Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors \begin{document}$ N_f $\end{document} and colors \begin{document}$ N_c $\end{document} using the Nambu-Jona-Lasinio (NJL) model of quarks in the Schwinger-Dyson equation framework, dressed with a color-flavor dependence of effective coupling. For fixed \begin{document}$ N_f = 2 $\end{document} and varying \begin{document}$ N_c $\end{document}, we observe that the dynamical chiral symmetry is broken when \begin{document}$ N_c $\end{document} exceeds its critical value \begin{document}$ N^{c}_{c}\approx2.2 $\end{document}. For a fixed \begin{document}$ N_c = 3 $\end{document} and varying \begin{document}$ N_f $\end{document}, we observe that the dynamical chiral symmetry is restored when \begin{document}$ N_f $\end{document} reaches its critical value \begin{document}$ N^{c}_{f}\approx8 $\end{document}. Strong interplay is observed between \begin{document}$ N_c $\end{document} and \begin{document}$ N_f $\end{document}, i.e., larger values of \begin{document}$ N_c $\end{document} tend to strengthen the dynamical generated quark mass and quark-antiquark condensate, while higher values of \begin{document}$ N_f $\end{document} suppress both parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at a finite temperature T and quark chemical potential μ for various \begin{document}$ N_c $\end{document} and \begin{document}$ N_f $\end{document}. At finite T and μ, we observe that the critical number of colors \begin{document}$ N^{c}_c $\end{document} is enhanced, whereas the critical number of flavors \begin{document}$ N^{c}_f $\end{document} is suppressed as T and μ increase. Consequently, the critical temperature \begin{document}$ T_c $\end{document}, \begin{document}$ \mu_c $\end{document}, and co-ordinates of the critical endpoint \begin{document}$ (T^{E}_c,\mu^{E}_c) $\end{document} in the QCD phase diagram are enhanced as \begin{document}$ N_c $\end{document} increases and suppressed when \begin{document}$ N_f $\end{document} increases. Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.     

Re-visiting supersymmetric Janus solutions: a perturbative construction

We construct holographic Janus solutions, which describe a conformal interface in the theory of M2-branes, in four-dimensional gauged supergravities using a perturbative method. In particular, we study three Einsteinscalar systems and their BPS equations, which are derived by Bobev, Pilch, and Warner(2014). The actions of our interest are all consistent truncations of D=11 supergravity, chosen to be invariant under SO(4)×SO(4),SU(3)×U(1)×U(1), and G_2 symmetry subgroups of SO(8). The utility of our semi-analytic result is illustrated by the calculation of minimal area surface and the associated holographic entanglement entropy.     

Null test for cosmic curvature using Gaussian process

The cosmic curvature \begin{document}$ \Omega_{K,0} $\end{document}, which determines the spatial geometry of the universe, is an important parameter in modern cosmology. Any deviation from \begin{document}$ \Omega_{K,0}=0 $\end{document} would have a profound impact on the primordial inflation paradigm and fundamental physics. In this work, we adopt a cosmological model-independent method to test whether \begin{document}$ \Omega_{K,0} $\end{document} deviates from zero. We use the Gaussian process to reconstruct the reduced Hubble parameter \begin{document}$ E(z) $\end{document} and the derivative of the distance \begin{document}$ D'(z) $\end{document} from observational data and then determine \begin{document}$ \Omega_{K,0} $\end{document} with a null test relation. The cosmic chronometer (CC) Hubble data, baryon acoustic oscillation (BAO) Hubble data, and supernovae Pantheon sample are considered. Our result is consistent with a spatially flat universe within the domain of reconstruction \begin{document}$ 0<z<2.3 $\end{document}, at the \begin{document}$ 1\sigma $\end{document} confidence level. In the redshift interval \begin{document}$ 0<z<1 $\end{document}, the result favors a flat universe, while at \begin{document}$ z>1 $\end{document}, it tends to favor a closed universe. In this sense, there is still a possibility for a closed universe. We also carry out the null test of the cosmic curvature at \begin{document}$ 0<z<4.5 $\end{document} using the simulated gravitational wave standard sirens, CC+BAO, and redshift drift Hubble data. The result indicates that in the future, with the synergy of multiple high-quality observations, we can tightly constrain the spatial geometry or exclude the flat universe.     

