2024 Vol. 48, No. 2

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2024-2 Contents
2024, 48(2): 1-2.
Abstract:
PARTICLES AND FIELDS
Performance and calibration of quark/gluon-jet taggers using 140 fb−1 of pp collisions at ${{\sqrt{\boldsymbol s}\bf = 13}}$ TeV with the ATLAS detector
G. Aad, B. Abbott, K. Abeling, N.J. Abicht, S.H. Abidi, A. Aboulhorma, H. Abramowicz, H. Abreu, Y. Abulaiti, B.S. Acharya, C. Adam Bourdarios, L. Adamczyk, S.V. Addepalli, M.J. Addison, J. Adelman, A. Adiguzel, T. Adye, A.A. Affolder, Y. Afik, M.N. Agaras, J. Agarwala, A. Aggarwal, C. Agheorghiesei, A. Ahmad, F. Ahmadov, W.S. Ahmed, S. Ahuja, X. Ai, G. Aielli, A. Aikot, M. Ait Tamlihat, B. Aitbenchikh, I. Aizenberg, M. Akbiyik, T.P.A. Åkesson, A.V. Akimov, D. Akiyama, N.N. Akolkar, K. Al Khoury, G.L. Alberghi, J. Albert, P. Albicocco, G.L. Albouy, S. Alderweireldt, M. Aleksa, I.N. Aleksandrov, C. Alexa, T. Alexopoulos, F. Alfonsi, M. Algren, M. Alhroob, B. Ali, H.M.J. Ali, S. Ali, S.W. Alibocus, M. Aliev, G. Alimonti, W. Alkakhi, C. Allaire, B.M.M. Allbrooke, J.F. Allen, C.A. Allendes Flores, P.P. Allport, A. Aloisio, F. Alonso, C. Alpigiani, M. Alvarez Estevez, A. Alvarez Fernandez, M. Alves Cardoso, M.G. Alviggi, M. Aly, Y. Amaral Coutinho, A. Ambler, C. Amelung, M. Amerl, C.G. Ames, D. Amidei, S.P. Amor D
2024, 48(2): 023001. doi: 10.1088/1674-1137/acf701
Abstract:
The identification of jets originating from quarks and gluons, often referred to as quark/gluon tagging, plays an important role in various analyses performed at the Large Hadron Collider, as Standard Model measurements and searches for new particles decaying to quarks often rely on suppressing a large gluon-induced background. This paper describes the measurement of the efficiencies of quark/gluon taggers developed within the ATLAS Collaboration, using \begin{document}$\sqrt{s} = 13$\end{document} TeV proton–proton collision data with an integrated luminosity of 140 fb\begin{document}$^{-1}$\end{document} collected by the ATLAS experiment. Two taggers with high performances in rejecting jets from gluon over jets from quarks are studied: one tagger is based on requirements on the number of inner-detector tracks associated with the jet, and the other combines several jet substructure observables using a boosted decision tree. A method is established to determine the quark/gluon fraction in data, by using quark/gluon-enriched subsamples defined by the jet pseudorapidity. Differences in tagging efficiency between data and simulation are provided for jets with transverse momentum between 500 GeV and 2 TeV and for multiple tagger working points.
U(1)Lμ-Lτ breaking phase transition, muon g–2, dark matter, collider, and gravitational wave
Jie Wang, Jinghong Ma, Jing Gao, Xiao-Fang Han, Lei Wang
2024, 48(2): 023101. doi: 10.1088/1674-1137/ad0f89
Abstract:
Combining the dark matter and muon \begin{document}$ g-2 $\end{document} anomaly, we study the \begin{document}$ U(1)_{L_\mu-L_\tau} $\end{document} breaking phase transition, gravitational wave spectra, and direct detection at the LHC in an extra \begin{document}$ U(1)_{L_\mu-L_\tau} $\end{document} gauge symmetry extension of the standard model. The new fields include vector-like leptons (\begin{document}$ E_1,\; E_2,\; N $\end{document}), the \begin{document}$ U(1)_{L_\mu-L_\tau} $\end{document}breaking scalar S, and the gauge boson \begin{document}$ Z' $\end{document}, as well as the dark matter candidate \begin{document}$ X_I $\end{document} and its heavy partner \begin{document}$ X_R $\end{document}. A joint explanation of the dark matter relic density and muon \begin{document}$ g-2 $\end{document} anomaly excludes the region where both \begin{document}$\min(m_{E_1},m_{E_2},m_N,m_{X_R})$\end{document} and \begin{document}$\min(m_{Z'},m_S)$\end{document} are much larger than \begin{document}$ m_{X_I} $\end{document}. In the parameter space accommodating the DM relic density and muon \begin{document}$ g-2 $\end{document} anomaly, the model can achieve a first-order \begin{document}$ U(1)_{L_\mu-L_\tau} $\end{document} breaking phase transition, whose strength is sensitive to the parameters of the Higgs potential. The corresponding gravitational wave spectra can reach the sensitivity of U-DECIGO. In addition, the direct searches at the LHC impose stringent bounds on the mass spectra of the vector-like leptons and dark matter.
