Search

We used an effective Lagrangian approach to investigate the production of the anticharmed pentaquark state $P_{\bar{c}s}^{(*)-}$ with the minimal quark content $\bar{c}sudd$ in the $\Lambda_b^0$ decay and its decay into the $\Lambda D^{(\ast)-}$ and $\Sigma D^{(\ast)-}$. In our calculation, the $P_{\bar{c}s}^{(*)-}$ is considered as the molecule state of the $nD_{s0(s1)}^{-}$ in an $S$ wave, and its production and decay occur via triangle loops at the hadron level. The predicted branching fractions for the processes $\Lambda_b^0\to P_{\bar{c}s}^{(*)-} D^+ $ are around $10^{-4}\sim 10^{-3}$. The partial decay widths of the $ P_{\bar{c}s}^{(*)-} \to \Lambda D^{(\ast)-}$ are between $0.1$ and $\sim 10~\mathrm{MeV}$, whereas the decay widths of the $ P_{\bar{c}s}^{(*)-} \to \Sigma D^{(\ast)-}$ are about one order of magnitude smaller. It is found that the width ratios for the $P_{\bar{c}s}^{(*)-}$ decays are nearly independent of the model parameter $\alpha$. It is hoped that these predictions could be helpful in searching for the anticharmed-strange pentaquark candidates in future LHCb experiments., Comment: 10 pages, 6 figures, update the Pcs* mass to be about 3.44 GeV

Focusing on the recent measurements of the scattering processes $\bar{\Lambda} p \rightarrow \bar{\Lambda} p$ and $\Lambda p \rightarrow \Lambda p$ reported by BESIII, we offer a dynamical interpretation of the differences in the measured total and differential cross sections for both processes. This discrepancy arises because the $u$-channel contribution is forbidden for $\bar{\Lambda} p \rightarrow \bar{\Lambda} p$ but allowed for $\Lambda p \rightarrow \Lambda p$. Additionally, we examine the enhancement effect in the forward angle region of the differential cross section for $\bar{\Lambda} p$ elastic scattering, attributed to the $t$-channel contribution. This work serves as a test to the scattering mechanism involved in these reactions., Comment: 4 pages, 4 figures, 1 tables

In this study, applying the effective Lagrangian approach, we investigate the reaction $\pi^-p\rightarrow K^{*}\Sigma$ to explore the production of the nucleon excited state $N^*(2080)$ and the constituent field scaling laws, also known as the constituent counting rules. Specifically, we analyze two scenarios, where the $J^P$ quantum numbers of $N^*(2080)$ are $3/2^-$ and $1/2^-$. Our results show that the contribution from $s$-channel $N^*$ exchange dominates the total cross section, surpassing those from $t$-channel $K^{(*)}$ exchange and $u$-channel $\Sigma$ exchange. Additionally, we present predictions for the differential cross section of the $\pi^-p\rightarrow K^{*}\Sigma$ process. Notably, in the large momentum transfer region ($\theta = 90^\circ$), the differential cross section in the $t$-distribution aligns with the energy-dependent scaling formula predicted by the constituent counting rule, specifically, $d\sigma/dt \sim 1/s^{8}$ for the $\pi^-p\rightarrow K^{*}\Sigma$ reaction. Finally, we extend the 2-to-2 scattering process to the 2-to-3 Dalitz process and provide theoretical predictions for this scenario. Our findings suggest that the cross section for the $\pi^-p \rightarrow K^{*}\Sigma\rightarrow K^+\pi^-\Sigma^0$ process can reach several tens of $\mu b$ near the threshold, making it highly favorable for experimental measurement. However, the current scarcity of experimental data for the $\pi^-p\rightarrow K^{*}\Sigma$ reaction at threshold energy limits our ability to precisely determine the properties of the nucleon excited state $N^*$ and related physical quantities. Therefore, additional experimental measurements of the $\pi^-p \rightarrow K^{*}\Sigma$ reaction at threshold are strongly encouraged, and correlation studies could be pursued at facilities such as J-PARC, AMBER, and upcoming HIKE and HIAF meson beam experiments., Comment: 13 Pages, 17 Figures, 6 Tables

Nonlinear circuits serve as crucial carriers and physical models for investigating nonlinear dynamics and chaotic behavior, particularly in the simulation of biological neurons. In this study, Chua's circuit and Lorenz circuit are systematically explored for the first time through machine learning correlation algorithms. Specifically, the upgraded and optimized SINDy-PI model, which is based on neural network and symbolic regression algorithm, is utilized to learn the numerical results of attractors generated by these two nonlinear circuits. Through error analysis, we examine the effects of the precision of input data and the amount of data on the algorithmic model. The findings reveal that when the input data quantity and data precision fall within a certain range, the algorithm model can effectively recognize and restore the differential equation expressions corresponding to the two circuits. Additionally, we test the anti-interference ability of different circuits and the robustness of the algorithm by introducing noise into the test data. The results indicate that under the same noise disturbance, the Lorenz circuit has better noise resistance than Chua's circuit, providing a starting point for further studying the intrinsic properties and characteristics of different nonlinear circuits. The above results will not only offer a reference for the further study of nonlinear circuits and related systems using deep learning algorithms but also lay a preliminary theoretical foundation for the study of related physical problems and applications., Comment: 13 pages, 7 figures, 4 tables

