arXiv subjects

G. R. Boroun

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

At least 37 records · Page 2Linked to original sources

arXiv2024

Effects of heavy quarks in the dipole cross section with the KLN model

The dipole cross-section behavior for protons and nuclei is analyzed with and without considering the heavy quark masses in the Bjorken variable $x$ using the Kharzeev-Levin-Nardi (KLN) model of low $x$ gluon distributions. The Color Glass Condensate (CGC) effects in the color dipole model are influenced by the heavy quark masses in the Bjorken variable $x$ at $Q^2<Q_{s}^2$. These non-linear saturation effects will be observable in the LHeC and EIC at very small $x$ values.

hep-ph↗

arXiv2024

Approximation method for the nuclear structure functions at small $x$

We have shown that the relationship between the DIS structure functions is stable for a nuclear target with mass number A at $x{\leq}10^{-3}$. Numerical results are provided for the specific nuclei 12C and 208Pb using the nuclear PDF parameterizations implemented in the HIJING2.0 model. These results fall whithin the EIC kinematic acceptance for heavy ion running. The ratio $R^{A}_{F_{L}}$ is calculated as the ratio $R^{A}_{F_{2}}$ in the HIJING2.0 model.

hep-ph↗

arXiv2024

Evolution of the color dipole cross section

Using Laplace transform techniques, we describe the evolution of the color dipole cross section, at the leading-order and next-to-leading order approximations, from the Bartels-Golec-Biernat-Kowalski model in a kinematical region of low values of the Bjorken variable $x$ and a wide range of transverse dipole size $r$. This evolution method shows that the saturation scale and geometric scaling are retained. We derived analytical results for the integrated and unintegrated color dipole gluon distribution functions and compared them with the CJ15 parametrization group and the unintegrated color dipole gluon distribution models respectively. The Sudakov form factor into the evolution of the unintegrated color dipole gluon distribution is incorporated and the results are considered at small and large values of $k_{t}^{2}$

hep-ph↗

arXiv2024

The improved saturation model in nuclei

We consider the nuclear shadowing in deep-inelastic scattering corresponding to kinematic regions accessible by future experiments at electron-ion colliders. The gluon distribution at small $x$ is obtained using an improved dipole model depended on the impact parameter for atomic nucleus and compared with nCETQ15 parametrization group. The nuclear shadowing at small $x$ is defined within the color dipole formalism with respect to the mass number $A$. Its behavior is predicted for light nuclei in a wide range of the impact parameter $b$ and the transverse dipole size $r$. The nuclear saturation at large-$r$ (small $μ^2$) is observable. The behavior of the nuclear ratio $σ^{A}_{\mathrm{dip}}/σ_{0}$ is similar to the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) model in a wide range of $r$ for light and heavy nuclei at small $x$.

nucl-th↗

arXiv2024

Color dipole cross-section from unifying the color dipole picture and improved saturation models

We present an analysis of the color-dipole picture (CDP) for determination of the gluon density at low-$x$ which is obtained from the Altarelli-Martinelli equation by expansion at distinct points of expansion. The dipole cross-sections with respect to the improved saturation model of Bartels-Golec-Biernat-Kowalski (BGK) are obtained in a wide range of transverse sizes $r$ and compared with the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) model. We find that the model gives a good description of the dipole cross-section at large $r$ which confirms saturation and matches the perturbative QCD result at a small $r$ due to the significant role of the running of the gluon distribution. The transition between these regions occurs with decreasing transverse sizes with a decrease of Bjorken $x$ and dependence on the expansion point.

hep-ph↗

arXiv2024

Decoupling of the structure functions in momentum space based on the Laplace transformation

Using Laplace transform techniques, we describe the determination of the longitudinal structure function $F_{L}(x,Q^2)$, at the leading-order approximation in momentum space, from the structure function $F_{2}(x,Q^2)$ and its derivative with respect to ${\ln}Q^2$ in a kinematical region of low values of the Bjorken variable $x$. Since the $x$ dependence of $F_2(x,Q^2)$ and its evolution with $Q^2$ are determined much better by the data than $F_L(x,Q^2)$, this method provides both a direct check on $F_L(x,Q^2)$ where measured, and a way of extending $F_L(x,Q^2)$ into regions of $x$ and $Q^2$ where there are currently no data. In our calculations, we ultilize the Block-Durand-Ha parametrization for the structure function $F_{2}(x,Q^2)$ [M. M. Block, L. Durand and P. Ha, Phys.Rev.D {\bf89}, 094027 (2014)]. We find that the Laplace transform method in momentum space provides correct behaviors of the extracted longitudinal structure function $F_{L}(x,Q^2)$ and that our obtained results are in line with data from the H1 Collaboration and other results for $F_{L}(x,Q^2)$ obtained using Mellin transform method.

