pentaquark molecular state with QCD sum rules

In this article, we tentatively assign \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state with the spin-parity \begin{document}$J^P={\frac{1}{2}}^-$\end{document} , and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the \begin{document}$\bar{D}\Sigma_c$\end{document} molecular state in detail to prove the reliability of the single pole approximation in the hadronic spectral density. We study its two-body strong decays with the QCD sum rules, and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths \begin{document}$\Gamma\left(P_c(4312)\to \eta_c p\right)=0.255\,\,{\rm{MeV}}$\end{document} and \begin{document}$\Gamma\left(P_c(4312)\to J/\psi p\right)=9.296^{+19.542}_{-9.296}\,\,{\rm{MeV}}$\end{document} , which are compatible with the experimental value of the total width, and support assigning \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state.     

Possibility of observation of hidden-bottom pentaquark resonances in bottomonium photoproduction on protons and nuclei near threshold

We study the \begin{document}$\Upsilon(1S)$\end{document} meson photoproduction on protons and nuclei at near-threshold center-of-mass energies below 11.4 GeV (or at the corresponding photon laboratory energies \begin{document}$E_{\gamma}$\end{document} below 68.8 GeV). We calculate the absolute excitation functions for the nonresonant and resonant photoproduction of \begin{document}$\Upsilon(1S)$\end{document} mesons off protons at incident photon laboratory energies of 63-68 GeV by considering direct (\begin{document}${\gamma}p \to {\Upsilon(1S)}p$\end{document}) and two-step (\begin{document}${\gamma}p \to P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11130) \to {\Upsilon(1S)}p$\end{document}) \begin{document}$\Upsilon(1S)$\end{document} production channels within different scenarios for the nonresonant total cross section of the elementary reaction \begin{document}${\gamma}p \to {\Upsilon(1S)}p$\end{document} and for branching ratios of the decays \begin{document}$P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}$P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, and \begin{document}$P^+_b(11130) \to {\Upsilon(1S)}p$\end{document}. We also calculate an analogous function for the photoproduction of \begin{document}$\Upsilon(1S)$\end{document} mesons on the ¹²C and ²⁰⁸Pb target nuclei in the near-threshold center-of-mass beam energy region of 9.0-11.4 GeV by considering the respective incoherent direct (\begin{document}${\gamma}N \to {\Upsilon(1S)}N$\end{document}) and two-step (\begin{document}${\gamma}p \to P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11130) \to {\Upsilon(1S)}p$\end{document} and \begin{document}${\gamma}n \to P^0_b$\end{document}\begin{document}$ (11080) \to{\Upsilon(1S)}n $\end{document}, \begin{document}${\gamma}n \to P^0_b(11125) \to {\Upsilon(1S)}n$\end{document}, \begin{document}${\gamma}n \to P^0_b(11130) \to {\Upsilon(1S)}n$\end{document}) \begin{document}$\Upsilon(1S)$\end{document}) production processes using a nuclear spectral function approach. We demonstrate that a detailed scan of the\begin{document}$\Upsilon(1S)$\end{document} total photoproduction cross section on proton and nuclear targets in the near-threshold energy region in future high-precision experiments at the proposed high-luminosity electron-ion colliders EIC and EicC in the US and China should provide a definite result for or against the existence of the nonstrange hidden-bottom pentaquark states\begin{document}$P_{bi}^+$\end{document} and \begin{document}$P_{bi}^0$\end{document} (\begin{document}$i$\end{document}=1, 2, 3) as well as clarify their decay rates.     

