arXiv subjects

G. R. Boroun

Publications and source records attributed to G. R. Boroun.

At least 19 recordsLinked to original sources

arXiv2026

Entropy and DIS structure functions

Entanglement entropy in Deep Inelastic Scattering (DIS) from the DIS structure functions has emerged as a novel tool for probing observable quantities. The method proposed by Kharzeev-Levin to determine entanglement entropy in DIS from parton distribution functions (PDFs) improves on the momentum-space approach proposed by Lappi et al.[Eur. Phys. J. C {\bf84}, 84 (2024)] and further developed by Boroun and Ha [Phys. Rev. D {\bf109}, 094037 (2024)] using Laplace transform techniques. The entropy of charged hadrons is obtained from the parameterization of the proton structure function and compared with H1 data, HSS, and HERA PDFs. Our results for the entanglement entropy align very well with the H1 data across a wide range of $x$ and $Q^2$. Finally, the behavior of the entanglement entropy is described at fixed $\sqrt{s}$ to the minimum value of $x$ given by $Q^2/s$, which indicates that the polarization of the exchanged photon for entropy determination is transverse at this specific kinematic point. The effect of adding a simple higher twist term to the description of entropy at low-$x$ and low-$Q^2$ values for comparison with HERA data is investigated.

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arXiv2026

Direct determination of the structure functions $F_L$, $F_S$ and $G$ from $F_2$ and $dF_2/dQ^2$ to $O(α_s^2)$

We extend the results of Lappi {\em et al.}, Eur.~Phys.~J.~C {\bf 84}, 84 (2024), to show that it is possible to obtain expressions for the longitudinal, singlet and gluon structure functions $F_L$, $F_S$ and $G$ in deep inelastic scattering directly in terms of the measured functions $F_2$ and $dF_2/\ln(Q^2)$ {\em modulo} non-singlet corrections expected to be small at very small $x$. The latter can be treated at low $x$ using existing quark distributions. Our results are presented consistently to $O(α_s^2)$, correcting and extending the mixed-order results of Lappi {\em et al.}.

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arXiv2026

The ratio of reduced cross-sections in $eA$ processes at Electron-Ion Colliders at $x_{\mathrm{min}}=Q^2/s$

We study the predictions of saturation effects in electron-ion colliders at high inelasticity, using a generalization for nuclear targets of the ASW and GBW models where the saturation scale, $Q_{\mathrm{sat}}$, drives the energy dependence and the corresponding nuclear effects. We expect to observe an enhancement of the ratio of nuclear reduced cross sections in the saturation region in future electron-ion colliders. The ratio $R^{A}_{σ_{r}}$ is discussed in the kinematic range of the electron-Ion collider with center-of-mass energy $\sqrt{s}=89~\mathrm{GeV}$ at high inelasticity $y{=}1$. The importance of the nuclear longitudinal structure function $F^{A}_{L}$ in the ratio $R^{A}_{σ_{r}}$ for the heavy nucleus lead and light nucleus deuteron at $x_{\mathrm{min}}=Q^2/s$ is discussed. This enhancement in the range $Q^2\sim(1-4~\mathrm{GeV}^2)$ in the ratio $R^{A}_{σ_{r}}$ is not observed in the ratio $R^{A}_{F_{2}}$ which is comparable with the nuclear ratio of the nuclear parton distribution functions. We demonstrate that the study of nuclear charm structure function allows us to estimate the magnitude of shadowing effects in high inelasticity in the nuclear gluon distribution.

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arXiv2026

The EIC reduced cross sections at high inelasticity

The impact of higher-twist corrections to the ratio $\frac{σ_{r}}{F_{2}}(A,Q^2/s,Q^2)$ for light and heavy nuclei is considered at fixed a $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$. The results are for the EIC center-of-mass energies. We apply the influence of higher-twist corrections to $\frac{σ_{r}}{F_{2}}(A,Q^2/s,Q^2)$ by the dimensionless variable $ξ'_{A}=Q_{s,A}^{2}/Q^2$ in the color dipole model and obtain bounds for the ratio in the linear region. The importance of contributing to twist-4 at small-$x$ is visible in the linear region where $ξ'_{A}{\leq}1$. We perform that twist-4 corrections of the saturation model are shown the successful behavior of $\frac{F_{L}}{F_{2}}(A=2,x,Q^2)$ in comparison with the JLab data at $ξ'_{A}{\leq}1$. The higher-twist corrections due to twist-6 and twist-8 are resummed by the non-linear approaches in the region $ξ'_{A}>1$. The ratio $\frac{F_{L}}{F_{2}}$ deuteron is considered in the low-$Q^2$ and small-$x$ region and compared with the JLab data which takes into account the non-linear corrections due to twist-6 and twist-8. A comparison with the JLab data shows that the impact of the distinct twists allows us to probe the presence of non-linear effects on the QCD dynamics as $F_{L}{\rightarrow}0$ and the polarization of the virtual photon is transverse in this region.

