Regge Model Research Articles

Analysis of data for γp → f 1(1285)p photoproduction* *Partially supported by the National Natural Science Foundation of China (12175240, 12147153, 11635009, 12305097, 12305137), the Fundamental Research Funds for the Central Universities, and the China Postdoctoral Science Foundation (2021M693141, 2021M693142)

The photoproduction of the meson off the proton target is investigated within an effective Lagrangian approach. The t-channel ρ- and ω-exchange diagrams, u-channel nucleon-exchange diagram, generalized contact term, and s-channel pole diagrams of the nucleon and a minimal number of nucleon resonances are taken into account in constructing the reaction amplitudes to describe the experimental data. Three different models, that is, the Feynman, Regge, and interpolated Regge models, are employed, where the t-channel reaction amplitudes are constructed in Feynman, Regge, and interpolated Regge types, respectively. The results show that neither the Feynman model with two nucleon resonances nor the interpolated Regge model with one nucleon resonance can satisfactorily reproduce the available data for . Nevertheless, in the Regge model, when any one of the , , , , , , , , and resonances is considered, the data can be well described. The resulting resonance parameters are consistent with those advocated in the Particle Data Group (PDG) review. Further analysis shows that, in the high-energy region, the peaks of differential cross sections at forward angles are dominated by the contributions from t-channel ρ- and ω-exchange diagrams, while in low-energy region, the s-channel pole diagrams of resonances also provide significant contributions to the cross sections.

A multidimensional study of the structure function ratio [formula omitted] from hard exclusive π+ electro-production off protons in the GPD regime

A multidimensional extraction of the structure function ratio σLT′/σ0 from the hard exclusive e→p→e′nπ+ reaction above the resonance region has been performed. The study was done based on beam-spin asymmetry measurements using a 10.6 GeV incident electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at Jefferson Lab. The measurements focus on the very forward regime (t/Q2 ≪ 1) with a wide kinematic range of xB in the valence regime (0.17 <xB < 0.55), and virtualities Q2 ranging from 1.5 GeV2 up to 6 GeV2. The results and their comparison to theoretical models based on Generalized Parton Distributions demonstrate the sensitivity to chiral-odd GPDs and the directly related tensor charge of the nucleon. In addition, the data is compared to an extension of a Regge formalism at high photon virtualities. It was found that the Regge model provides a better description at low Q2, while the GPD model is more appropriate at high Q2.

Pseudoscalar and scalar meson photoproduction interpreted by Regge phenomenology

We have evaluated pseudoscalar and scalar neutral pion photoproduction in $\stackrel{P\vec}{\ensuremath{\gamma}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$ and ${a}_{0}^{0}p$ above the resonance region and within Regge phenomenology. Our fit, including GlueX $\mathrm{\ensuremath{\Sigma}}$ pseudoscalar photoproduction data, shows that previous Stanford Linear Accelerator Center (SLAC) $\mathrm{\ensuremath{\Sigma}}$ measurements for $\stackrel{P\vec}{\ensuremath{\gamma}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$ above ${E}_{\ensuremath{\gamma}}=4\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$ vary substantially from SLAC data with more recent measurements made by GlueX in the vicinity of ${E}_{\ensuremath{\gamma}}=9\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$. The Regge model predicts that the beam polarization asymmetry $\mathrm{\ensuremath{\Sigma}}$ of the scalar meson is opposite to that of pseudoscalar meson photoproduction; however, the cross sections are similar. While the natural parity vector meson exchange is dominant in both cases, the contribution of the unnatural parity pseudovector meson exchange is very small. Using Regge phenomenology, we predicted high-energy behavior for double polarized observables $\mathbb{E}$, $\mathbb{F}$, $\mathbb{G}$, and $\mathbb{H}$ for the reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$ and ${a}_{0}^{0}p$.