Simulation of neutron-tagged deep inelastic scattering at EicC

Measuring the pionic structure function is of high interest, as it provides a new area for understanding the strong interaction among quarks and testing QCD predictions. To this end, we investigate the feasibility and expected impact of a possible experiment at EicC(Electron-ion collider in China). We show the simulation results on the statistical precision of an EicC measurement, based on the model of leading neutron tagged DIS process and the parton distribution functions of the pion from JAM18 global analysis. The simulation shows that at EicC, the kinematics cover the x π range from 0.01 to 1, and the Q~2 range from 1 to 50 GeV~2, within the acceptable statistical uncertainty. Assuming an integrated luminosity of 50 fb~(-1), in the low-Q~2 region( 10 GeV~2), the Monte Carlo data show that the suggested measurement in the whole x π range reaches very high precision( 3%). To perform such an experiment, only the addition of a far-forward neutron calorimeter is needed.     

Charged-current non-standard neutrino interactions at the LHC and HL-LHC

A series of new physics scenarios predict the existence of the extra charged gauge boson \begin{document}$ W' $\end{document}, which can induce charged-current (CC) non-standard neutrino interactions (NSIs). The theoretical constraints on the simplified \begin{document}$ W' $\end{document} model and further on the CC NSI parameters \begin{document}$ \widetilde{\epsilon}^{ qq'Y}_{\alpha\beta} $\end{document} from partial wave unitarity and \begin{document}$ W' $\end{document} decays are considered. The sensitivity of the process \begin{document}$ p p \rightarrow W'\rightarrow \ell\nu $\end{document} to the \begin{document}$ W' $\end{document} model at the LHC and high-luminosity (HL) LHC experiments is investigated by estimating the expected constraints on \begin{document}$ \widetilde{\epsilon}^{qq'Y}_{\alpha\beta} $\end{document} (\begin{document}$ \alpha = \beta = e $\end{document} or μ) using a Monte-Carlo (MC) simulation. We find that the interference effect plays an important role, and the LHC can strongly constrain \begin{document}$ \widetilde{\epsilon}^{qq'L}_{\alpha\beta} $\end{document}. Compared with those at the \begin{document}$ 13 \;{\rm TeV} $\end{document} LHC with \begin{document}$ {\cal{L}}=139\;{\rm fb}^{-1} $\end{document}, the expected constraints at the \begin{document}$ 14 \;{\rm TeV} $\end{document} LHC with \begin{document}$ {\cal{L}}=3\;{\rm ab}^{-1} $\end{document} can be strengthened to approximately one order of magnitude.     

Constraints on the generalized natural inflation after Planck 2018

Based on the dynamics of single scalar field slow-roll inflation and the theory of reheating, we investigate the generalized natural inflationary (GNI) model. We introduce constraints on the scalar spectral index \begin{document}$n_{s}$\end{document} and the tensor-to scalar ratio r for the \begin{document}$\Lambda$\end{document}CDM \begin{document}$+r$\end{document} model, according to the latest data from Planck 2018 TT, TE, EE+low E+lensing (P18) and BICEP2/Keck 2015 season (BK15), i.e., with \begin{document}$n_{s}=0.9659\pm0.0044$\end{document} at 68% confidence level (CL), and \begin{document}$r<0.0623$\end{document} at 95% CL. We find that the GNI model is favored by P18 and BK15 in the ranges \begin{document}$\log_{10}(f/M_{p})= 0.62^{+0.17}_{-0.18}$\end{document} and \begin{document}$m=0.35^{+0.13}_{-0.23}$\end{document} at 68% CL. In addition, the corresponding predictions of generalized and two-phase reheating are discussed. It follows that the parameter m has significant effect on the model behavior.     

Hadronic coupling constants of the lowest hidden-charm pentaquark state,using QCD sum rules with rigorous quark-hadron duality

In this article,we illustrate how to calculate the hadronic coupling constants of the pentaquark states with QCD sum rules based on rigorous quark-hadron quality.We then study the hadronic coupling constants of the lowest diquark-diquark-antiquark type hidden-charm pentaquark state with spin-parity J~P=1/2~-in detail,and calculate the partial decay widths.The total width Г(P_c)=14.32±3.31 MeV is compatible with the experimental value T_(P_c(4312))=9.8±2.7_(-4.5)~(+3.7) MeV from the LHCb collaboration and favors assigning the P_c(4312) to be the [ud][uc]c pentaquark state with J~P=1/2~-.The hadronic coupling constants have the relation ■,and favor the hadronic dressing mechanism.The P_c(4312) may have a diquark-diquark-antiquark type pentaquark core with the typical size of the qqq-type baryon states.The strong couplings to the meson-baryon pairs DE_c lead to some pentaquark molecule components,and the P_c(4312) may spend a rather large time as the DE_c molecular state.     