Note on rare Z-boson decays to double heavy quarkonia

Within the standard model, we have investigated rare Z-boson decays into double heavy quarkonia, \begin{document}$ Z\to VV $\end{document} and \begin{document}$ Z\to VP $\end{document}, with V and P denoting vector and pseudoscalar quarkonia, respectively. It is assumed that the leading-order QCD diagrams would give the dominant contributions to these processes, and the corresponding branching fractions, for instance, \begin{document}$ {\cal B}(Z\to J/\Psi J/\Psi) $\end{document}, have been estimated to be approximately\begin{document}$ 10^{-13} $\end{document} in literature. However, these decays could also happen through electromagnetic transitions \begin{document}$ Z\to V\gamma^* $\end{document} and \begin{document}$ Z\to P\gamma^* $\end{document}, with the virtual photon transforming into V. Interestingly, the smallness of the vector quarkonium mass can give rise to a large factor \begin{document}$ m_Z^2/m_V^2 $\end{document} relative to the QCD contributions, which thus counteracts the suppression from the electromagnetic coupling. We systematically include these two types of contributions in our calculation to predict branching fractions for these decays. Particularly, owing to the virtual photon effects, it is found that \begin{document}$ {\cal B}(Z\to J/\Psi J/\Psi) $\end{document} will be significantly enhanced, up to \begin{document}$ 10^{-10} $\end{document}.     

One-loop formulas for H → Zνlνl for l = e, μ, τ in 't Hooft-Veltman gauge

In this paper, we present analytical results for one-loop contributions to the decay processes \begin{document}$ H\rightarrow Z \nu_l\bar{\nu}_l $\end{document} (for \begin{document}$ l = e, \mu, \tau $\end{document}). The calculations are performed within the Standard Model framework in the 't Hooft-Veltman gauge. One-loop form factors are then written in terms of scalar one-loop functions in the standard notations of \begin{document}$ {\tt LoopTools}$\end{document}. As a result, one-loop decay rates for the decay channels can be evaluated numerically by using the package. Furthermore, we analyze the signals of \begin{document}$ H\rightarrow Z \nu_l\bar{\nu}_l $\end{document} via the production processes \begin{document}$ e^-e^+ \rightarrow ZH^* \rightarrow Z (H^* \rightarrow Z \nu_l\bar{\nu}_l) $\end{document}, including the initial beam polarizations at future lepton colliders. The Standard Model backgrounds, such as the processes \begin{document}$ e^-e^+ \rightarrow \nu_l\bar{\nu}_l ZZ $\end{document}, are also examined in this study. Numerical results indicate that one-loop corrections make contributions of approximately 10% to the decay rates. These are sizeable contributions and should be taken into account at future colliders. We show that the signals \begin{document}$ H\rightarrow Z\nu_l\bar{\nu}_l $\end{document} are clearly visible at the center-of-mass energy \begin{document}$ \sqrt{s}=250 $\end{document} GeV and are difficult to probe in higher-energy regions owing to the dominant backgrounds.     

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.     

Analysis of Pcs(4338) and related pentaquark molecular states via QCD sum rules

In this study, we tentatively identify \begin{document}$ P_{cs}(4338) $\end{document} as the \begin{document}$ \bar{D}\Xi_c $\end{document}molecular state and distinguish the isospins of current operators to explore in detail the\begin{document}$ \bar{D}\Xi_c $\end{document}, \begin{document}$ \bar{D}\Lambda_c $\end{document}, \begin{document}$ \bar{D}_s\Xi_c $\end{document}, \begin{document}$ \bar{D}_s\Lambda_c $\end{document}, \begin{document}$ \bar{D}^*\Xi_c $\end{document}, \begin{document}$ \bar{D}^*\Lambda_c $\end{document}, \begin{document}$ \bar{D}^*_s\Xi_c $\end{document}, and \begin{document}$ \bar{D}^*_s\Lambda_c $\end{document} molecular states without strange, with strange, and with double strange in the framework of QCD sum rules. The present exploration favors identifying \begin{document}$ P_{cs}(4338) $\end{document} (\begin{document}$ P_{cs}(4459) $\end{document}) as the \begin{document}$ \bar{D}\Xi_c $\end{document} (\begin{document}$ \bar{D}^*\Xi_c $\end{document}) molecular state with the spin-parity \begin{document}$ J^P={\dfrac{1}{2}}^- $\end{document} (\begin{document}$ {\dfrac{3}{2}}^- $\end{document}) and isospin \begin{document}$ (I,I_3)=(0,0) $\end{document}, and the observation of their cousins with the isospin \begin{document}$ (I,I_3)=(1,0) $\end{document} in the \begin{document}$ J/\psi\Sigma^0/\eta_c\Sigma^0 $\end{document} invariant mass distributions would decipher their inner structures.     