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arXiv2026

Heavy quark distributions from the Color Dipole Picture

To study charm -quark pair production processes, we utilized the color dipole picture gluon distribution function in a collinear generalized double asymptotic scaling approach at small Bjorken $x$ values ($x{\leq}10^{-2}$). Our results show good agreement with the latest HERA experimental data for reduced cross sections $σ_{\mathrm{red}}^{c\overline{c}} (W^2,Q^2)$ across a wide range of $x$ and $Q^2$ values, yielding an effective pomeron intercept. A Hard pomeron intercept with the coefficient $C_{2}=0.29$ in the color dipole model provides comparable results at very low $x$ values ($x{<}10^{-3}$). We demonstrate that the experimental data from HERA in the region $2.5{\leq}Q^2{\leq}2000~\mathrm{GeV}^2$ confirms the symmetry between the saturation and color transparency regions in the scaling variable $η$, shifting towards the color transparency region when we incorporate the threshold mass production of $J/ψ$ meson in the color dipole picture.

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arXiv2026

A limit on top quark pair production at future electron-proton colliders

The ratio of the structure functions for deep inelastic scattering in top pair production at future electron-proton colliders is analyzed at a fixed $\sqrt{s}$ and $Q^2$ relative to the minimum value of $x$ given by $Q^2/s$ using collinear factorization. This compact formula for the ratio $F_{L2}(Q^2/s,Q^2,m_{t})$ is useful for extracting a bound on the top structure function. The reduced cross-section for top production at this limit is determined, establishing a bound value for $t\overline{t}$ production at the LHeC and FCC-eh center-of-mass energies based on renormalization scales. The modification of the Bjorken scaling is applied to this bound of the reduced top cross-section at the renormalization scale $μ^2=Q^2+4m_{t}^{2}$, which improves the scaling quantity at $Q^2{<}4m_{t}^{2}$. The dipole cross-section for top pair production is examined across a wide range of dipole sizes, denoted as $r$. It is expected that there will be limited behavior in observing top saturation in future electron-proton colliders according to the bound behavior. The probability of the Higgs boson in $γ^{*}g$ interactions is compared to the $gg$ process at the order of $\mathcal{O}(α^{\mathrm{em}}/α_{s})$.

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arXiv2026

Photoabsorption cross section in the low-$x$ and low-$Q^2$ domain, and DGLAP evolution

The behavior of the gluon distribution of the proton in the low-$x$, low-$Q^2$ domain of deep inelastic electron-proton scattering (DIS) is being investigated. By considering two-gluon exchange as the dominant interaction in the low-$x$, low-$Q^2$ domain, we imply the well-known result of scaling of the photoabsorption cross section in terms of the scaling variable $η(W^2,Q^2)$. From this, we derive a reliable result for the gluon distribution at the leading order of the perturbative QCD improved parton model, based on evolution from a starting scale of $Q_0^2\cong 2$ GeV$^2$. The validity of evolution, when considering its quantitative modification at low-$Q^2$ without any alteration at larger values of $Q^2$, leads to a quantitative improvement in the extraction of the gluon distribution based on evolution from a starting scale of $Q^2$ conventionally chosen as $Q^2= Q_0^2\cong 2$ GeV$^2$.

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arXiv2026

Investigation of the ratio $\frac{σ_{r}}{F_{2}}(Q^2/s,Q^2)$ in the momentum-space approach

We present a calculation of the ratio $\frac{σ_{r}}{F_{2}}(x, Q^2)$ in momentum-space approach using the Block-Durand-Ha (BDH) parameterization of the proton structure function $F_{2}(x,Q^2)$. The results are compared with H1 data and extended to high inelasticity. We also examine the ratio $\frac{σ_{r}}{F_{2}}(\frac{Q^2}{s}, Q^2)$ obtained at a fixed $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$, comparing them with both the HERA data and the color dipole model bounds. These results and comparisons with HERA data demonstrate that the suggested method for the ratio $\frac{σ_{r}}{F_{2}}$ can be applied in analyses of the Large Hadron Collider and Future Circular Collider projects. The effect of adding a simple higher twist term of the form $F_{2}{\ast}H_{2}/Q^2$ to the description of the ratio $\frac{σ_{r}}{F_{2}}(\frac{Q^2}{s}, Q^2)$ at low-$x$ and low-$Q^2$ values for comparison with the color dipole bounds and the HERA data is investigated.