In this work, the production of the hidden-strange pentaquarklike state $N^{*}(2080)$ via the $\pi^{-} p$ scattering process is studied by the effective Lagrangian approach. Concretely, we consider the $\rho$ meson exchange of $t$-channel and the nucleon exchange of $u$-channel, which are treated as the background terms, and take into account the contribution of the $N^{*}(2080)$ via the $s$-channel as a signal term. By global fitting of the total and differential cross sections of the $\pi^{-} p\rightarrow\phi n$ process, it is shown that the $N^{*}(2080)$ contributes an obvious peak at the threshold energy point of the differential cross section at the forward angle ($\cos\theta = 1$), which provides clues to the detection of the $N^{*}(2080)$ by the $\pi^{-} p$ scattering process. However, due to the limited accuracy of the experimental data, it is an objective limitation for us to determine the properties of the $N^{*}(2080)$ by the $\pi^{-} p$ scattering process. Therefore, more accurate experimental measurements of the $\pi^{-} p\rightarrow\phi n$ reaction are highly desirable, and we have also proposed that correlation measurements can be performed on J-PARC, AMBER, and future HIKE and HIAF meson beam experiments., Comment: 9 pages, 10 figures

In this work, under the framework of vector meson dominance model, the trace anomaly contribution value inside neutrons are extracted for the first time based on vector meson photoproduction data. Furthermore, we systematically compare and analyze the trace anomaly contributions of protons and neutrons. The results show that the trace anomaly contributions of protons and neutrons are close, which indirectly confirms that their internal structures and dynamic properties may have certain similarities. In addition, the main factors affecting the extraction of the trace anomaly contribution of nucleons are discussed in detail. This study not only provides a theoretical basis for us to better understand the source of nucleon mass, but also makes a useful exploration and discussion on how to extract the trace anomaly contribution of nucleon more accurately in the future., Comment: 6 pages, 2 figures

We embark on a systematical analysis of the quark and gluon gravitational form factors (GFFs) of the proton, by connecting energy-momentum tensor (EMT) and the near-threshold vector meson photoproduction (NTVMP). Concretely, the quark contributions of GFFs are determined by global fitting the cross section of the lightest vector meson $\rho^0$ photoproduction. Combined with the gluon GFFs achieved from heavy quarkonium $J/\psi$ photoproduction data, the complete GFFs are obtained and compared with the experimental results and Lattice QCD determinations. In addition, we use the Resonances Via Pad\'{e} (RVP) method based on the Schlessinger Point Method (SPM) to obtain a model-independent quark $D$-term distribution by direct analytical continuation of Deep Virtual Compton Scattering (DVCS) experimental data. If errors are considered, the results obtained by RVP are basically consistent with those obtained by NTVMP. Moreover, the comprehensive information on GFFs helps us to uncover the mass distribution and mechanical properties inside the proton. This work is not only an important basis for delving the proton enigmatic properties, unraveling the secrets of the proton internal nature but also have significance theoretical guiding for future JLab and EICs experimental measurements., Comment: 9 pages,8 figures

In this study, we comprehensively investigate the production of isovector scalar meson $a_{0}(1817)$ using the effective Lagrangian approach. Specifically, we employ the Reggeized $t$ channel Born term to calculate the total and differential cross sections for the reaction $K^{-}p \rightarrow a_{0}(1817)\Lambda$. Our analysis reveals that the optimal energy range for detecting the $a_{0}(1817)$ meson lies between $W=3.4$ GeV and $W=3.6$ GeV, where the predicted total cross section reaches a minimum value of 112 nb. Notably, the $t$ channel, as predicted by the Regge model, significantly enhances the differential cross sections, particularly at extreme forward angles. Furthermore, we investigate the Dalitz processes of $2\rightarrow 3$ and discuss the feasibility of detecting the $a_{0}(1817)$ meson in experiments such as J-PARC., Comment: 6 pages, 6 figures

Under the framework of the vector meson dominance model (VMD), the absolute scattering lengths of light vector mesons ($\phi$, $\omega$, and $\rho$) with the deuteron are calculated from the cross sections of vector meson photoproduction off a deuteron. Additionally, a fitting function is used to predict the scattering lengths of the heavy vector mesons $J/\psi$-$d$ and $% \Upsilon$-$d$. Based on these results, the distribution of the scattering lengths $|\alpha_{V d}|$ between vector mesons and the deuteron is presented for the first time and compared with the scattering lengths $|\alpha_{V p}|$ between vector mesons and the proton. It is found that as the mass of the vector meson increases, the scattering lengths $|\alpha_{V d}|$ become closer to $|\alpha_{V p}|$. In addition, the correlation analysis indicates a strong positive relationship between the scattering length and the vector meson radius, with a high correlation coefficient. The implications of results are essential for improving our understanding of the interaction between hadron and nucleus., Comment: 6 pages, 7 figures