hep-ph↗

arXiv2024

Reduced cross-section in Electron-Ion Colliders at small $x$

The nuclear reduced cross section $σ^{A}_{r}$, in the kinematic range of the electron-Ion collider with center-of-mass energy $\sqrt{s}=140~\mathrm{GeV}$ and $y{\leq}1$, is discussed. The importance of the nuclear longitudinal structure function $F^{A}_{L}$ and its behavior owing to the impact parameter for the heavy and light nucleus of Pb-208 and C-12 at $Q^2=5$ and $10~\mathrm{GeV}^2$ is considered. The dependence of the ratios $R^{A}_{F_{L}}$ and $R^{A}_σ$ on the impact parameter and the expanding point of the gluon density at small $x$ are investigated. The factorized form of parton distributions in nuclei is used in HIJING2.0 model.

hep-ph↗

arXiv2024

Heavy quark structure functions from unifying the color dipole picture and double asymptotic scaling approaches

We present an analysis of the heavy quark structure functions from the $k_{t}$ factorization scheme, using unifying the color dipole picture and double asymptotic scaling approaches at small $x$. The gluon distribution is obtained from the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) and Bartels, Golec-Biernat and Kowalski (BGK )models. The main elements are based on the color dipole picture (CDP) and the generalized double asymptotic scaling (DAS) approach for usual parton distribution functions (PDFs). The comparisons with the HERA data are made and predictions for the proposed LHeC and FCC-he colliders are also provided in a wide range of the transverse separation $r$. In particular, the ratio $R^{h}=F_{L}^{h}/F_{2}^{h}, h=c,b,t$ is well described by the dipole models and is sensitive to the collider energies from HERA until FCC-he. We derive correlated bounds on the ratio $F^{c}_{2}/F_{2}$ and $F^{b}_{2}/F_{2}$ and compared them with the BGK and IP-sat models. The uncertainties are due to the renormalization and factorization scales at large and low $r$ values. The Sudakov form factor into the heavy quark structure functions is incorporated and the results are considered, which are dependent on the hard scale in a wide range of the transverse separation $r$.

hep-ph↗

arXiv2024

Nonlinear corrections for the nuclear gluon distribution in $eA$ processes

An analytical study with respect to the nonlinear corrections for the nuclear gluon distribution function in the next-to-leading order approximation at small $x$ is presented. We consider the nonlinear corrections to the nuclear gluon distribution functions at low values of $x$ and $Q^{2}$ using the parametrization $F_{2}(x,Q^{2})$ and using the nuclear modification factors where they have been obtained with the Khanpour-Soleymaninia-Atashbar-Spiesberger-Guzey model. The CT18 gluon distribution is used as baseline proton gluon density at $Q_{0}^{2}=1.69~\mathrm{GeV}^2$. We discuss the behavior of the gluon densities in the next-to-leading order and the next-to-next-to-leading order approximations at the initial scale $Q_{0}^{2}$, as well as the modifications due to the nonlinear corrections. We find the QCD nonlinear corrections are significant for the next-to-leading order accuracy than the next-to-next-to-leading order for light and heavy nuclei. The results of the nonlinear GLR-MQ evolution equation are similar to those obtained with the Rausch-Guzey-Klasen gluon upward and downward evolutions within the uncertainties. The magnitude of the gluon distribution with the nonlinear corrections increases with a decrease of $x$ and an increase of the atomic number A.

hep-ph↗

arXiv2024

A simple model for the charm structure function of nuclei

In this paper, we have investigated the importance of quark charm in nuclear structure functions in the color dipole model at small $x$. The charm structure function per nucleon $F_{2}^{cA}/A$ for light and heavy nuclei in a wide range of transverse separations $\mathrm{r}$ with renormalization and factorization scales are considered. Bounds on the ratio $F^{cA}_{2}/AF^{A}_{2}$ for nuclei are well described with respect to the electron-ion future colliders kinematic range, i.e, EIC and EIcC colliders.

hep-ph↗

arXiv2023

Nonlinear Corrections to the Momentum Sum Rule

The importance of the nonlinear corrections on the momentum sum rule is investigated on the initial scale $Q_{0}^2$. Nonlinear corrections are found to play an indispensable role in the singlet and gluon momentum sum rule in the high-order approximations in the parameterization groups for nucleons and light nuclei at low $x$ in future colliders. In this way, we obtain a significantly different low $x$ behavior of the singlet and gluon momentum sum rule at the hotspot point.

hep-ph↗

arXiv2023

The unintegrated gluon distribution from the GBW and BGK models

The gluon distribution is obtained from the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) and Bartels, Golec-Biernat and Kowalski (BGK) models at low $x$. We derive analytical results for the unintegrated color dipole gluon distribution function at small transverse momentum, which provides useful information to constrain the $k_{t}$-shape of the unintegrated gluon distribution in comparison with the unintegrated gluon distribution (UGD) models. The longitudinal proton structure function $F_{L}(x,Q^2)$ from the $k_{t}$ factorization scheme, using the unintegrated gluon density is computed. We compare the predictions for the on-shell and twist-2 corrections with the HERA data and the CJ15 parametrization method for $F_{L}$. We show that this method is very well described the experimental data within the on-shell and twist-2 framework. Effects of parameters on $F_{L}$, where charm contribution is taken into account, are investigated. These results are in good agreement with the data at fixed $W$.