The two-component complex coupled integrable dispersionless equations: Darboux transformation and soliton solutions

The complex coupled integrable dispersionless (CID)system is an important system. It has been shown that complex CID equation is gauge equivalent to the Pohlmeyer–Lund–Regge model (a complex sine-Gordon equation) and can also be transformed to the complex short pulse equation. CID system can describe a current-fed string interacting with an external magnetic field. In this paper, we investigate the two-component complex coupled integrable dispersionless system. By using the Darboux transformation, we obtain a new type of solution (the breather-like soliton solution) with zero boundary condition and a large number of solutions (the breather-II type solution, bright–dark soliton solution, the resonance solutions and the semi-rational solutions) with non-zero boundary condition. In particular, these solutions are not available for the scalar complex integrable dispersionless system.

Rational Form of Amplitude and Its Asymptotic Factorization

We provide arguments for the use of the rational form of unitarization, its relation with the diffraction peak shrinkage and asymptotics of the inelastic cross-section. The particular problems of the Regge model and the exponential form of unitarization with a factorized eikonal are discussed as well. A central role belongs to the asymptotic amplitude factorization resulting from Mandelstam analyticity and its symmetry over the scattering variables.

Photo- and hadron-production of mesons

We discuss the πη(‘) production in the double Regge model. We also identify the dominant exchanges necessary to describe the πη(‘) system for energies above the resonance region. The model explains the forward-backward asymmetry observed in this reaction by associating it with the exotic P−wave, which in turn is related to the production of the putative π1 hybrid meson. We also discuss the π +π − production through two complementary mechanisms - direct resonance production (with subsequent π +π − decay) and the Deck mechanism. The interference of the Deck and direct production explains the di-pion mass distribution for invariant masses below 2 GeV. Model predictions are compatible with the qq¯ nature of the lightest P− and D−wave resonances, whereas they hint towards substantial molecular or tetraquark component of the f0(980).

Direct-Channel Option of the Forward Slope Increase

The LHC data on the elastic scattering indicate that the forward slope increase is not consistent with the contributions of the simple Regge poles only with the linear Regge trajectories. The dynamics might be associated with unitarization in the direct channel of reaction. We discuss the problems of the Regge model and provide a respective illustration of the direct-channel option.

Photoproduction of Λ* and Σ* resonances with JP=1/2− off the proton

We study the photoproduction of the $\Lambda(1405)$ and $\Sigma(1400)$ hyperon resonances, the latter of which is not a well established state. We evaluate the $s$-, $t$- and $u$-channel diagrams in the Born approximation by employing the effective Lagrangians. A new ingredient is the inclusion of a nucleon resonance $N^*(1895)$ that is dynamically generated with predictions for its coupling to the $K\Lambda(1405)$ and $K\Sigma(1400)$ channels. To extend the applicability of the model to energies beyond the threshold region, we consider a Regge model for the $t$-channel $K$- and $K^*$-exchanges. Our results are in good agreement with the CLAS data available on $\Lambda(1405)$, while for $\Sigma(1400)$ we predict observables for its production. We also provide polarization observables for both hyperon productions, which can be useful in future experimental investigations. The present study provides new information on the nucleon resonance $N^*(1895)$ which can be an alternative source for generating the hyperon resonances $\Lambda(1405)$ and $\Sigma(1400)$.

Production of bottomonium-like Zb states in e-h and ultraperipheral h-h collisions * *This project is supported by the National Natural Science Foundation of China (12065014, 11705076, 11747160), and by the Strategic Priority Research Program of Chinese Academy of Sciences, (XDB34030301). This work is partly Supported by HongLiu Support Funds for Excellent Youth Talents of Lanzhou University of Technology. We also

The photoproduction of the bottomonium-like states and via scattering is studied within an effective Lagrangian approach and the vector-meson-dominance model. The Regge model is employed to calculate the photoproduction of states via the t-channel with exchange. The numerical results show that the values of the total cross-sections of and 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 states near the energy region around GeV are suggested. Moreover, with the help of eSTARlight and STARlight programs, we have obtained the cross-sections and numbers of events for production in electron-ion collisions (EIC) and ultraperipheral collisions (UPCs). The results show that a considerable number of events can be produced in the relevant experiments on EICs and UPCs. We have also calculated the rates and kinematic distributions for in and 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 states.