In this work, we investigate the nature of the strong coupling constant and related physics. Through the analysis of accumulated experimental data from around the world, we employ the ability of machine learning to unravel its physical laws. The result of our efforts is a formula that captures the expansive panorama of the distribution of the strong coupling constant across the entire energy range. Importantly, this newly derived expression is very similar to the formula derived from the Dyson-Schwinger equations based on the framework of Yang-Mills theory. By introducing the Euler number, $e$, into the functional formula of the strong coupling constant at high energies, we have successfully solved the puzzle of the infrared divergence, which allows for a seamless transition of the strong coupling constant from the perturbative to the non-perturbative energy regime. Moreover, the obtained ghost and gluon dressing function distribution results confirm that the obtained strong coupling constant formula can well describe the physical properties of the non-perturbed regime. In addition, we investigate the QCD strong coupling constant result of the Bjorken sum rule $\Gamma_1^{p-n}$ and the quark-quark static energy $E_0(r)$, and find that the global energy scale can effectively interpret the experimental data. The results presented in this work shed light on the puzzling properties of quantum chromodynamics and the intricate interplay of strong coupling constants at both low and high energy scales., Comment: 10 pages, 7 figures

Synchronous control of nonlinear circuits is of great importance in many fields. In this paper, a capacitor is used for closed-loop coupling of three dual-vortex attractor Chua circuits with the same circuit parameters and different initial conditions, and the corresponding synchronization processes and synchronization effects are investigated. It is found that, for the capacitor, the closed-loop coupling can completely synchronize the three Chua circuits. And there exists a critical coupling strength $\delta_{critical}^C$ that can be calculated, and when the coupling strength is between the critical coupling strength $\delta_{critical}^C$ and the upper coupling strength $\delta_{max}^C$, the three circuits can be completely synchronized very quickly. Moreover, the results show that the unidirectional coupling cannot make the circuit system completely synchronized. Finally, we also verify the correctness of the calculation by circuit simulation experiments., Comment: 10 pages

In this work, we use the artificial neural network (ANN) method to study and predict the distribution of strong coupling constants by fitting the existing data. Our approach takes advantage of the ability of ANN to learn complex nonlinear relations and excellent generalization, and allows for a systematic treatment of the uncertainties associated with the data. To ensure the reliability of our results, we apply three evaluation indexes to evaluate the accuracy of model during training. Finally, we obtained the predicted values of the strong coupling constants at different energy scales, and compared and verified them with the existing experimental data. Our approach represents a promising way to improve the determination of the strong coupling constant at low energies, and could have important implications for future experimental and theoretical studies in quantum chromodynamics., Comment: This work is a very preliminary result of using machine learning to study strong coupling constants. It is not a very mature work, and there are still certain uncertainties in the results. In a responsible manner, we decided to withdraw this manuscript after deliberation, and readers are invited to pay attention to our follow-up work on strong coupling constants in machine learning

We investigate the production of $X_b$ in the process $\Upsilon(5S,6S)\to \gamma X_b$, where $X_b$ is assumed to be a $B {\bar B}^*$ molecular state. Two kinds of meson loops of $B^{(*)}{\bar B}^{(*)}$ and $B_1^{\prime}{\bar B}^{(*)}$ were considered. To explore the rescattering mechanism, we calculated the relevant branching ratios using the effective Lagrangian based on the heavy quark symmetry. The branching ratios for the $\Upsilon(5S\,,6S) \to \gamma X_b$ were found to be at the orders of $10^{-7} \sim 10^{-6}$. Such sizeable branching ratios might be accessible at BelleII, which would provide important clues to the inner structures of the exotic state $X_b$., Comment: 9 pages, 2 figures, comments are welcome

We study the radiative decays $Z_c(3900)/Z_c(4020) \to \gamma \chi_{cJ}(\gamma\chi_{cJ}^\prime)$ ($J=0, 1, 2$), with the assumption that the $Z_c(3900)$ and $Z_c(4020)$ couple strongly to $D\bar D^* +c.c$ and $D^*{\bar D}^*$ channel, respectively. By considering the contributions of intermediate charmed mesons triangle loops within an effective Lagrangian approach, it is shown that the calculated partial widths of $Z_c(3900) \to \gamma \chi_{cJ}$ are about a few hundreds keVs, while the obtained partial widths $Z_c(4020) \to \gamma \chi_{cJ}$ are about tens of keVs. The predicted partial widths of $Z_c(3900)\to\gamma\chi_{c0,1}^\prime$ are less than 1 keV, which mainly due to the very small phase space. For $Z_c(4020)\to\gamma\chi_{c0,2}^\prime$, the calculated partial widths are usually smaller than 1 keV. For the $Z_c(4020)\to\gamma\chi_{c1}^\prime$ process, the obtained partial widths can reach up to the order of 10 keV. Furthermore, the dependence of these ratios between different decay modes on the masses of $Z_c(3900)$ or $Z_c(4020)$ are also investigated, which may be a good quantity for the experiments. It is hoped that these calculations here could be tested by future experiments., Comment: 9 pages, 6 figures. Accepted by Physical Review D