Temperature and volume dependence of pion-pion scattering lengths
Qing-Wu Wang, Hua-Zhong Guo
2024, 48(2): 023102. doi: 10.1088/1674-1137/ad123f
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The s-wave pion-pion scattering lengths \begin{document}$ a_0 $\end{document} and \begin{document}$ a_2 $\end{document} are studied at finite temperature and in finite spatial volume under the framework of the Nambu–Jona-Lasinio model. The behavior beyond the pseudo transition temperature is investigated using proper time regularization. The scattering length \begin{document}$ a_0 $\end{document} exhibits singularity near the Mott temperature, and \begin{document}$ a_2 $\end{document} is a continuous but non-monotonic function of temperature. We present the effect of finite volume on the scattering length and find that \begin{document}$ a_0 $\end{document} can be negative and its singularity disappears at small volumes, which may hint at the existence of a chiral phase transition with decreasing volume.
Radiative decays ${{\boldsymbol{D^{*}}}_{\boldsymbol{(s)}} {{\bf\to}\boldsymbol{ D}_{\boldsymbol{(s)}}\boldsymbol\gamma}}$ in covariant confined quark model
C. T. Tran, M. A. Ivanov, P. Santorelli, Q. C. Vo
2024, 48(2): 023103. doi: 10.1088/1674-1137/ad102c
Abstract:
Radiative decays \begin{document}$ D^*_{(s)}\to D_{(s)}\gamma $\end{document} are revisited in light of new experimental data from the BaBar and BESIII Collaborations. The radiative couplings \begin{document}$ g_{D^*D\gamma} $\end{document} encoding nonperturbative QCD effects are calculated in the framework of the covariant confined quark model developed by us. We compare our results with other theoretical studies and experimental data. The couplings (in \begin{document}$ \rm{GeV}^{-1} $\end{document}) \begin{document}$ |g_{D^{*+}D^+\gamma}| = 0.45(9) $\end{document} and \begin{document}$ |g_{D^{*0}D^0\gamma}| = 1.72(34) $\end{document} calculated in our model agree with the corresponding experimental data \begin{document}$ |g_{D^{*+}D^+\gamma}|=0.47(7) $\end{document} and \begin{document}$ |g_{D^{*0}D^0\gamma}|=1.77(16) $\end{document}. The most interesting case is the decay \begin{document}$ D^*_s\to D_s\gamma $\end{document}, for which a recent prediction based on light-cone sum rules at next-to-leading order \begin{document}$ |g_{D^*_s D_s\gamma}|=0.60(19) $\end{document} deviates from the first (and only to date) lattice QCD result \begin{document}$ |g_{D^*_s D_s\gamma}|=0.11(2) $\end{document} at nearly \begin{document}$ 3\sigma $\end{document}. Our calculation yields \begin{document}$ |g_{D^*_s D_s\gamma}|=0.29(6) $\end{document}, which falls somehow between the two mentioned results, although it is larger than those predicted in other studies using quark models or QCD sum rules.