Fine tuning problem of the cosmological constant in a generalized Randall-Sundrum model

To solve the cosmological constant fine tuning problem, we investigate an \begin{document}$(n+1)$\end{document}-dimensional generalized Randall-Sundrum brane world scenario with two \begin{document}$(n-1)$\end{document}-branes instead of two 3-branes. Adopting an anisotropic metric ansatz, we obtain the positive effective cosmological constant \begin{document}$\Omega_{\rm eff}$\end{document} of order \begin{document}$10^{-124}$\end{document} and only require a solution \begin{document}$\simeq50-80$\end{document}. Meanwhile, both the visible and hidden branes are stable because their tensions are positive. Therefore, the fine tuning problem can be solved quite well. Furthermore, the Hubble parameter \begin{document}$H_{1}(z)$\end{document} as a function of redshift \begin{document}$z$\end{document} is in good agreement with the cosmic chronometers dataset. The evolution of the universe naturally shifts from deceleration to acceleration. This suggests that the evolution of the universe is intrinsically an extra-dimensional phenomenon. It can be regarded as a dynamic model of dark energy that is driven by the evolution of the extra dimensions on the brane.     

Proton-halo breakup dynamics for the breakup threshold in the ε0 → 0 limit

Proton-halo breakup behavior in the \begin{document}$ \varepsilon_0\to 0 $\end{document} limit (where \begin{document}$ \varepsilon_0 $\end{document} is the ground-state binding energy) is studied around the Coulomb barrier in the \begin{document}$ ^8{\rm{B}}+{}^{58}{\rm{Ni}} $\end{document} reaction for the first time. For practical purposes, apart from the experimental \begin{document}$ ^8{\rm{B}} $\end{document} binding energy of 137 keV, three more arbitrarily chosen values (1, 0.1, 0.01 keV) are considered. It is first shown that the Coulomb barrier between the core and the proton prevents the \begin{document}$ ^7{\rm{Be}}+p $\end{document} system from reaching the state of an open proton-halo system, which, among other factors, would require the ground-state wave function to extend to infinity in the asymptotic region, as \begin{document}$ \varepsilon_0\to 0 $\end{document}. The elastic scattering cross section, which depends on the density of the ground-state wave function, is found to have a negligible dependence on the binding energy in this limit. The total, Coulomb and nuclear breakup cross sections are all reported to increase significantly from \begin{document}$ \varepsilon_0 = 137 $\end{document} to 1.0 keV, and converge to their maximum values as \begin{document}$ \varepsilon_0\to 0 $\end{document}. This increase is mainly understood as coming from a longer tail of the ground-state wave function for \begin{document}$ \varepsilon_0\leqslant 1.0 $\end{document} keV, compared to that for \begin{document}$ \varepsilon_0 = 137 $\end{document} keV. It is also found that the effect of the continuum-continuum couplings is to slightly delay the convergence of the breakup cross section. The analysis of the reaction cross section indicates a convergence of all the breakup observables as \begin{document}$ \varepsilon_0\to 0 $\end{document}. These results provide a better sense of the dependence of the breakup process on the breakup threshold.     