Generally, multi-particle spring system is an important and widely used physical model. However, with the increase of the number of particles, the difficulty of solving the kinematic trajectory of the particles becomes more and more difficult. The key to solving this problem lies in whether it is possible to construct a dynamic model of the multi-particle spring system which is convenient for numerical solution. In this work, by defining a new physical quantity, the spring action $\mathcal{K}$, we study and reconstruct the dynamic models of two common types of multi-particle spring systems. The calculation results show that the multi-particle spring dynamic model constructed by us has obvious advantages in calculating the spring system with a large number of particles. This will provide important theoretical solutions for the application of multi-particle spring systems to engineering or scientific problems., Comment: 9 pages, 13 figures

Inspired by the recent Hall C and GlueX measurements of $J/\psi$ photoproduction, a systematic analysis of the contribution of quantum anomalous energy (QAE) to the proton mass is carried out under the framework of the vector meson dominance model. The results show that the effective Pomeron model and the parametrized two gluon exchange model can explain the cross section of $J/\psi$ photoproduction well. Based on the predicted cross section values given by the two models, the distribution of the QAE contribution with the energy is extracted for the first time. Finally, the average value of the QAE contribution is estimated to be (3.50$\pm$0.70)$\%$, which suggests that the QAE contribution to the proton mass is small. Accordingly, we compared this result with those of other groups and explored the causes for the differences., Comment: 8 pages, 9 figures

The productions of the exotic states $ X_0(2900) $ and $ X_1(2900) $ in $K^{+}p \to \Sigma_{c}^{++}X_{0}(2900)$ and $K^{+}p \to \Sigma_{c}^{++}X_{1}(2900)$ reactions are studied within an effective Lagrangian approach. The $t-$channel Born term is included to calculate the production cross sections. The numerical results show that the total cross section may reach up to about 0.5 nb and 25 nb for the production of $ X_0(2900) $ and $ X_1(2900) $, respectively. The predicted differential cross sections are sensitive to the scattering angles and have strong forward enhancements. The cross sections for the $K^{+}n \to \Lambda_{c}^{+}X_{0,1}$ are also calculated and found to be larger than that in $K^{+}p$ collisions by more than one order of magnitude. The results are helpful to the possible experiments at J-PARC and COMPASS., Comment: 5 pages, 5 figures

In the quantum chromodynamics, the mass source of the proton is decomposed into four parts by the energy momentum tensor : quark energy term, gluon energy term, quark mass term and trace anomaly term. And the trace anomaly term is the most crucial contribution for studying the internal structure of the proton. In this work, under the definition of the vector meson dominant model, the trace anomaly contribution of the proton is extracted from the experimental datas of light vector mesons $\rho$, $\omega$ and $\phi$ photoproduction at the near-threshold, which are ($1.15\pm0.08$)$\%$, ($2.70\pm0.04$)$\%$ and ($5.58\pm0.25$)$\%$, respectively. Eventually, the average trace anomaly contribution of the proton is ($4.36\pm0.40$) $\%$, which only account for a small fraction of the total proton mass. The result of this work will provide theoretical information support for further study of proton internal structure., Comment: 7 pages, 4 figures

In this work, we systematically study the $\phi$ meson and nucleus interaction by analyzing and fitting the cross sections of $\gamma N$$\rightarrow \phi$$N$ ($N$ represent the nucleus) reactions near the threshold. With the help of vector meson dominant model, the distribution of $\phi$-$N$ scattering length as a function of energy is presented, and the results show that there is a slight increase in scattering length with increasing energy. Based on this, the average scattering length of $\phi$-proton is obtained as $0.10\pm0.01$ fm by combining experimental data and theoretical models. Moreover, the average scattering length of $\phi$-deuteron interaction is derived to be $0.014\pm0.002$ fm for the first time. Further, the effect of the momentum transfer $|t_{min}|$ on the $\phi$-$N$ scattering length at the threshold is discussed. The obtained results not only provide important theoretical information for a more comprehensive and accurate study of the $\phi$-$N$ scattering length, but also provide a basis for future experimental measurements of $\phi$ meson production., Comment: 9 pages, 12 figures. To be published in Chinese Physics C

Inspired by the recent near-threshold $J/\psi$ photoproduction measurements, we discuss gluon gravitational form factors (GFFs) and internal properties of the proton. This work presents a complete analysis of the proton gluon GFFs connecting the gluon part of the energy-momentum tensor and the heavy quarkonium photoproduction. In particular, a global fitting of the $J/\psi$ differential and total cross section experimental data is used to determine the gluon GFFs as functions of the squared momentum transfer $t$. Combined with the quark contributions to the $D$-term form factor extracted from the deeply virtual Compton scattering experiment, the total $D$-term is obtained to investigate their applications in describing the proton mechanical properties. These studies provide a unique perspective on investigating the proton gluon GFFs and important information for enhancing QCD constraints on the gluon GFFs., Comment: 8 pages, 4 figures

