Classical model for diffusion and thermalization of heavy quarks in a hot medium: memory and out-of-equilibrium effects

We consider a simple model for the diffusion of heavy quarks in a hot bath,modeling the latter by an ensemble of oscillators distributed according to either a thermal distribution or to an out-of-equilibrium distribution with a saturation scale.In this model it is easy to introduce memory effects by changing the distribution of oscillators:we model them by introducing a Gaussian distribution,dN/dω.which can be deformed continuously from a δ-function,giving a Markov dissipation, to a broad kernel with memory.Deriving the equation of motion of the heavy quark in the bath,we remark how dissipation comes out naturally as an effect of the back-reaction of the oscillators on the bath.Moreover,the exact solution of this equation allows to define the thermalization time as the time necessary to remove any memory of the initial conditions.We find that the broadening of the dissipative kernel,while keeping the coupling fixed,lowers the thermalization time.We also derive the fluctuation-dissipation theorem for the bath,and use it to estimate the kinematic regime in which momentum diffusion of the heavy quark dominates over drift.We find that diffusion is more important as long as K_0/ε is small,where K_0 and ε denote the initial energy of the heavy quark and the average energy of the bath,respectively.     

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.     

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.     

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.     

Exact recession velocity and cosmic redshift based on cosmological principle and Yang-Mills gravity

Based on the cosmological principle and quantum Yang-Mills gravity in the super-macroscopic limit, we obtain an exact recession velocity and cosmic redshift z, as measured in an inertial frame F ≡ F(t, x, y, z). For a matter-dominated universe, we have the effective cosmic metric tensor G_(μν)(t) =(B~2(t),-A~2(t),-A~2(t),-A~2(t)),A ∝ B ∝ t~(1/2), where t has the operational meaning of time in F frame. We assume a cosmic action S ≡ S cos involving Gμν(t) and derive the ‘Okubo equation' of motion, G μν(t)?μS ?νS-m2= 0, for a distant galaxy with mass m. This cos-√mic equation predicts an exact recession velocity, ■, where H = A˙(t)/A(t) and Co = B/A, as observed in the inertial frame F. For small velocities, we have the usual Hubble's law r≈ rH for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in F. It is natural to assume the massless Okubo equation, G μν(t)?μψe?νψe= 0, for light emitted from accelerated distant galaxies. Based on the principle of limiting continuation of physical laws, we obtain a transformation for covariant wave 4-vectors between and inertial and an accelerated frame, and predict a relationship for the exact recession velocity and cosmic redshift, z = [(1 + V_r)/(1-V_r~2)~(1/2)]-1, where Vr= r˙/Co 1, as observed in the inertial frame F. These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.     

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.     

Simple Woods-Saxon-type form for Ωα and Ξα interactions using folding model

We derive a simple Woods-Saxon-type form for potentials between Y=Ξ,Ωandαusing a single-folding potential method,based on a separable Y-nucleon Potential.The PotentialsΞ+αandΩ+αare accordingly obtained using the ESC08 c Nijmegens potential(in 3 S1 channel)and HAL QCD collaborationΩN interactions(in lattice QCD),respectively.In deriving the potential between Y andα,the same potential between Y and N is employed.The binding energy,scattering length,and effective range of the Y particle on the alpha particle are approximated by the resulting potentials.The depths of the potentials inΩαandΞαsystems are obtained at-61 MeV and-24.4 MeV,respectively.In the case of theΞαpotential,a fairly good agreement is observed between the single-folding potential method and the phenomenological potential of the Dover-Gal model.These potentials can be used in 3-,4-and 5-body cluster structures ofΩandΞhypernuclei.     