Elastic pp scattering in the Regge model

Elastic pp scattering in the Regge model

Photoproduction of η mesons off the proton for 1.2&lt;Eγ&lt;4.7GeV using CLAS at Jefferson Laboratory

Photoproduction cross sections are reported for the reaction $\gamma p\to p\eta$ using energy-tagged photons and the CLAS spectrometer at Jefferson Laboratory. The $\eta$ mesons are detected in their dominant charged decay mode, $\eta\to \pi^+\pi^-\pi^0$, and results on differential cross sections are presented for incident photon energies between 1.2 and 4.7 GeV. These new $\eta$ photoproduction data are consistent with earlier CLAS results but extend the energy range beyond the nucleon resonance region into the Regge regime. The normalized angular distributions are also compared with the experimental results from several other experiments, and with predictions of $\eta$ MAID\,2018 and the latest solution of the Bonn-Gatchina coupled-channel analysis. Differential cross sections $d\sigma/dt$ are presented for incident photon energies $E_\gamma > 2.9$ GeV ($W > 2.5$ GeV), and compared with predictions which are based on Regge trajectories exchange in the $t$-channel (Regge models). The data confirm the expected dominance of $\rho$, $\omega$ vector-meson exchange in an analysis by the Joint Physics Analysis Center.

Pion-induced production with baryon off proton target

In this work, the reaction is investigated with an effective Lagrangian approach. The contributions from the Born terms, including the s, t, and u channel, are considered, and the Regge model and the Feynman model are applied to treat the t-channel contribution. The existing experimental data can be reproduced with the best-fitted χ 2 being 2.38 and 1.54 for the Feynman and Regge models, respectively. Moreover, it is found that the contribution from the t channel is dominant in the cross-section. The contribution of the u channel is mainly distributed at backward angles, and the contribution from the s channel is small and negligible. In the Feynman model, the contribution of the t-channel K exchange is much larger than the contribution of the exchange, while in the Regge model the contribution of the t-channel K exchange is comparable to that of the exchange. Prediction about the differential cross-section of the reaction is also presented, which is helpful for clarifying the role of the Regge treatment. The current results suggest high-precision experimental measurements which can be performed at J-PARC and COMPASS.

Photoproduction of D¯0Λc+ within the Regge-plus-resonance model

${\overline{D}}^{0}$-meson photoproduction off the proton is studied at energies from the process threshold up to 20 GeV. The background part of the process is modeled within the Regge model with the help of ${\overline{D}}^{0}$-meson trajectories that are being exchanged in the $t$ channel or ${\mathrm{\ensuremath{\Lambda}}}_{c}^{+}$-baryon trajectories exchanged in the $u$ channel. These contributions create cross sections which are smooth functions of energy. The introduction of exchanges of three hidden-charm pentaquarks with spin $1/2$ and $3/2$ in the $s$ channel then creates sharp peaks in the cross section predictions. In order to account for the finite size of the particles involved, we introduce hadron form factors. In analysis of model predictions with pseudoscalar and pseudovector couplings in the strong vertex, the contact term was shown to play a non-negligible role. A great merit of the proposed approach is its limited number of parameters that need to be adjusted as there are to this date no data available for this process. Being limited by the broken SU(4) symmetry and guided by other works that show their predictions of this process, we could adjust the parameters manually in order to provide at least qualitative results.