Observability of parameter space for charged Higgs boson in its bosonic decays in two Higgs doublet model Type-1
Ijaz Ahmed, Waqas Ahmad, M. S. Amjad, Jamil Muhammad
2024, 48(2): 023104. doi: 10.1088/1674-1137/ad13f8
Abstract:
This study explores the possibility of discovering \begin{document}$ H^{\pm} $\end{document} through its bosonic decays, i.e., \begin{document}$ H^{\pm}\rightarrow W^\pm\phi $\end{document} (where ϕ = h or A), within the Type-I two Higgs doublet model (2HDM). The main objective is to demonstrate the available parameter space after applying recent experimental and theoretical exclusion limits. We suggest that \begin{document}$ m_{H^\pm} $\end{document}= 150 GeV is the most probable mass for the \begin{document}$ H^\pm\rightarrow W^\pm\phi $\end{document} decay channel in \begin{document}$ pp $\end{document} collisions at \begin{document}$ \sqrt{s} $\end{document}= 8, 13, and 14 TeV. We also report on the application of a modern machine learning approach to a multivariate technique for heavy charged Higgs production in association with a single top quark through weak interaction to demonstrate its observability in comparison with the most relevant Standard Model backgrounds using the neural networks of boosted decision Tree (BDT), likelihood (LH), and multilayer perceptron (MLP).
Strong decay of $ { \boldsymbol Y({\bf{4230}}){\bf\to}\boldsymbol J/\boldsymbol\psi \boldsymbol f_{\bf 0}({\bf{980}}) }$ in light cone sum rules
Yiling Xie, Hao Sun
2024, 48(2): 023105. doi: 10.1088/1674-1137/ad13f9
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In this study, we assign the tetraquark state for the \begin{document}$ Y(4230) $\end{document} resonance and investigate the mass and decay constant of \begin{document}$ Y(4230) $\end{document} in the framework of SVZ sum rules through a different calculation technique. Then, we calculate the strong coupling \begin{document}$ g_{Y J/\psi f_0} $\end{document} by considering soft-meson approximation techniques within the framework of light cone sum rules, and we use the strong coupling \begin{document}$ g_{Y J/\psi f_0} $\end{document} to obtain the width of the decay \begin{document}$ Y(4230)\to $\end{document}\begin{document}$ J/\psi f_0(980) $\end{document}. Our prediction for the mass agrees with the experimental measurement, and that for the decay width of \begin{document}$ Y(4230)\to J/\psi f_0(980) $\end{document} is within the upper limit.
NUCLEAR PHYSICS
Investigation of 58Ni (n, p)58Co reaction cross-section with covariance analysis
Akash Hingu, S. Mukherjee, Siddharth Parashari, Arora Sangeeta, A. Gandhi, Mahima Upadhyay, Mahesh Choudhary, Sumit Bamal, Namrata Singh, G. Mishra, Sukanya De, Saurav Sood, Sajin Prasad, G. Saxena, Ajay Kumar, R.G. Thomas, B.K. Agrawal, K. Katovsky, A. Kumar
2024, 48(2): 024001. doi: 10.1088/1674-1137/ad0e5a
Abstract:
The excitation function of the \begin{document}$ {}^{58}{\rm{Ni}} (n, p){}^{58}{\rm {Co}} $\end{document} reaction was measured using the well-established neutron activation technique and γ-ray spectroscopy. Neutrons in the energy range of 1.7 to 2.7 \begin{document}$ \rm MeV $\end{document} were generated using the \begin{document}$ ^{7}{\rm{Li}}(p, n) $\end{document} reaction. The neutron flux was measured using the standard \begin{document}$ {}^{115}{\rm{In}} (n, n'){}^{115{\rm m}}{\rm{In}} $\end{document} monitor reaction. The results of the neutron spectrum averaged cross-section of \begin{document}$ {}^{58}{\rm{Ni}} (n, p){}^{58}{\rm{Co}} $\end{document} reactions were compared with existing cross-section data available in the EXFOR data library as well as with various evaluated data libraries such as ENDF/B-VIII.0, JEFF-3.3, JENDL-4.0, and CENDL-3.2. Theoretical calculations were performed using the nuclear reaction code TALYS. Various nuclear level density (NLD) models were tested, and their results were compared with the present findings. Realistic NLDs were also obtained through the spectral distribution method (SDM). The cross-section results, along with the absolute errors, were obtained by investigating the uncertainty propagation and using the covariance technique. Corrections for γ-ray true coincidence summing, low-energy background neutrons, and γ-ray self attenuation were performed. The experimental cross-section obtained in the present study is consistent with previously published experimental data, evaluated libraries, and theoretical calculations carried out using the TALYS code.