Charmonia and bottomonia in asymmetric magnetized hot nuclear matter

We investigate the mass-shift of P-wave charmonium(χ_(c0),χ_(c1)),and S and P-wave bottomonium(η_b,■,χ_(b0),and χ_(b1)) states in magnetized hot asymmetric nuclear matter using the unification of QCD sum rules(QCDSR)and the chiral S U(3) model.Within QCDSR,we use two approaches,i.e.,the moment sum rule and the Borel sum rule.The magnetic field induced scalar gluon condensate α_s/πG_(μν)~aG~(aμν) and the twist-2 gluon operatorα_s/πG_(μσ)~aG~a ν~σcalculated in the chiral S U(3) model are utilised in QCD sum rules to calculate the in-medium mass-shift of the above mesons.The attractive mass-shift of these mesons is observed,which is more sensitive to magnetic field in the high density regime for charmonium,however less so for bottomonium.These results may be helpful to understand the decay of higher quarkonium states to the lower quarkonium states in asymmetric heavy ion collision experiments.     

Revisiting D-meson twist-2, 3 distribution amplitudes

Owing to the significant difference between the experimental measurements and the theoretical predictions of the standard model (SM) for the value of \begin{document}$ {\cal{R}}(D) $\end{document} of the semileptonic decay \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}, researchers speculate that this decay may be evidence of new physics beyond the SM. Usually, the D-meson twist-2, 3 distribution amplitudes (DAs) \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document} , and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document} are the main error sources when perturbative QCD factorization and light-cone QCD sum rules are used to study \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}. Therefore, it is important to obtain more reasonable and accurate behaviors for these DAs. Motivated by our previous work [Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit D-meson twist-2, 3 DAs \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document}, and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document}. New sum rule formulae for the \begin{document}$\xi $\end{document}-moments of these three DAs are suggested for obtaining more accurate values. The light-cone harmonic oscillator models for the DAs are improved, and their parameters are determined by fitting the values of ξ-moments via the least squares method.     

Gluon-pair-creation production model of strong interaction vertices

By studying the \begin{document}$\eta_c$\end{document} exclusive decay to double glueballs, we introduce a model to phenomenologically mimic the gluon-pair-vacuum interaction vertices, namely the \begin{document}$0^{++}$\end{document} model. Based on this model, we study glueball production in pseudoscalar quarkonium decays, explicitly \begin{document}$\eta_c \to f_0(1500)\eta(1405)$\end{document}, \begin{document}$\eta_b\to f_0(1500)\eta(1405)$\end{document} , and \begin{document}$\eta_b\to f_0(1710)\eta(1405)$\end{document} processes. Among them \begin{document}$f_0(1500)$\end{document} and \begin{document}$f_0(1710)$\end{document} are well-known scalars possessing large glue components, while \begin{document}$\eta(1405)$\end{document} is a potential candidate for a pseudoscalar glueball. The preliminary calculation results indicate that these processes are marginally accessible in the presently running experiments BES III, BELLE II, and LHCb.     

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.     

Electromagnetic field produced in high-energy small collision systems within charge density models of nucleons

Recent experiments show that \begin{document}$ \Delta\gamma $\end{document}, an observable designed to detect the chiral magnetic effect (CME), in small collision systems (\begin{document}$ p+A $\end{document}) is similar to that in heavy ion collisions (\begin{document}$ A+A $\end{document}). This introduces a challenge to the existence of the CME because it is believed that no azimuthal correlation exists between the orientation of the magnetic field (\begin{document}$ \Phi_B $\end{document}) and participant plane (\begin{document}$ \Phi_2 $\end{document}) in small collision systems. In this work, we introduce three charge density models to describe the inner charge distributions of protons and neutrons and calculate the electric and magnetic fields produced in small \begin{document}$ p+A $\end{document} collisions at both RHIC and LHC energies. Our results show that the contribution of the single projectile proton is the main contributor to the magnetic field after averaging over all participants. The azimuthal correlation between \begin{document}$ \Phi_B $\end{document} and \begin{document}$ \Phi_2 $\end{document} is small but not vanished. Additionally, owing to the large fluctuation in field strength, the magnetic-field contribution to \begin{document}$ \Delta\gamma $\end{document} may be large.     