In this work, the cross sections of $\phi$ photoproduction are systematically investigated with the two gluon exchange model and the pomeron model. The results obtained show that the theoretical values of the two models agree well with the experimental data. Since the mass radius and mechanical properties of the proton are encoded in the scalar gravitational form factor of the momentum energy tensor, based on the differential cross sections of $\phi$ photoproduction at near-threshold predicted by the two gluon exchange model, the average mass radius of the proton is derived as $\sqrt{\left\langle r^{2}\right\rangle_\mathrm{m} }=0.78 \pm 0.06$ fm. As a comparison, we directly extract the proton mass radius from the experimental data of $\phi$ photoproduction to obtain an average value of $0.80\pm0.05$ fm, which is very close to the result given by the two gluon exchange model. Taking a similar approach, we extracted the average value of $m_{D}$ to obtain the distribution of the pressure and shear force contributed within the proton, and compared the results with other groups. The results of this paper may provide necessary theoretical information for the subsequent in-depth study of the internal structure and properties of proton., Comment: 11 pages, 13 figures

As it involves the lightest physical states excited from the vacuum by the vector quark current, near-threshold $\rho^0$ photoproduction is considered a possible way to research the proton radius and the absolute value of the scattering lengths of the $\rho^0$--proton interaction. In this work, under the assumption of a scalar form factor of dipole form, the value of the proton mass radius is calculated as $0.85\pm 0.06 \text{ fm }$ by fitting the differential cross section of the $\gamma p \rightarrow \rho^0 p$ reaction at near-threshold energy. For light vector meson photoproduction, because the exchange of a scalar quark--antiquark pair is not suppressed and should dominate the scalar gluon exchange, the radius we extract from $\rho^0$ photoproduction is likely to represent the quark radius of the proton. This fact may explain why the value obtained in this work is very near the proton charge radius. Moreover, the absolute value of the $\rho^0$--proton scattering length $|\alpha_{\rho^0 p}|= 0.31 \pm 0.06 \text{ fm}$ is obtained for the first time within the vector meson dominance model. This result disobeys the rule that the absolute value of the vector meson and proton scattering length $|\alpha_{V p}|$ increases with the meson's mass, which can be attributed to treating the $\rho^0$ meson as a point in the analysis. These results provide useful theoretical information for an in-depth understanding of proton structure and the proton--vector meson interaction., Comment: 6pages, 6 figures. To be published in Science China Physics, Mechanics & Astronomy

By the reaction of kaon interacting with a proton, we investigate the production of the newly observed $\eta _{1}(1855)$ predicted in the picture of the $K\bar{K}_1(1400)$ molecular state and hybrid state. The total and differential cross sections of the concrete $K^{-}p\to\eta _{1}(1855)\Lambda$ reaction are calculated. Taking the partial decay width of the $\eta _{1}$ to $K\bar{K}^{\ast }$ as 0.9 MeV and 98.1 MeV, the minimum cross section of the $\eta _{1}(1855)$ production via the $K^{-}p$ reaction can reach up 0.59 $nb$ and 63.8 $nb$ at the center of mass energies $W\simeq 3.5$ GeV, respectively. The differential cross sections for the $\eta _{1}(1855)$ production at the different center of mass energies are also available. Furthermore, we present the Dalitz processes of $2\rightarrow 3$ and $2\rightarrow 4$, and initially discuss the feasibility of finding out the $\eta _{1}(1855)$ in experiments like J-PARC.

Under the framework of Vector Meson Dominance model, the value of scattering length can be expressed as a function of the ratio between total cross section $\sigma (W)$ and $R (W)$, where $R(W)$ is the ratio between final momentum $|{\bf p}_3 |$ and initial momentum $|{\bf p}_1|$ and positively correlated with the center-of-mass energy. Based on the theoretical study of charmoniums photoproduction within two gluon exchange model and effective pomeron model, we research the scattering lengths of vector mesons and proton interaction in this work. Results show that the scattering length $\left|\alpha_{J/\psi p}\right|$ obtained from the two models are close and basically in agreement with the theoretical prediction of Strakovsky and co-workers. Additionally, we first calculate the scattering length of $\psi(2S) $-proton interaction in two gluon exchange model and effective pomeron model as $ 1.31\pm 0.92$ am (1 am = $10^{-3}$ fm) and $ 3.24 \pm 0.63$ am, respectively. This is a little bit different from the two models and requires precise measurements from subsequent experiments. In short, our results will provide a theoretical reference for future studies on characterizing the vector meson-proton scattering length., Comment: 7 pages, 7 figures