Photoproductions of f1(1285) and η′(958) from the analysis of CLAS data with the Primakoff effect at high energies

We investigate photoproduction of axial vector meson $f_1(1285)$ based on the CLAS experiment $\gamma p\to pf_1(1285)\to p\eta\pi^+\pi^-$ using the Regge model for $\rho^0+\omega$ exchanges. The combined analysis of $\gamma p\to p\eta'\to p\eta\pi^+\pi^-$ reaction including $\eta(1295)$ is accompanied to evaluate the decay mode $\eta(1295)\to \eta\pi^+\pi^-$ from the potential overlap with the $f_1$ reaction. The predominance of $\rho^0(770)$ exchange over the $\omega(782)$ with the coupling constant $\gamma\rho^0f_1$ extracted from the CLAS experiment leads to a good description of the measured cross sections for $f_1$, while the scale of the cross section is corrected by the branching fraction $\eta'\to\eta\pi^+\pi^-$, and $f_1\to\eta\pi^+\pi^-$, respectively. As an extension to study the nonmesonic production mechanism, the Primakoff effect by the virtual photon exchange is investigated in the exclusive reaction $\gamma p\to pf_1$ up to $\sqrt{s}\approx50$ GeV, finding that it plays a similar role to the Pomeron in the vector meson photoproduction at high energies. Such an unique role of the virtual photon exchange similar to the $f_1$ case is identified up to $\sqrt{s}\approx250$ GeV in the $\gamma p\to p\pi^0$ and $\gamma p\to p\eta$ as well as $\gamma p\to p\eta'$ reaction.

An improved hadronic model for pion electroproduction

Current measurements of the high energy behavior of the pion form factor are obtained from pion electroproduction data. These values are model dependent, utilizing the Vanderhaeghen, Guidal and Laget Regge (VGL) Model for their extraction. Recent work which examined the implementation of gauge invariance in that model suggested that it might lead to extracted pion form factors larger than the true values. Here we introduce a new model which preserves the successes of the VGL Model but implements gauge invariance in a new way. To demonstrate the validity of this new approach, we first use it to extract the pion form factor in a simple toy model. When compared with the previous extraction method, the improved model leads to a more reliable extraction. The success in this simple model leads us to reanalyze the electroproduction cross section data, where we obtain comparable values for the pion form factor to those obtained using the VGL procedure.

Searching for classical geometries in spin foam amplitudes: a numerical method

We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano–Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude with three vertices. We study the summation over bulk spins, and we identify the stationary phase points that dominate it and that correspond to classical geometries. We complement with the numerical analysis of a four vertex transition amplitude and with a modification of the model that includes local curvature. We discuss the generalization of our results to the four-dimensional EPRL spin foam model, and we provide suggestions for new computations.

Longitudinal short-distance constraints for the hadronic light-by-light contribution to (g \u2212 2)\u03bc with large-Nc Regge models

While the low-energy part of the hadronic light-by-light (HLbL) tensor can be constrained from data using dispersion relations, for a full evaluation of its contribution to the anomalous magnetic moment of the muon (g − 2)μ also mixed- and high-energy regions need to be estimated. Both can be addressed within the operator product expansion (OPE), either for configurations where all photon virtualities become large or one of them remains finite. Imposing such short-distance constraints (SDCs) on the HLbL tensor is thus a major aspect of a model-independent approach towards HLbL scattering. Here, we focus on longitudinal SDCs, which concern the amplitudes containing the pseudoscalar-pole contributions from π0, η, η′. Since these conditions cannot be fulfilled by a finite number of pseudoscalar poles, we consider a tower of excited pseudoscalars, constraining their masses and transition form factors from Regge theory, the OPE, and phenomenology. Implementing a matching of the resulting expressions for the HLbL tensor onto the perturbative QCD quark loop, we are able to further constrain our calculation and significantly reduce its model dependence. We find that especially for the π0 the corresponding increase of the HLbL contribution is much smaller than previous prescriptions in the literature would imply. Overall, we estimate that longitudinal SDCs increase the HLbL contribution by varDelta {a}_{mu}^{mathrm{LSDC}}=13(6) × 10-11. This number does not include the contribution from the charm quark, for which we find {a}_{mu}^{c- quark} = 3(1) × 10−11.