Sequential single pion production explaining the dibaryon "d*(2380)" peak

In this study, we investigate the two step sequential one pion production mechanism, that is, \begin{document}$ np(I=0)\to $\end{document}\begin{document}$ \pi^-pp $\end{document} followed by the fusion reaction \begin{document}$ pp\to \pi^+d $\end{document}, to describe the \begin{document}$ np\to \pi^+\pi^-d $\end{document} reaction with \begin{document}$ \pi^+\pi^- $\end{document} in state \begin{document}$ I=0 $\end{document}. In this reaction, a narrow peak identified with a "\begin{document}$ d(2380) $\end{document}" dibaryon has been previously observed. We discover that the second reaction step \begin{document}$ pp\to \pi^+d $\end{document} is driven by a triangle singularity that determines the position of the peak of the reaction and the high strength of the cross section. The combined cross section of these two mechanisms produces a narrow peak with a position, width, and strength, that are compatible with experimental observations within the applied approximations made. This novel interpretation of the peak accomplished without invoking a dibaryon explains why this peak has remained undetected in other reactions.     

Using simulated Tianqin gravitational wave data and electromagnetic wave data to study the coincidence problem and Hubble tension problem

In this study, we used electromagnetic wave data (H0LiCOW, \begin{document}$ H(z) $\end{document}, SNe) and gravitational wave data (Tianqin) to constrain the interacting dark energy (IDE) model and investigate the Hubble tension and coincidence problems. By combining these four types of data (Tianqin+H0LiCOW+SNe+\begin{document}$ H(z) $\end{document}), we obtained the following parameter values with a confidence interval of \begin{document}$ 1\sigma $\end{document}: \begin{document}$ \Omega_m=0.36\pm0.18 $\end{document}, \begin{document}$ \omega_x=-1.29^{+0.61}_{-0.23} $\end{document}, \begin{document}$ \xi=3.15^{+0.36}_{-1.1} $\end{document}, and \begin{document}$H_0=70.04\pm $\end{document}\begin{document}$ 0.42~ {\rm kms}^{-1}{\rm Mpc}^{-1}$\end{document}. According to our results, the best value of \begin{document}$ H_0 $\end{document} shows that the Hubble tension problem can be alleviated to some extent. In addition, the center value of \begin{document}$ \xi+3\omega_x = -0.72^{+2.19}_{-1.19}(1\sigma) $\end{document} indicates that the coincidence problem is slightly alleviated. However, \begin{document}$ \xi+3\omega_x = 0 $\end{document} is still within the \begin{document}$ 1\sigma $\end{document} error range, which indicates that the ΛCDM model is still the model in best agreement with the observational data at present. Finally, we compared the constraint results of the electromagnetic and gravitational waves on the model parameters and found that the constraint effect of electromagnetic wave data on model parameters is better than that of simulated Tianqin gravitational wave data.     

Effects of Λ hyperons on the deformations of even–even nuclei

The deformations of multi-\begin{document}$ {\Lambda} $\end{document} hypernuclei corresponding to even–even core nuclei ranging from \begin{document}$ ^8 $\end{document}Be to \begin{document}$ ^{40} $\end{document}Ca with 2, 4, 6, and 8 hyperons are studied using the deformed Skyrme–Hartree–Fock approach. It is found that the deformations are reduced when adding 2 or 8 \begin{document}$ {\Lambda} $\end{document} hyperons, but enhanced when adding 4 or 6 \begin{document}$ {\Lambda} $\end{document} hyperons. These differences are attributed to the fact that \begin{document}$ {\Lambda} $\end{document} hyperons are filled gradually into the three deformed \begin{document}$ p $\end{document} orbits, of which the [110]1/2\begin{document}$ ^- $\end{document} orbit is prolately deformed and the degenerate [101]1/2\begin{document}$ ^- $\end{document} and [101]3/2\begin{document}$ ^- $\end{document} orbits are oblately deformed.     

Is X(3872) a bound state?

All existing experimental evidence for the bound state nature of X(3872) relies on observing its decay products,which are measured with a finite experimental mass resolution that is typically △m≥2 MeV,and much larger than its alleged binding energy,B_X=0.00(18) MeV.On the other hand,we have found recently that there is a clear cancellation in the 1~(++) channel of the invariant DD~*mass around the threshold between continuum and the bound state.This is very much like a similar cancellation in the proton-neutron continuum with the deuteron in the1~(++) channel.Based on comparative fits with a common Tsallis distribution of the experimental cross-sections for prompt production of deuterons and X(3872) in pp collisions with a finite p_T,we find a strong argument for questioning the bound state nature of this state,which also suggests that the large observed production rate could be consistent with a half-bound state.     