In this work, the cross-section of the reaction $\gamma p \rightarrow V(J/\psi,\psi(2S)) p$ from the production threshold to medium energy is studied and systematically analyzed within two gluon exchange model. The obtained numerical results are in agreement with experimental data and other theoretical predictions. Under the assumption of the scalar form factor of dipole form, the value of proton mass radius is calculated as $0.55\pm 0.09$ fm and $ 0.77\pm 0.12$ fm from the fit to the predicted $J/\psi $ and $\psi(2S)$ differential cross-section, respectively. Finally the average value of proton mass radius is estimated to be $\sqrt{\left}=0.67\pm 0.11$ fm. Moreover, one find that extracting mass radius from the near-threshold differential cross-section of heavy quarkoniums is always affected by large $|t|_{min}$. These obtained results may provide important theoretical reference for understanding of nucleon structure and future relevant experiments., Comment: 7pages, 10figures

Plasmonics is a rapid growing field, which has enabled both fundamental science and inventions of various quantum optoelectronic devices. An accurate and efficient method to calculate the optical response of metallic structures with feature size in the nanoscale plays an important role. Quantum hydrodynamic theory (QHT) provides an efficient description of the free-electron gas, where quantum effects of nonlocality and spill-out are taken into account. In this work, we introduce a general QHT that includes diffusion to account for the broadening, which is a key problem in practical applications of surface plasmon. We will introduce a density-dependent diffusion coefficient to give very accurate linewidth. It is a self-consistent method, in which both the ground and excited states are solved by using the same energy functional, with the kinetic energy described by the Thomas-Fermi and von Weizs\"{a}cker (vW) formalisms. In addition, our QHT method is stable by introduction of an electron density-dependent damping rate. For sodium nanosphere of various sizes, the plasmon energy and broadening by our QHT method are in excellent agreement with those by density functional theory and Kreibig formula. By applying our QHT method to sodium jellium nanorods, we clearly show that our method enables a parameter-free simulation, i.e. without resorting to any empirical parameter, such as size-dependent damping rate and diffusing coefficient. It is found that there exists a perfect linear relation between the resonance wavelength and aspect radio. The width decreases with increasing aspect ratio and height. The calculations show that our QHT method provides an explicit and unified way to account for size-dependent frequency shifts and broadening of arbitrarily shaped geometries. It is reliable and robust with great predicability, and hence provides a general and efficient platform to study plasmonics.

Exclusive production of charmonium-like XYZ states in hadron-hadron ultraperipheral collisions(UPCs) and electron-proton scattering is studied employing effective Lagrangian method. Total cross sections and rapidity distributions of charmonium-like XYZ states are obtained in hadron-hadron UPCs and electron-proton scattering process. These predictions can be applied to estimate the observed event number of exclusive charmonium-like XYZ states in hadron-hadron UPCs and electron-proton scattering. The results indicate that it is significant to search $X(3872)$ and $Z^+_c(3900)$ in pA UPCs and Electron-Ion Collider in China will be an advantage platform to observe XYZ states in the future.

The photoproduction of bottomonium-like states $Z_{b}(10610)$ and $Z_{b}(10650)$ via $\gamma p$ scattering is studied within an effectiv Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of $Z_{b}$ states via $t$-channel with $\pi$ 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. The experimental measurements and studies on the photoproduction of $Z_{b}$ states near energy region around $W\simeq 22$ GeV is suggested. Moreover, with the help of eSTARlight and STARlight programs, one obtains the cross-sections and event numbers of $Z_{b}(10610)$ production in electron-ion collision (EIC) and Ultraperipheral collisions (UPCs). The results show that a considerable number of events from $Z_{b}(10610)$ can be produced on the relevant experiments of EICs and UPCs. Also, one calculates the rates and kinematic distributions for $\gamma p\rightarrow Z_{b}n$ in $ep$ and $pA$ collisions via EICs and UPCs, and the relevant results will provide an important reference for the RHIC, LHC, EIC-US, LHeC, and FCC experiments to search for the bottomonium-like $Z_{b}$ states., Comment: 9 pages, 5 figures

The near-threshold photoproduction of $J/\psi$ is regarded as one golden process to unveil the nucleon mass structure, pentaquark state involving the charm quarks, and the poorly constrained gluon distribution of the nucleon at large $x$ ($>0.1$). In this paper, we present an analysis of the current experimental data under a two-gluon exchange model, which shows a good consistency. Using a parameterized function form with three free parameters, we have determined the nucleonic gluon distribution at the $J/\psi$ mass scale. Moreover, we predict the differential cross section of the electroproduction of $J/\psi$ as a function of the invariant mass of the final hadrons $W$, at EicC, as a practical application of the model and the obtained gluon distribution. According to our estimation, thousands of $J/\psi$ events can be detected per year on EicC near the threshold. Therefore, the relevant experimental measurements are suggested to be carried out on EicC., Comment: 6 pages, 7 figures

Ultraperipheral collisions (UPCs) of protons and nuclei are important for the study of the photoproduction of vector mesons and exotic states. The photoproduction of vector mesons in the pentaquark resonance channel in $p\mbox{-}Au$ UPCs at the Relative Heavy Ion Collider (RHIC) and $p$-$Pb$ UPCs at the Large Hadron Collider (LHC) is investigated by employing STARlight package. The cross sections of vector mesons via pentaquark state resonances channel are obtained using effective Lagrangian method. The pseudo-rapidity and rapidity distributions of $J/\psi $ and $\Upsilon(1S) $ are given for $p\mbox{-}Au$ UPCs at the RHIC and $p$-$Pb$ at the LHC. It is found that the RHIC is a better platform for discovering the pentaquark states than the LHC. Moreover, $P_{b}(11080)$ is easier to identify than $P_c(4312)$ because the background of $\Upsilon (1S)$ is weaker than $J/\psi$ in the $t$-channel at the RHIC., Comment: 9 pages, 5 figures