Studying X(2100) hadronic decays and predicting its pion and kaon induced productions

The newly observed $X(2100)$ by the BESIII Collaboration inspires our interest in studying the light meson system, especially axial-vector mesons. Since the $X(2100)$ has $J^P=1^+$ possibilities but cannot be distinguished only by mass, we make use of flux-tube model to study the strong decay behavior of $X(2100)$ under this assignment. The experimental width of the newly reported $X(2100)$ can be reproduced in our calculation, which favors an assignment of $X(2100)$ as the second radial excitation of $h_1(1380)$ with $I(J^P)=0(1^+)$. And the $\mathcal{B}(X(2100)\to \phi \eta^\prime)$ has a sizable contribution to the total width. Furthermore, we focus on the production of $X(2100)$ and its flavour partner $h_1(1965)$ induced by pion and kaon on a proton target with the Feynman model and the Regge model, which is an available platform to further identify their nature. The numerical results indicate that the total cross section are similar in the two models. When the range of momentum ${\mathrm{p_{Lab}}}$ is 10 to 30 GeV/$c$, the total cross sections for $\pi^-p\to X(2100)n$ and $K^-p\to X(2100)\Lambda$ are predicted to be at an order of magnitude of 0.1 $\mu$b. Whereas, the total cross section for $\pi^-p\to h_1(1965)n$ is near an order of magnitude of 10 $\mu$b when $p_{\mathrm{Lab}}$ is from 10 to 30 GeV/$c$, and much larger than that of reaction $K^-p\to h_1(1965)\Lambda$. These predictions can provide some valuable information to search for $X(2100)$ and $h_1(1965)$ in experiments at J-PARC, COMPASS, OKA@U-70 and SPS@CERN.

Model dependence of the pion form factor extracted from pion electroproduction

In 2008 the Jefferson Laboratory $F_\pi$ Collaboration released results for the pion electromagnetic form factor, which they extracted from pion electro-production data. The measured values for the pion form factor are model dependent, and require the use of the Vanderhaeghen, Guidal and Laget Regge Model for their extraction. While agreement between this model and data is impressive, the theoretical implementation of gauge invariance is less satisfying. We would like to establish how well the extracted form factor corresponds to the true form factor. To do this, we use a simple toy model, which imposes gauge invariance in a more theoretically satisfying way. The model form factor is extracted from our model cross section using the method employed by the $F_\pi$ Collaboration to extract the experimental pion form factor. We conclude that the reconstructed model form factor is a reasonable representation of the true model form factor for the kinematics chosen, although we note that the extracted form factor is smaller than the true form factor. This suggests that current extracted values of pion form factor may be overestimated.

Productions of f1(1420) in pion and kaon induced reactions

The $f_{1}(1420)$ productions via pion and kaon induced reactions on a proton target are investigated in an effective Lagrangian approach. Two treatments of the $t$-channel Born term, the Feynman model and the Regge model, are introduced to calculate the total and differential cross sections of the $\pi^{-}p\rightarrow f_{1}(1420)n$ and $K^{-}p\rightarrow f_{1}(1420)\Lambda $ reactions. The numerical results indicate that the experimental data of the total cross section of the $\pi ^{-}p\rightarrow f_{1}(1420)n$ reaction can be reproduced in both the Feynman and the Regge models. Based on the parameters determined in the pion induced reaction, the cross sections of the $K^{-}p\rightarrow f_{1}(1420)\Lambda $ reaction, about which there is little data found in the literature, are predicted in the same beam momentum range. It is found that the line shapes of the total cross section obtained in a kaon induced reaction with two treatments are quite different. The cross sections for both reactions are at an order of magnitude of $\mu$b, or larger, at a beam momenta up to 10 GeV/c. The differential cross sections for both pion and kaon induced reactions are also present. It is found that in the Regge model, the $t$ channel provides a sharp increase at extreme forward angles. The results suggest that the experimental study of the $f_1(1420)$ in the kaon induced reaction on a proton target is as promising as in the pion induced reaction. Such an experimental measurement is also very helpful to clarify the production mechanism of the $f_1(1420)$.