Impact of lepton p_T threshold on charge asymmetry predictions for inclusive W boson production in pp collisions at 13 TeV

This paper presents the impact of the lepton transverse momentum p_T~l threshold on the W boson charge asymmetry predictions in perturbative QCD for the inclusive W~++X→l~±v+X production in proton-proton(pp)collisions.The predictions are obtained at various low-p_T~l thresholds p_T~l 20,25,30,and 40 GeV in a fiducial region encompassing both the central and forward detector acceptances in terms of the lepton pseudorapidity0 ≤η_l≤4.5.The predicted distributions for the lepton charge asymmetry,which is defined by η_l(A_(η_l)),at the nextto-next-to-leading order(NNLO) accuracy are compared with the CMS and LHCb data at 8 TeV center-of-mass collision energy.The 8 TeV predictions reproduce the data fairly well within the quoted uncertainties.The predictions from the CT14 parton distribution function(PDF) model are in a slightly better agreement with the data over the other PDF sets that are tested.The 13 TeV predictions using various p_T~l thresholds are reported for A_(η_l) and the charge asymmetries that are defined in terms of the differential cross sections in bins of the W boson rapidity yw(A_(y_w)) and transverse momentum p_T~W(A_(p_T~W)).The NNLO predictions for the A_(η_l),A_(y_w).and A_(p_T~W) distributions are assessed to be in close correlation with the p_T~l value.The A_(η_l) and A_(y_w) distributions are particularly shown to be more correlated at a higher p_T~l threshold.The A_(p_T~W) distributions are also reported from the merged predictions with improved accuracy by the inclusion of the next-to-next-to-next-to-leading logarithm(N'LL) corrections,i.e.,at NNLO+N~3 LL.The predicted distributions from various p_T~l thresholds represent a finer probe in terms of the capability to provide more constraints on the ratio of u and d quark distribution functions in the parton momentum fraction range 10~(-4) x1.     

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.     

The angular distributions of elastic scattering of 12,13C+Zr

To obtain the neutron spectroscopic amplitudes for \begin{document}${}^{90-96}$\end{document}Zr overlaps, experimental data of elastic scattering with small experimental errors and precise optical potentials were analyzed. In this study, the elastic scattering angular distributions of \begin{document}${}^{12,13}$\end{document}C + \begin{document}${}^{A} {\rm{Zr}}$\end{document} (A = 90, 91, 92, 94, 96) were measured using the high-precision Q3D magnetic spectrometer in the Tandem accelerator. The S?o Paulo potential was used for the optical potential. The optical model and coupled channel calculations were compared with the experimental data. The theoretical results were found to be very close to the experimental data. In addition, the possible effects of the couplings to the inelastic channels of the \begin{document}${}^A {\rm{Zr}}$\end{document} targets and \begin{document}${}^{12, 13}$\end{document}C projectiles on the elastic scattering were studied. It was observed that the couplings to the inelastic channels of the \begin{document}${}^{12,13}$\end{document}C projectiles could improve the agreement with the experimental data, while the inelastic couplings to the target states are of minor importance. The effect of the one-neutron stripping in the \begin{document}${}^{13}$\end{document}C+\begin{document}${}^A {\rm{Zr}}$\end{document} elastic scattering was also studied. The one-neutron stripping channel in \begin{document}${}^{13}$\end{document}C + \begin{document}${}^A {\rm{Zr}}$\end{document} was found to be not relevant and did not affect the elastic scattering angular distributions. Our results also show that in the reactions with the considered zirconium isotopes, the presence of the extra neutron in \begin{document}${}^{13}$\end{document}C does not influence the reaction mechanism, which is governed by the collective excitation of the \begin{document}${}^{12}$\end{document}C core.