Photonuclear reactions on stable isotopes of selenium at bremsstrahlung end-point energies of 10−23 MeV
F.A. Rasulova, N.V. Aksenov, S.I. Alekseev, R.A. Aliev, S.S. Belyshev, I. Chuprakov, N.Yu. Fursova, A.S. Madumarov, J.H. Khushvaktov, A.A. Kuznetsov, B.S. Yuldashev
2024, 48(2): 024002. doi: 10.1088/1674-1137/ad11e4
Abstract:
In this study, experiments were performed at bremsstrahlung end-point energies of 10−23 MeV with the beam from the MT-25 microtron using the γ-activation technique. The experimental values of relative yields were compared with theoretical results obtained on the basis of TALYS with the standard parameters and the combined model of photonucleon reactions. Including isospin splitting in the combined model of photonucleon reactions allows describing experimental data on reactions with proton escape in the energy range from 10 to 23 MeV. Therefore, taking into account isospin splitting is necessary for a correct description of the decay of the giant dipole resonance.
From masses and radii of neutron stars to EOS of nuclear matter through neural network
Zehan Wu, Dehua Wen
2024, 48(2): 024101. doi: 10.1088/1674-1137/ad0e04
Abstract:
The equation of state (EOS) of dense nuclear matter is a key factor for determining the internal structure and properties of neutron stars. However, the EOS of high-density nuclear matter has great uncertainty, mainly because terrestrial nuclear experiments cannot reproduce matter as dense as that in the inner core of a neutron star. Fortunately, continuous improvements in astronomical observations of neutron stars provide the opportunity to inversely constrain the EOS of high-density nuclear matter. Several methods have been proposed to implement this inverse constraint, including the Bayesian analysis algorithm, the Lindblom's approach, and so on. Neural network algorithm is an effective method developed in recent years. By employing a set of isospin-dependent parametric EOSs as the training sample of a neural network algorithm, we set up an effective way to reconstruct the EOS with relative accuracy using a few mass-radius data. Based on the obtained neural network algorithms and according to the NICER observations on masses and radii of neutron stars with assumed precision, we obtain the inversely constrained EOS and further calculate the corresponding macroscopic properties of the neutron star. The results are basically consistent with the constraint on EOS in Huth et al. [Nature 606, 276 (2022)] based on Bayesian analysis. Moreover, the results show that even though the neural network algorithm was obtained using the finite parameterized EOS as the training set, it is valid for any rational parameter combination of the parameterized EOS model.
Nuclear mass predictions based on a deep neural network and finite-range droplet model (2012)
To Chung Yiu, Haozhao Liang, Jenny Lee
2024, 48(2): 024102. doi: 10.1088/1674-1137/ad021c
Abstract:
A neural network with two hidden layers is developed for nuclear mass prediction, based on the finite-range droplet model (FRDM12). Different hyperparameters, including the number of hidden units, choice of activation functions, initializers, and learning rates, are adjusted explicitly and systematically. The resulting mass predictions are achieved by averaging the predictions given by several different sets of hyperparameters with different regularizers and seed numbers. This can provide not only the average values of mass predictions but also reliable estimations in the mass prediction uncertainties. The overall root-mean-square deviations of nuclear mass are reduced from 0.603 MeV for the FRDM12 model to 0.200 MeV and 0.232 MeV for the training and validation sets, respectively.
Dynamics of 7Li breakup and its influence on elastic scattering: a study of 7Li + 144Sm system
A. Morzabayev, N. Amangeldi, Awad A. Ibraheem, D. Soldatkhan, G. Yergaliuly, B. Mauyey, Anuar. A. Orazalievna, Sh. Hamada
2024, 48(2): 024103. doi: 10.1088/1674-1137/ad1029
Abstract:
The angular distributions of 7Li + 144Sm elastic scattering over the energy range of 21.6–52 MeV are reanalyzed utilizing various interaction potentials. The analysis aims to study the consistency of the implemented potentials in representing the considered data and investigate the cluster nature of the weakly bound 7Li projectile. This will aid in the better understanding the impacts of 7Li breakup on the elastic scattering channel. Strong coupling to the breakup channel has a substantial impact on the elastic data and reproduces a repulsive dynamical polarization potential, which drastically diminishes the real potential strength. This reported impact was simulated by introducing a semi-microscopic repulsive DPP and by implementing the method of continuum discretized coupled channels. The analysis was also extended to understand the impact of triton transfer on the elastic scattering data.