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.     

New behaviors of α-particle preformation factors near doubly magic 100Sn

The \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei above doubly magic nuclei \begin{document}$ ^{100} $\end{document}Sn and \begin{document}$ ^{208} $\end{document}Pb are investigated within the generalized liquid drop model. The results show that the \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei near self-conjugate doubly magic \begin{document}$ ^{100} $\end{document}Sn are significantly larger than those of analogous nuclei just above \begin{document}$ ^{208} $\end{document}Pb, and they will be enhanced as the nuclei move towards the \begin{document}$ N = Z $\end{document} line. The proton–neutron correlation energy \begin{document}$ E_{p-n} $\end{document} and two protons–two neutrons correlation energy \begin{document}$ E_{2p-2n} $\end{document} of nuclei near \begin{document}$ ^{100} $\end{document}Sn also exhibit a similar situation, indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance the \begin{document}$ \alpha $\end{document}-particle preformation factors and result in superallowed \begin{document}$ \alpha $\end{document} decay. This also provides evidence of the significant role of the proton–neutron interaction on \begin{document}$ \alpha $\end{document}-particle preformation. Also, the linear relationship between \begin{document}$ \alpha $\end{document}-particle preformation factors and the product of valence protons and valence neutrons for nuclei around \begin{document}$ ^{208} $\end{document}Pb is broken in the \begin{document}$ ^{100} $\end{document}Sn region because the \begin{document}$ \alpha $\end{document}-particle preformation factor is enhanced when a nucleus near \begin{document}$ ^{100} $\end{document}Sn moves towards the \begin{document}$ N = Z $\end{document} line. Furthermore, the calculated \begin{document}$ \alpha $\end{document} decay half-lives fit well with the experimental data, including the recent observed self-conjugate nuclei \begin{document}$ ^{104} $\end{document}Te and \begin{document}$ ^{108} $\end{document}Xe [Phys. Rev. Lett. 121, 182501 (2018)].     

Z0 boson associated b-jet production in high-energy nuclear collisions

The production of vector boson tagged heavy quark jets potentially provides new tools to probe the jet quenching effect. In this paper, we present the first theoretical study on the angular correlations (\begin{document}$ \Delta\phi_{bZ} $\end{document}), transverse momentum imbalance (\begin{document}$ x_{bZ} $\end{document}), and nuclear modification factor (\begin{document}$ I_{AA} $\end{document}) of \begin{document}$ Z^0 $\end{document} boson tagged b-jets in heavy-ion collisions, which was performed using a Monte Carlo transport model. We find that the medium modification of the \begin{document}$ \Delta\phi_{bZ} $\end{document} for \begin{document}$ Z^0$\end{document} + b-jet has a weaker dependence on \begin{document}$ \Delta\phi_{bZ} $\end{document} than that for \begin{document}$ Z^0$\end{document} + jet, and the modification patterns are sensitive to the initial jet \begin{document}$ p_T $\end{document} distribution. Additionally, with the high purity of the quark jet in \begin{document}$ Z^0$\end{document} + (b-) jet production, we calculate the momentum imbalance \begin{document}$ x_{bZ} $\end{document} and the nuclear modification factor \begin{document}$ I_{AA} $\end{document} of \begin{document}$ Z^0$\end{document} + b-jet in Pb+Pb collisions. We observe a smaller \begin{document}$ \Delta \langle x_{jZ} \rangle $\end{document} and larger \begin{document}$ I_{AA} $\end{document} of \begin{document}$ Z^0$\end{document} + b-jet in Pb+Pb collisions relative to those of \begin{document}$ Z^0$\end{document} + jet, which may be an indication of the mass effect of jet quenching and can be tested in future measurements.     

Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules

In this study, we investigate the \begin{document}$\bar{D}\Sigma_c$\end{document}, \begin{document}$\bar{D}\Xi^\prime_c$\end{document}, \begin{document}$\bar{D}\Sigma_c^*$\end{document}, \begin{document}$\bar{D}\Xi_c^*$\end{document}, \begin{document}$\bar{D}^{*}\Sigma_c$\end{document}, \begin{document}$\bar{D}^{*}\Xi^\prime_c$\end{document}, \begin{document}$\bar{D}^{*}\Sigma_c^*$\end{document}, and \begin{document}$\bar{D}^{*}\Xi_c^*$\end{document} pentaquark molecular states with and without strangeness via the QCD sum rules in detail, focusing on the light flavor, \begin{document}$SU(3)$\end{document} , breaking effects, and make predictions for new pentaquark molecular states besides assigning \begin{document}$P_c(4312)$\end{document}, \begin{document}$P_c(4380)$\end{document}, \begin{document}$P_c(4440)$\end{document}, \begin{document}$P_c(4457)$\end{document} , and \begin{document}$P_{cs}(4459)$\end{document} self-consistently. In the future, we can search for these pentaquark molecular states in the decay of \begin{document}$\Lambda_b^0$\end{document}, \begin{document}$\Xi_b^0$\end{document} , and \begin{document}$\Xi_b^-$\end{document} . Furthermore, we discuss high-dimensional vacuum condensates in detail.     

Mixing of X and Y states from QCD sum rules analysis

We study \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions of \begin{document}$ J^{PC} = 1^{++} $\end{document}, \begin{document}$1^{--}$\end{document}, and \begin{document}$ 1^{-+} $\end{document} states. By calculating the two-point mixed correlation functions of \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} currents, we estimate the mass and coupling constants of the corresponding "physical state" that couples to both \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} currents. Our results suggest that for \begin{document}$ 1^{++} $\end{document} states, the \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document} components are more likely to mix, while for \begin{document}$ 1^{--} $\end{document} and \begin{document}$ 1^{-+} $\end{document} states, there is less mixing between \begin{document}$ \bar{Q}Q\bar{q}q $\end{document} and \begin{document}$ \bar{Q}qQ\bar{q} $\end{document}. Our results suggest the Y series of states have more complicated components.     

Radial excited heavy mesons

In this study, the first radial excited heavy pseudoscalar and vector mesons (\begin{document}$\eta_c(2S)$\end{document}, \begin{document}$\psi(2S)$\end{document}, \begin{document}$B_c(2S)$\end{document}, \begin{document}$B^*_c(2S)$\end{document}, \begin{document}$\eta_b(2S)$\end{document}, and \begin{document}$\varUpsilon(2S)$\end{document}) are investigated using the Dyson-Schwinger equation and Bethe-Salpeter equation approach. It is shown that the effective interactions of the radial excited states are harder than those of the ground states. With the interaction well determined by fitting the masses and leptonic decay constants of \begin{document}$\psi(2S)$\end{document} and \begin{document}$\varUpsilon(2S)$\end{document}, the first radial excited heavy mesons could be quantitatively described in the rainbow ladder approximation. The masses and leptonic decay constants of \begin{document}$\eta_c(2S)$\end{document}, \begin{document}$B_c(2S)$\end{document}, \begin{document}$B^*_c(2S)$\end{document}, and \begin{document}$\eta_b(2S)$\end{document} are predicted.     

Investigating S-wave bound states composed of two pseudoscalar mesons

In this study, we systematically investigated two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations. By solving the Bethe-Salpeter equation numerically with the kernel containing the one-particle exchange diagrams, we found that the \begin{document}$ K\bar{K} $\end{document}, \begin{document}$ DK $\end{document}, \begin{document}$ B\bar{K} $\end{document}, \begin{document}$ D\bar{D} $\end{document}, \begin{document}$ B\bar{B} $\end{document}, \begin{document}$ BD $\end{document}, \begin{document}$ D\bar{K} $\end{document}, \begin{document}$ BK $\end{document}, and \begin{document}$ B\bar{D} $\end{document} systems with \begin{document}$ I=0 $\end{document} can exist as bound states. We also studied the contributions from heavy meson (\begin{document}$ J/\psi $\end{document} and \begin{document}$\Upsilon $\end{document}) exchanges and found that the contributions from heavy meson exchanges cannot be ignored.     

Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at E_(lab)= 0.09 ～ 1.5 GeV/nucleon

By incorporating an iso spin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics(UrQMD) model,we systematically investigate effects of the neutron-proton effective mass splitting m*_(n-p)=m*_n-m*_p/m and the density-dependent nuclear symmetry energy E_(sym)(ρ) on the elliptic flow v_2 in~(197)Au+~(197) Au collisions at beam energies from 0.09 to 1.5 GeV/nucleon.It is found that at higher beam energies(≥0.25 GeV/nucleon) with the approximately 75 MeV difference in slopes of the two different E_(sym)(ρ),and the variation of m*_(n-p) ranging from-0.03 to 0.03 at saturation density with isospin asymmetry δ=(ρ_n-ρ_p)/ρ-0.2,the E_(sym)(ρ) has a stronger influence on the difference in v_2 between neutrons and protons,i.e.,v_2~n-v_2~p,than m*_(n-p) has.Meanwhile,at lower beam energies(≤0.25 GeV/nucleon),v_2~n-v_2~p is sensitive to both the E_(sym)(ρ) and the m*_(n-p).Moreover,the influence of m*_(n-p) on v_2~n-v_2~p is more evident with the parameters of this study when using the soft,rather than stiff,symmetry energy.     

Same-sign tetralepton signature in type-Ⅱ seesaw at lepton colliders

The same-sign tetralepton signature via the mixing of neutral Higgs bosons and their cascade decays to charged Higgs bosons is a unique signal in the type-Ⅱ seesaw model with the mass spectrum M_A⁰≈M_H⁰>M_H⁺>M_H^±±.In this study,we investigate this signature at future lepton colliders,such as the ILC,CLIC,and MuC.Direct searches for doubly charged scalar H^±±at the LHC have excluded MHg+t<350(870) GeV in the H^±±+W^±W(±)(l^±±)decay mode.Therefore,we choose M_A⁰=400,600,1000,1500 GeV as our benchmark scenarios.Constrained by direct search,H^±±+W^±W(±)(l^±±)d=is the only viable decay mode for Mρ=400 GeV at the √s=1 TeV ILC.With an integrated luminosity L=8 ab^-1,the promising region,with approximately 150 signal events,corresponds to a narrow band in the range of 10^-4 GeV≤v△≤10^-2GeV.Meanwhile,for Mpo=600 GeV at the √s=1.5 TeV CLIC,approximately 10 signal events can be produced with L=2.5 ab^-1.For heavier triplet scalars M_A⁰■870 GeV,although the H^±± decay mode is allowed,the cascade decays are suppressed.A maximum event number~16 can be obtained at approximately v△~4×10⁴GeV and λ₁₄~0.26 for M_A⁰=1000 GeV with L=5 ab^-1 at the √s=3 TeV CLIC.Finally,we find that this signature is not promising for M_A⁰= 1500 GeV at the √s=6 TeV MuC.Based on the benchmark scenarios,we also study the observability of this signature.In the H^±±+W^±W(±)(l^±±)d mode,one can probe MρS 800(1160) GeV at future lepton colliders.     

Nuclear mass parabola and its applications

We propose a method for extracting the properties of the isobaric mass parabola based on the total doubleβ-decay energies of isobaric nuclei.Two important parameters of the mass parabola,the location of the most β-stable nuclei Z_A and the curvature parameter b_A,are obtained for 251 A values,based on the total double β-decay energies of nuclei compiled in the AME2016 database.The advantage of this approach is that the pairing energy term P_A caused by the odd-even variation can be removed in the process,as well as the mass excess M(A,Z_A) of the most stable nuclide for the mass number A,which are employed in the mass parabolic fitting method.The Coulomb energy coefficient a_c=0.6910 MeV is determined by the mass difference relation for mirror nuclei,and the symmetry energy coefficient is also studied by the relation a_(sym)(A)=025 b_AZ_A.     

