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.     

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.     

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.     

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.     

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.     

Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective

In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate \begin{document}$\gamma$\end{document}-vibrational bands in transitional nuclei of \begin{document}$^{118-128}{\rm{Xe}}$\end{document}. We report that each triaxial intrinsic state has a \begin{document}$\gamma$\end{document}-band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the \begin{document}$\gamma$\end{document}-vibrational band are calculated.     

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}.     

Search for invisible decays of the Higgs boson produced at the CEPC

The Circular Electron Positron Collider (CEPC), proposed as a future Higgs boson factory, will operate at a center-of-mass energy of 240 GeV and will accumulate 5.6 ab^?1 of integrated luminosity in 7 years. In this study, we estimate the upper limit of BR(\begin{document}$H \rightarrow$\end{document} inv) for three independent channels, including two leptonic channels and one hadronic channel, at the CEPC. Based on the full simulation analysis, the upper limit of BR(\begin{document}$H \rightarrow$\end{document} inv) could reach 0.26% at the 95% confidence level. In the Stand Model (SM), the Higgs boson can only decay invisibly via \begin{document}$H\rightarrow ZZ^\ast\rightarrow\nu\overline{\nu}\nu\overline{\nu}$\end{document}, so any evidence of invisible Higgs decays that exceed BR(\begin{document}$H \rightarrow$\end{document} inv) of the SM will indicate a phenomenon that is beyond the SM (BSM). The invariant mass resolution of the visible hadronic decay system \begin{document}$ZH(Z \rightarrow qq$\end{document}, \begin{document}$ H \rightarrow$\end{document} inv) is simulated, and the physics requirement at the CEPC detector for reaching this is given.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Properties of the P_c(4312) pentaquark and its bottom partner

We present an analysis of the newly observed pentaquark P_c(4312)~+ to shed light on its quantum numbers.To do that,the QCD sum rules approach is used.The measured mass of this particle is close to the ∑_c~(++)D~-threshold and has a small width,which supports the possibility of its being a molecular state.We consider an interpolating current in a molecular form and analyze both the positive and negative parity states with spin-1/2.We also consider the bottom counterpart of the state with similar molecular form.Our mass result for the charm pentaquark state supports that the quantum numbers of the observed state are consistent with J~P=1/2~-.     

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.