Interaction of photons with silver and indium nuclei at energies up to 20 MeV
J. H. Khushvaktov, M. A. Demichev, D. L. Demin, S. A. Evseev, M. I. Gostkin, V. V. Kobets, F. A. Rasulova, S. V. Rozov, E. T. Ruziev, A. A. Solnyshkin, T. N. Tran, E. A. Yakushev, B. S. Yuldashev
2024, 48(2): 024104. doi: 10.1088/1674-1137/ad1028
Abstract:
The yields of photonuclear reactions in the 107Ag, 113In, and 115In nuclei were measured. Monte Carlo simulations were performed using the Geant4 code, and the results were compared with the experimental values. The isomeric ratios of the yields in the reactions 107Ag(γ, n)106m,gAg and 113In(γ, n)112m,gIn were determined, and the cross sections for the reactions 107Ag(γ, n)106gAg and 107Ag(γ, 2n)105Ag at an energy of 20 MeV were calculated based on the experimental data.
Analysis of data for γpf1(1285)p photoproduction
Ai-Chao Wang, Neng-Chang Wei, Fei Huang
2024, 48(2): 024105. doi: 10.1088/1674-1137/ad0f13
Abstract:
The photoproduction of the \begin{document}$ f_1(1285) $\end{document} meson off the proton target is investigated within an effective Lagrangian approach. The t-channel ρ- and ω-exchange diagrams, u-channel nucleon-exchange diagram, generalized contact term, and s-channel pole diagrams of the nucleon and a minimal number of nucleon resonances are taken into account in constructing the reaction amplitudes to describe the experimental data. Three different models, that is, the Feynman, Regge, and interpolated Regge models, are employed, where the t-channel reaction amplitudes are constructed in Feynman, Regge, and interpolated Regge types, respectively. The results show that neither the Feynman model with two nucleon resonances nor the interpolated Regge model with one nucleon resonance can satisfactorily reproduce the available data for \begin{document}$ \gamma p \to f_1(1285) p $\end{document}. Nevertheless, in the Regge model, when any one of the \begin{document}$ N(1990){7/2}^+ $\end{document}, \begin{document}$ N(2000){5/2}^+ $\end{document}, \begin{document}$ N(2040){3/2}^+ $\end{document}, \begin{document}$ N(2060){5/2}^- $\end{document}, \begin{document}$ N(2100){1/2}^+ $\end{document}, \begin{document}$ N(2120){3/2}^- $\end{document}, \begin{document}$ N(2190){7/2}^- $\end{document}, \begin{document}$ N(2300){1/2}^+ $\end{document}, and \begin{document}$ N(2570){5/2}^- $\end{document} resonances is considered, the data can be well described. The resulting resonance parameters are consistent with those advocated in the Particle Data Group (PDG) review. Further analysis shows that, in the high-energy region, the peaks of \begin{document}$ \gamma p \to f_1(1285) p $\end{document} differential cross sections at forward angles are dominated by the contributions from t-channel ρ- and ω-exchange diagrams, while in low-energy region, the s-channel pole diagrams of resonances also provide significant contributions to the \begin{document}$ \gamma p \to f_1(1285) p $\end{document} cross sections.
Description of elastic scattering for 7Li-induced reactions on 1p-shell nuclei
Yong-Li Xu, Xin-Wu Su, Zhi-Hao Sun, Yin-Lu Han, Xiao-Jun Sun, Dong-Hong Zhang, Chong-Hai Cai
2024, 48(2): 024106. doi: 10.1088/1674-1137/ad1924
Abstract:
The experimental data of elastic scattering angular distributions for 9Be, 10B, 11B, 12C, 13C, 15N, and 16O targets from 4.5 to 131.8 MeV and 7Li target from 8.0 to 42.0 MeV are fitted to realize the global phenomenological optical potentials (GPOPs) for the 7Li-induced reactions on 1p-shell nuclei. Thus, the 7Li elastic scattering from the 1p-shell nuclei can be systematically described using the established GPOPs. The elastic scattering angular distributions are also reanalyzed using a microscopic method within the framework of the new version of double folding São Paulo potential (SPP2). To better describe the elastic scattering at backward angles, the contribution of elastic transfer is further estimated by the distorted wave Born approximation (DWBA) method. Based on the obtained GPOPs, the inelastic scattering angular distributions are also obtained through the coupled channels (CC) method for the different excited states.