Toward discovering low-lying P-wave excited Σc baryon states

In this study, by combining the equal spacing rule with recent observations of \begin{document}$ \Omega_c(X) $\end{document} and \begin{document}$ \Xi_c(X) $\end{document} baryons, we predict the spectrum of the low-lying \begin{document}$ \lambda $\end{document}-mode \begin{document}$ 1P $\end{document}-wave excited \begin{document}$ \Sigma_c $\end{document} states. Furthermore, their strong decay properties are predicted using the chiral quark model and the nature of \begin{document}$ \Sigma_c(2800) $\end{document} is investigated by analyzing the \begin{document}$ \Lambda_c\pi $\end{document} invariant mass spectrum. The \begin{document}$ \Sigma_c(2800) $\end{document} structure observed in the \begin{document}$ \Lambda_c \pi $\end{document} mass spectrum was found to potentially arise from two overlapping \begin{document}$ P $\end{document}-wave \begin{document}$ \Sigma_c $\end{document} resonances, \begin{document}$ \Sigma_c(2813)3/2^- $\end{document} and \begin{document}$ \Sigma_c(2840)5/2^- $\end{document}. These resonances have similar decay widths of \begin{document}$ \Gamma\sim 40 $\end{document} MeV and predominantly decay into the \begin{document}$ \Lambda_c \pi $\end{document} channel. The \begin{document}$ \Sigma_c(2755)1/2^- $\end{document} state is likely to be a very narrow state with a width of \begin{document}$ \Gamma\sim 15 $\end{document} MeV, with its decays almost saturated by the \begin{document}$ \Lambda_c \pi $\end{document} channel. Additionally, evidence of the \begin{document}$\Sigma_c(2755) {1}/{2}^-$\end{document} resonance as a very narrow peak may be seen in the \begin{document}$ \Lambda_c\pi $\end{document} invariant mass spectrum. The other two \begin{document}$ P $\end{document}-wave states, \begin{document}$\Sigma_c(2746) {1}/{2}^-$\end{document} and \begin{document}$\Sigma_c(2796) {3}/{2}^-$\end{document}, are relatively narrow states with similar widths of \begin{document}$ \Gamma\sim 30 $\end{document} MeV and predominantly decay into \begin{document}$ \Sigma_c\pi $\end{document} and \begin{document}$ \Sigma^{*}_c\pi $\end{document}, respectively. This study can provide useful references for discovering these low-lying \begin{document}$ P $\end{document}-wave states in forthcoming experiments.     

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.     

Exploring HVV amplitudes with CP violation using decomposition and the on-shell scattering amplitude method

\begin{document}$ CP $\end{document} violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders. We study the \begin{document}$ CP $\end{document} properties of \begin{document}$ HVV $\end{document} vertexes between Higgs and gauge boson pairs by defining a \begin{document}$ CP $\end{document} violation phase angle ξ, which indicates the mixture of \begin{document}$ CP $\end{document}-even and \begin{document}$ CP $\end{document}-odd Higgs states in \begin{document}$ HVV $\end{document} in new physics. A series of \begin{document}$ HVV $\end{document} amplitudes, \begin{document}$ H\to\gamma\gamma, H\to\gamma V\to \gamma \ell\ell $\end{document}, and \begin{document}$ H\to VV\to 4\ell $\end{document}, with a \begin{document}$ CP $\end{document} phase angle are studied systematically to explicitly explain why \begin{document}$ CP $\end{document} violation can only be probed independently in the \begin{document}$ 4\ell $\end{document} process. We obtain a novel amplitude decomposition relation that illustrates that if two preconditions (multilinear momentum dependent vertexes, and the current \begin{document}$ J_\mu $\end{document} of \begin{document}$ V\to \ell^+ \ell^- $\end{document} is formally proportional to a photon's polarization vector) are satisfied, a higher-point amplitude can be decomposed into a summation of a series of lower-point amplitudes. As a practical example, the amplitude of the \begin{document}$ H\to\gamma V\to \gamma \ell\ell $\end{document} and \begin{document}$ H\to VV\to 4\ell $\end{document} processes can be decomposed into a summation of many \begin{document}$ H\to\gamma\gamma $\end{document} amplitudes. We calculate these amplitudes in the framework of the on-shell scattering amplitude method, considering both massless and massive vector gauge bosons with the \begin{document}$ CP $\end{document} violation phase angle. The above two approaches provide consistent results and clearly reveal the \begin{document}$ CP $\end{document} violation ξ dependence in the amplitudes.