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arXiv2025

Longitudinal Structure Function at the Limit $x=Q^2/s$

The longitudinal structure function for nucleons and nuclei is considered at fixed $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$. This is done using the expansion method and color dipole model in the next-to-leading order approximation. The extracted longitudinal structure functions were consistent with HERA hepdata [ https://www.hepdata.net/record/ins1377206] and the determination of $F_{L}$ at $x=Q^2/s$ [Frank E.Taylor, Phys. Rev. D {\bf111}, 052001 (2025)] at moderate and large $Q^2$ values. The results, consistent with the dipole picture at low $Q^2$ values, show that the longitudinal structure function is small as expected due to the transverse polarization of the exchanged photon and the strong suppression of the dominant gluon component. Nonlinear corrections to the nuclear longitudinal structure function at low values of $x$ and $Q^2$ are also considered. These results may enhance the deep inelastic scattering neutral current data in future colliders at low $x$ and low $Q^2$. The longitudinal structure functions for deuterium at low four-momentum transfer squared, $Q^2<1~\mathrm{GeV}^2$ at the LO and NLO approximations are determined and compared with the JLab E00-002 data.

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arXiv2025

Transverse momentum dependent gluon density in a proton at low $x$ in the Laplace transform method

We investigate the gluon distribution in a proton at very low $x$, both integrated and transverse momentum dependent, using the Laplace transform technique. By accounting for leading and main next-to-leading contributions, we derive compact analytical expressions for the gluon densities valid in the asymptotic limit $x \to 0$. Our results closely match those from other analytical and numerical approaches, with the main advantage being the simplicity of the expressions, which capture the essential features of more complex calculations.

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arXiv2025

An analysis of the fragmentation function of gluon at next-to-leading order approximation

We are investigating the behavior of the fragmentation function of a gluon, denoted as $ D_{g}(x,μ^2)$, where $μ$ represents the observable scale. This function is derived from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. Our objective is to evolve the fragmentation function of a gluon for heavy-quark-antiquark bound states with large transverse momentum using a Laplace transform technique. This method enables us to calculate numerical solutions for two and four quarkonium states based on the known initial fragmentation function of gluons. We examine both leading-order (LO) and higher-order approximations for the fragmentation function of a gluon, $[g{\rightarrow}T_{nQ}]$, by integrating the evolved fragmentation function of the gluon at the initial scale. In our computations, we utilize the initial scales for $T^{2c}_{g}$ from Braaten-Yuan [E.Braaten and T.C.Yuan, Phys. Rev. Lett. {\bf71}, 1673 (1993)] and for $T^{4c}_{g}$ and $T^{4b}_{g}$ from Celiberto-Gatto-papa [ F. G. Celiberto, G. Gatto and A. Papa, Eur. Phys. J. C {\bf84}, 1071 (2024)] and Celiberto-Gatto [ F. G. Celiberto and G. Gatto, Phys. Rev. D {\bf111}, 034037 (2025)] respectively. Through comparing our predictions with existing literature results, we can accurately determine the evolution of the fragmentation function of a gluon at scale $μ$.

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arXiv2025

Investigation of nonlinear dipole cross sections

The nonlinear corrections to the Golec-Biernat Wusthoff (GBW) and Bartels- Golec- Kowalski (BGK) models, as discussed by Peredo-Hentschinski [M.A.Peredo and M.Hentschinski, Phys.Rev.D{109}, 014032 (2024)], are analyzed in terms of the gluon density$^{,}$s nonlinear behavior. We incorporate these nonlinear corrections into the low $x$ gluon distribution of the modified BGK model for electron-ion colliders. By verifying that these results allow for a more direct assessment of the relevance of nonlinear corrections in describing the dipole cross section of heavy nuclei, we determine the dipole cross section at a fixed $\sqrt{s}$ and $Q^2$ to the minimum value of $x$ given by $Q^2/s$ of the center-of-mass energy of electron-ion colliders. Additionally, we examine the nonlinear gluon density in the photoproduction cross sections of vector mesons $Ψ(2s)$ and $J/Ψ$ on a lead nucleus.

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arXiv2025

Evolution of entropy at small $x$

We explore the evolution of the Deep Inelastic Scattering (DIS) entropy, defined as $ S(x,μ^2) \simeq \ln[xg(x,μ^2)]$ at small Bjorken variable $x$, where $μ$ is the observable scale and the gluon distribution $xg(x,μ^2)$ is derived from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. We aim to evolve the DIS entropy, which is not directly observable, using a Laplace transform technique. This approach allows us to obtain an analytical solution for the DIS entropy based on known initial gluon distribution functions. We consider both leading-order (LO) and higher-order approximations for the DIS entropy, incorporating the evolved gluon distribution function at the initial scale. The DIS entropy, influenced by purely gluonic emissions, varies with higher-order corrections to the running coupling. By comparing theoretical predictions with charged hadron multiplicity data, we define the evolution. Additionally, we investigate the derivative of the scaling entropy, modeling it as a function of the running coupling, to determine the parameter $λ$, known as the Pomeron intercept. We find that the values of $λ(x,μ^2)$ decrease as the order of evolution increases, which is consistent with the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron in the LO and NLO approximations. This investigation provides insights into the dynamics of Quantum Chromodynamics (QCD) at high energies.