Inspired by the observation of the fully-charm tetraquark $X(6900)$ state at LHCb, the production of $X(6900)$ in $\bar{p}p\rightarrow J/\psi J/\psi $ reaction is studied within an effective Lagrangian approach and Breit-Wigner formula. The numerical results show that the cross section of $X(6900)$ at the c.m. energy of 6.9 GeV is much larger than that from the background contribution. Moreover, we estimate dozens of signal events can be detected by D0 experiment, which indicates that searching for the $X(6900)$ via antiproton-proton scattering may be a very important and promising way. Therefore, related experiments are suggested to be carried out., Comment: 4 pages, 2 figures

In this paper we discuss epicycloid approximation of the trajectories of charged particles in axisymmetric magnetic fields. Epicycloid trajectories are natural in the Guiding Center approximation and we study in detail the errors arising in this approach. We also discuss how using exact results for particle motion in the equatorial plane of a magnetic dipole the accuracy of this approximation can be significantly extended. We also show that the epicycloids approximate the trajectory of a charged particle more accurately than the position of the particle along the trajectory., Comment: 8 pages, 10 figures

The production of hidden-bottom pentaquark $P_{b}$ states via $\gamma p$ and $\pi ^{-}p$ scatterings is studied within an effective Lagrangian approach and the vector-meson-dominance mechnism. For the $P_{b}$ production in the process $\gamma p\rightarrow \Upsilon p$, the dipole Pomeron model is employed to calculate the background contribution, and the experimental data can be well described. For the process $\pi ^{-}p\rightarrow \Upsilon n$, the Reggeized $t$-channel with $\pi $ exchange is considered as the main background for the $P_{b}$ production. Near the threshold, two-peak structure from the states $P_{b (11080)$ and $P_{b}(11125)$ can be observed if energy bin width is chosen as 0.01 GeV, and the same result is obtained in the $\pi ^{-}p$ scattering. Moreover, by taking the branching ratio of Br$[{P_{b}\rightarrow \pi N}]\simeq 0.05\%$, the numerical result shows that the average value of cross section from the $P_{b}(11080)$ state produced in the $\gamma p$ or $\pi ^{-}p$ scattering reaches at least 0.1 nb with a bin of 0.1 GeV. Even if we reduce the branching ratio of the $P_{b}$ state into $\pi N$ channel by one order, the theoretical average of the cross section from $P_{b}(11080)$ production in $\pi ^{-}p$ scattering can reach the order of 0.01 nb with a bin of 0.1 GeV, which means that the signal can still be clearly distinguished from the background. The experimental measurements and studies on the hidden-bottom pentaquark $P_{b}$ state production in the $\gamma p $ or $\pi ^{-}p$ scattering near-threshold energy region around $W\simeq 11$ GeV are strongly suggested, which are accessible at COMPASS and JPARC. Particularly, the result of the photoproduction suggests that it is very promising to observe the hidden-bottom pentaquark at proposed EicC facility in China., Comment: 7 pages, 7 figures

In this work, we study the production of strange quarkoniums, the $\phi(2170)$, also named $Y(2175)$, and the $\eta(2225)$, via a kaon induced reaction on a proton target in an effective Lagrangian approach. The total and differential cross sections of the reactions $K^{-}p\rightarrow \phi (2170)\Lambda $ and $K^{-}p\rightarrow \eta (2225)\Lambda $ are calculated by the Reggeized $t $-channel Born term under an assumption that the $\phi(2170)$ and $\eta(2225)$ are $\Lambda\bar{\Lambda}$ molecular states. At the center of mass energies of about 4.2 GeV, the total cross section for the $\phi(2170)$ production is predicted to be about 1 $\mu $b. The numerical results indicate that it is feasible to produce the $\phi (2170)$ via kaon beam scattering at the best energy window near 4.2 GeV. The total cross section for the $\eta(2225)$ production is smaller than that for the $\phi(2170)$ production and it may reach an order of the magnitude of 0.1 $\mu$b. The differential cross sections for both reactions at different center of mass energies are also presented. It is found that the Reggeized $t$ channel gives a considerable contribution at forward angles. As the energy increases, the contribution from the $t$-channel almost concentrates at extreme forward angles. From these theoretical predictions, the relevant experimental research is suggested, which could provide important information to clarify the internal structure and production mechanism of these two strange quarkoniums., Comment: 5 pages, 3 figures

A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the QE is partially stabilized in its excited state. We put forward a general approach for calculating the energy level shift at a negative frequency $\omega$, which is just the negative of the nonresonant part for the energy level shift at positive frequency $-\omega$. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics in the presence of a bound state can be obtained by the method based on the Green's function expression for the evolution operator. A general criterion for identifying the existence of a bound state is presented. These are numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. These findings are instructive in the fields of coherent light-matter interactions.