PARTICLE AND NUCLEAR ASTROPHYSICS AND COSMOLOGY
Radiation properties of the accretion disk around a black hole in Einstein-Maxwell-scalar theory
Mirzabek Alloqulov, Sanjar Shaymatov, Bobomurat Ahmedov, Abdul Jawad
2024, 48(2): 025101. doi: 10.1088/1674-1137/ad137f
Abstract:
In this study, we explore the properties of a non-rotating black hole in the Einstein-Maxwell-scalar (EMS) theory and investigate the luminosity of the accretion disk surrounding it. We determine all the orbital parameters of particles in the accretion disk, including the radius of the innermost stable circular orbit (ISCO) with angular velocity, angular momentum, and energy. Further, we study the radiative efficiency for different values of black hole parameters. Finally, we analyze the flux, differential luminosity, and temperature of the accretion disk.
Cosmic implications of the ${^{12}{\bf C}(\boldsymbol n,\bf\gamma)^{13}{\bf C} }$ reaction: a nuclear astrophysical perspective
Soumya Saha
2024, 48(2): 025102. doi: 10.1088/1674-1137/ad102a
Abstract:
We conducted a comprehensive study of the neutron capture cross section of \begin{document}$ ^{12}\mathrm C $\end{document} within the relevant astrophysical energy range. Through rigorous R-matrix analysis, we determined the Maxwellian-averaged cross section to be 11.98\begin{document}$ \pm $\end{document}0.25 μb at kT = 30 keV. This result is approximately four times higher than the thermal neutron capture cross section estimated in earlier studies assuming the \begin{document}$ \dfrac{1}{v} $\end{document} law. The implications of our findings extend to the region of inhomogeneous Big-Bang models in nuclear astrophysics, where understanding the behaviour of neutron capture cross sections plays a crucial role in elucidating the intricate processes that shaped the early universe.
Impact of a nearby subhalo on the constraint of dark matter annihilation from cosmic ray antiprotons
Yi Zhao, Xiao-Jun Bi, Su-Jie Lin, Peng-Fei Yin
2024, 48(2): 025103. doi: 10.1088/1674-1137/ad13f7
Abstract:
Numerous simulations indicate that a large number of subhalos should be hosted by the Milky Way. The potential existence of a nearby subhalo could have important implications for our understanding of dark matter (DM) annihilation. In this study, we investigate the hypothetical presence of a nearby subhalo and set the upper limits on the DM annihilation cross section by analyzing the cosmic-ray antiproton spectrum. By presenting the ratios of annihilation cross section limits for scenarios with and without a nearby subhalo, we can quantitatively evaluate the potential impact of the nearby subhalo on the limits of the DM annihilation cross section. The impacts of the concentration model and the subhalo probability distribution have been considered. We explore the antiproton contribution of the potential nearby DM subhalo accounting for the DAMPE \begin{document}$ e^\pm $\end{document} spectrum at \begin{document}$ \sim 1.4 $\end{document} TeV and find that the current AMS-02 antiproton results do not limit this contribution.
Shadow and weak gravitational lensing for Ellis-Bronnikov wormhole
Mirzabek Alloqulov, Farruh Atamurotov, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, Vokhid Khamidov
2024, 48(2): 025104. doi: 10.1088/1674-1137/ad1677
Abstract:
In this study, we investigated the gravitational weak lensing and shadow of the Ellis-Bronnikov wormhole. First, we studied the photon motion in a plasma medium and a wormhole shadow. It was shown that the radius of the photon sphere of the Ellis-Bronnikov wormhole and the size of the wormhole shadow become larger under the influence of the parameter a. The upper limit of the parameter a in the Ellis-Bronnikov wormhole spacetime was obtained. Second, we investigated the weak gravitational lensing for the Ellis-Bronnikov wormhole and calculated the deflection angle for uniform and non uniform plasma cases. The value of the deflection angle for uniform plasma increased with the increase in plasma parameter value, and vice versa for non uniform plasma. We found that, under the influence of the parameter a, the values of the deflection angles for two cases decreased. Finally, we investigated the magnification of image brightness using the deflection angle of the light rays around the wormhole in the Ellis-Bronnikov theory.