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arXiv2025

Dipole-pion cross section in the saturation regime

The scale-dependent dipole-pion cross section is analyzed as a function of the dipole size $r$ and the impact parameter $b$. This analysis relies on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in $μ{\sim} 1/r +μ_{0}$ at the next-to-leading order (NLO) approximation, with a specific initial condition at $μ_{0}$. The dipole-pion cross section at small Bjorken variable $β$ is being considered over a wide range of transverse separations $r$. Using the Laplace transformation technique, we describe the determination of the dipole-pion cross section based on the gluon distribution at the initial scale $μ_{0}$ within a kinematic region characterized by low values of the Bjorken variable $β$. We found that geometric scaling for the dipole-pion cross section holds approximately within a wide kinematic region of $rQ_{s}$. The cross section saturates at large dipole sizes.

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arXiv2025

Propagation and Dynamics of Oscillating Tetraquark Systems

We have presented a theoretical investigation into the behavior of tetraquark states. These states are modeled as a non-relativistic four-body quantum system governed by harmonic interactions. Our goal is to capture the fundamental dynamics of quark-antiquark interactions in the tetraquark configuration. Within this framework, we have derived an analytical expression for the quantum propagator. This expression was then used to compute the time evolution of the wave function and the associated probability density. We examined the time evolution and oscillation patterns to gain a better understanding of the wave function and its probability of presence in space. This approach offers valuable insights into the dynamics of the tetraquark system. This model can serve as a basis for predicting complex structures such as entanglement and multipartite dependence of quarks.

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arXiv2025

Reduced cross section and gluon distribution in a momentum-space approach

We present a calculation of the reduced cross section in momentum-space approach utilizing the Block-Durand-Ha (BDH) parameterization of the proton structure function $F_{2}(x,Q^2)$ and the leading-order (LO) longitudinal structure function $F_{L}(x,Q^2)$, proposed by Boroun and Ha [G.R. Boroun and P.Ha, Phys. Rev. D {\bf 109} (2024) 094037] using Laplace transform techniques. Our results are compared with the HERA data and extended to the Large Hadron electron Collider (LHeC) domain. We also examine the ratio $F_{L2}(x, Q^2)=F_{L}(x, Q^2)/F_{2}(x, Q^2)$ obtained from our work, comparing it with both the H1 data and the color dipole (CDP) bounds. We find that our results for the reduced cross section and the ratio $F_{L2}(x, Q^2)$ agree with the H1 data. Finally, our evaluation of the gluon distribution functions $G(x,Q^2)$ in momentum-space approach shows very good concordance with the NNPDF3.0LO gluon structure functions for moderate $Q^2$ in the range $10^{-5}{\leq}x{\leq}1$.

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arXiv2025

Non-linear corrections to the derivative of nuclear reduced cross-section at small $x$ at a future electron-ion collider

The determination of non-linear corrections to the nuclear distribution functions due to the HIJING parametrization within the framework of perturbative QCD, specifically the GLR-MQ equations, is discussed. We analyze the possibility of constraining the non-linear corrections present in distribution functions using the inclusive observables that will be measured in future electron-ion colliders (EIC and EICc). The results show that non-linear corrections play an important role in heavy nuclear reduced cross sections at low $x$ and low $Q^2$ values. We find that the non-linear corrections provide the correct behavior of the extracted nuclear cross sections and that our results align with data from the nCETQ15 parametrization group. We are currently discussing a satisfactory description of the non-linear corrections to the shadowing effect at small $x$.

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arXiv2024

An analysis of the longitudinal structure function at next-to-leading order approximation at small-$x$

The longitudinal structure function is considered at the next-to-leading order approximation using the expansion method, as defined by M.B.Gay Ducati and P.B.Goncalves [Phys.Lett.B {\bf390}, 401 (1997)] and further developed by Jingxuan Chen et al., [Chin.Phys.C {\bf48}, 063104 (2024)]. This method provides results for a wide range of $x$ and $Q^2$ values. It is observed that the behavior of the longitudinal structure function depends on the fractional momentum carried by gluons at low $x$. The extracted longitudinal structure functions $F_{L}(x,Q^2)$ are in line with data from the H1 Collaboration [V. Andreev et al. (H1 Collaboration), Eur. Phys. J. C 74, 2814 (2014)] and the CT18 parametrization method [T.-J. Hou et al., Phys. Rev. D 103, 014013 (2021)].

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