Emission time sequence of neutrons and protons as probes of α-clustering structure

Neutron–proton momentum correlation functions are constructed from a three-body photodisintegration channel, i.e., core\begin{document}$ + n + p$\end{document}, and used to explore the spatial-time information of the non-clustering Woods–Saxon spherical structure as well as the \begin{document}$\alpha$\end{document}-clustering structures of \begin{document}$^{12}{\rm{C}}$\end{document} or \begin{document}$^{16}{\rm{O}}$\end{document} based on an extended quantum molecular dynamics model. The emission time sequence of neutrons and protons is indicated by the ratio of velocity-gated neutron–proton correlation functions, demonstrating its sensitivity to \begin{document}$\alpha$\end{document}-clustering structures. This work sheds light on a new probe for \begin{document}$\alpha$\end{document}-clustering structures.     

Relative probabilities of breakup channels in reactions of ~(6,7)Li with ~(209)Bi at energies around and above the Coulomb barrier

Coincidence measurements of breakup fragments in reactions of~ (6,7) Li with ~(209)Bi at energies around and above the Coulomb barrier were carried out using a large solid-angle covered detector array. Through the Q values along with the relative energies of the breakup fragments, different breakup components(prompt breakups and delayed breakups) and different breakup modes(α + t, α + d, α + p, and α + α) are distinguished. A new breakup mode, α + t, is observed in ~6Li-induced reactions at energies above the Coulomb barrier. Correlations between breakup modes and breakup components as well as their variations with the incident energy are investigated. The results will help us better understand the breakup effects of weakly bound nuclei on the suppression of a complete fusion, particularly for the above-barrier energies.     

P-wave contributions to B_((s))→ψKπ decays in perturbative QCD approach

We study the quasi-two-body decays B_((s)) ψ[K~*(892) K~*(1410) K~*(1680)] ψKπ by employing the perturbative QCD(PQCD) factorization approach, where the charmonia ψ represents J/ψ and ψ(2S). The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude(DA) Φ_(Kπ)~P, which comprises important final state interactions between the kaon and pion in the resonant region. Relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor F_(Kπ) appearing in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between the kaon and pion is taken into account,which makes significant contributions to the longitudinal polarizations. The observed branching ratios and the polarization fractions of B_((s)) ψK~*(892) ψKπ are accommodated by tuning hadronic parameters for the kaon-pion DAs. The PQCD predictions for B_((s)) ψ[K~*(1410) K~*(1680)] ψKπ modes from the same set of parameters can be tested by precise data obtained in the future from LHCb and Belle Ⅱ experiments.     

Revisiting radiative leptonic B decay

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist \begin{document}$B$\end{document}-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors \begin{document}$F_{A,V}$\end{document} in the \begin{document}$B \to \gamma \ell\nu$\end{document} decay at leading power in \begin{document}$\Lambda/m_b$\end{document}. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by \begin{document}$1/E_\gamma$\end{document} and \begin{document}$1/m_b$\end{document}), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.     

Direct CP violation of three body decay processes from the resonance effect

The physical state of \begin{document}$ \rho-\omega-\phi $\end{document} mesons can be mixed using the unitary matrix. The decay processes \begin{document}$ \omega \rightarrow \pi^{+}\pi^{-} $\end{document} and \begin{document}$ \phi \rightarrow \pi^{+}\pi^{-} $\end{document} originate from isospin symmetry breaking. The \begin{document}$ \rho-\omega $\end{document}, \begin{document}$ \rho-\phi $\end{document}, and \begin{document}$ \omega-\phi $\end{document} interferences lead to a resonance contribution to produce strong phases. \begin{document}$ CP $\end{document} violation is considered from isospin symmetry breaking due to the new strong phase of the first order. \begin{document}$ CP $\end{document} violation can be enhanced greatly for the decay process \begin{document}$ B^{0}\rightarrow \pi^+\pi^{-}\eta^{(')} $\end{document} when the invariant masses of \begin{document}$ \pi^+\pi^{-} $\end{document} pairs are in the area around the \begin{document}$ \omega $\end{document} resonance range and \begin{document}$ \phi $\end{document} resonance range in perturbative QCD. We also discuss the possibility of searching for the predicted \begin{document}$ CP $\end{document} violation at the LHC.