The production of the hidden-charm pentaquarks $P_{c}$ via pion-induced reaction on a proton target is investigated within an effective Lagrangian approach. Three experimentally observed states, $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$, are considered in the calculation, and the Reggeized $t$-channel meson exchange is considered as main background for the reaction $\pi ^{-}p\rightarrow J/\psi n$. The numerical results show that the experimental data of the total cross section of the reaction $\pi^{-}p\rightarrow J/\psi n$ at $W\simeq 5$ GeV can be well explained by contribution of the Reggeized $t$ channel with reasonable cutoff. If the branching ratios $Br[P_{c}\rightarrow J/\psi N]\simeq 3\%$ and $Br[P_{c}\rightarrow \pi N]\simeq 0.05\%$ are taken, the average value of the cross section from the $P_{c}(4312)$ contribution is about 1.2 nb/100 MeV, which is consistent with existing rude data at near-threshold energies. The results indicate that the branching ratios of the $P_{c}$ states to the $J/\psi N$ and $\pi N$ should be small. The shape of differential cross sections shows that the Reggeized $t$-channel provides a sharp increase at extreme forward angles, while the differential cross sections from the $P_{c}$ states contributions are relatively flat. High-precision experimental measurements on the reaction $\pi ^{-}p\rightarrow J/\psi n$ at near-threshold energies are suggested to confirm the LHCb hidden-charm pentaquarks as genuine states, and such experiments are also helpful to understand the origin of these resonance structures., Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1904.11706

Inspired by the observation of the pentaquark states $P_{c}(4312),P_{c}(4440)$ and $P_{c}(4457)$ at LHCb, photoproduction of these three $P_{c}$ states via the interaction $\gamma p\rightarrow J/\psi p$ is investigated in an effective Lagrangian approach. The $t$-channel Pomeron exchange diffractive process is considered as the main background for the $J/\psi $ photoproduction. The numerical results show that the theoretical cross section, which is calculated by assuming a branching ratio $Br[P_{c}\rightarrow J/\psi p]\simeq 3\%$, is consistent with the existing experimental data of the $ \gamma p\rightarrow J/\psi p$ process. With such a branching ratio, if experimental precision reaches 0.1 nb within a bin of 100 MeV for photon energy, two peaks are expected to be obviously observed in the $J/\psi $ photoproduction. To observe the two-peak structure from $P_{c}(4440)$ and $ P_{c}(4457)$, higher precision, about 0.1nb/10 MeV, is required to distinguish two close pentaquarks. If the physical branching ratio is larger, the requirement of experimental precision will be reduced. The differential cross sections for reaction $\gamma p\rightarrow J/\psi p$ are also present. It is found that the $t$-channel Pomeron exchange provides a sharp increase at extreme forward angles and gives a sizable contribution at most energy points, while the contributions from the $s$-channel $P_{c}$ exchanges play important roles at threshold energies. The experimental measurement of the $\gamma p\rightarrow J/\psi p$ process in the near-threshold energy region around $E_{\gamma }\simeq 9.4-10.5$ GeV is suggested, and is accessible at CEBAF@JLab and COMPASS., Comment: 7 pages, 7 figures, version to be published in PRD

We put forward a general approach for calculating the quantum energy level shift for emitter in arbitrary nanostructures, in which the energy level shift is expressed by the sum of the real part of the scattering photon Green function (GF) and a simple integral about the imaginary part of the photon GF in the real frequency range without principle value. Compared with the method of direct principal value integral over the positive frequency axis and the method by transferring into the imaginary axis, this method avoids the principle value integral and the calculation of the scattering GF with imaginary frequency. In addition, a much narrower frequency range about the scattering photon GF in enough to get a convergent result. It is numerically demonstrated in the case for a quantum emitter (QE) located around a nanosphere and in a gap plasmonic nanocavity. Quantum dynamics of the emitter is calculated by the time domain method through solving Schr\"{o}dinger equation in the form of Volterra integral of the second kind and by the frequency domain method based on the Green's function expression for the evolution operator. It is found that the frequency domain method needs information of the scattering GF over a much narrower frequency range. In addition, reversible dynamics is observed. These findings are instructive in the fields of coherent light-matter interactions.

Photon Green function (GF) is the vital and most decisive factor in the field of quantum light-matter interaction. It is divergent with two equal space arguments in arbitrary-shaped lossy structure and should be regularized. We introduce a finite element method for calculating the regularized GF. It is expressed by the averaged radiation electric field over the finite-size of the photon emitter. For emitter located in homogeneous lossy material, excellent agreement with the analytical results is found for both real cavity model and virtual cavity model. For emitter located in a metal nano-sphere, the regularized scattered GF, which is the difference between the regularized GF and the analytical regularized one in homogeneous space, agrees well with the analytical scattered GF.