hep-ph↗

arXiv2023

The Proton Gluon Distribution from the Color Dipole Picture

Employing the representation of the experimental data on deep inelastic electron-proton scattering (DIS) in the color-dipole picture (CDP), we determine the gluon distribution of the proton at small Bjorken $x$. At sufficiently large momentum transfer, $Q^2$, the extracted gluon distribution fulfills the standard evolution equation for the proton structure function. For low values of $Q^2$, e.g. for $Q^2 = 1.9 {\rm GeV}^2$, the evolution equation for the proton structure function is violated. The standard procedure of adopting a low-$Q^2$ starting scale for the extraction of the gluon density is questionable and requires further investigations.

hep-ph↗

arXiv2023

Nonlinear terms from GLR-MQ evolution

We show that the saturation exponent is more effective than the hard pomeron exponent in the nonlinear terms for the GLR-MQ evolution equations. For the gluon distribution the nonlinear terms are found to play an increasingly important role than the singlet distribution. The nonlinear corrections for the singlet and gluon distributions are important in a limited range of $Q^2$ and are independent of the upward and downward evolution. This allows us to single out the region where the nonlinear corrections may provide evidence for recombination. We numerically study the nonlinear terms for nuclear singlet and gluon distributions and quantify the impact of gluon recombination in a wide range of $Q^2$. This analysis indicates that the nonlinear effects are most pronounced for heavy nuclei and are sizable at $2{\lesssim}Q^2{\lesssim}20~\mathrm{GeV}^2$ for light and heavy nuclei.

hep-ph↗

arXiv2023

The dipole cross section by the unintegrated gluon distribution at small $x$

We apply a previously developed scheme to consistently include the improved saturation model for the unintegrated gluon distribution (UGD) in order to evaluate, in the framework of $k_{t}$ factorization, at small $x$ at the next-to-leading order (NLO) in $α_{s}$. We start the unintegrated gluon distribution with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section, which preserves its behavior success in a wide range of $k_{t}^{2}$ in comparisons with the UGD models (M. Hentschinski, A. Sabio Vera and C. Salas (HSS), I.P.Ivanov and N.N.Nikolaev (IN) and G. Watt, A.D. Martin and M.G. Ryskin (WMR)) . These results show that the geometric scaling holds for the improved saturation model in a wide kinematic region $rQ_{s}$, and are comparable with the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) model. The unintegrated gluon distribution at low and high momentum transfer in a wide range of $x$ is considered.

hep-ph↗

arXiv2023

Parametrization of the nuclear structure function

In this paper, the parametrization of the nuclear structure function which is directly constrained by the dynamics of QCD in its high-energy limit is considered. This simple parameterization of the nuclear structure function is obtained from the proton experimental data by relying on a Froissart-bounded parametrization of the proton structure function. This phenomenological model describes high-energy QCD in the presence of saturation effects. Numerical calculations and comparison with available data from NMC, EMC and E665 Collaborations demonstrate that the suggested method by N.Armesto, C.A.Salgado and U.A. Wiedemann (ASW model) provides reliable ratio of nuclear structure functions $F_{2}^{A}/AF^{p}_{2}$ at low $x$ for light and heavy nuclei. The magnitude of nuclear shadowing is predicted for various kinematic regions and can be applied as well in analysis of ultra-high energy processes by future experiments at electron-ion colliders.

hep-ph↗

arXiv2023

Top cross section in the LHeC and FCC-he energy range

Predictions of the top-pair production cross section in electron-proton (ep) collisions at the future circular collider hadron-electron (FCC-he) and the large hadron electron collider (LHeC) in the leading order (LO) and the next-to-leading order (NLO) approximations in perturbative quantum chromodynamics (QCD) are presented. Numerical results for the top structure functions and the ratio of structure functions are computed at the renormalization scale $μ^{2}=Q^{2}+4m^{2}_{t}$ in the collinear generalized double asymptotic scaling (DAS) approach. These results are presented in terms of the effective parameters of the parameterization of $F_{2}(x,Q^{2})$, where relying on a Froissart-bounded. These quantitative results can be important for future collider experiments at the center-of-mass energy frontier and the improvement of the phenomenological models for the development of the cosmic ray cascades in ultra-high-energy domain. We obtained the uncertainties because of the power-law behavior $x^{-Δ}$ of the collinear parton distribution functions (PDFs), the factorization, and renormalization scales, on the top properties at high inelasticity for the FCC-he center-of-mass (CM) energy at the NLO approximation.

hep-ph↗

arXiv2023

One-to-One correspondence of soft and hard Pomeron with the CDP of the gluon density at low $x$

The correspondence between the gluon density behavior of the color dipole picture and the two-Pomeron approach at low $x$ deep inelastic scattering is considered. For photon virtualities of $Q^{2}{\gtrsim}10~\mathrm{GeV}^{2}$, the results for the parametrization and CDP models are defined by the CDP asymptotic limit and are compatible with the soft and hard-Pomeron approach. These results show that the hard-Pomeron trajectory does not guarantee converging towards the asymptotic representation at low and large $Q^{2}$ ($Q^{2}{\lesssim}100~\mathrm{GeV}^{2}$) values in a wide range of the virtual-photon-proton energy squared. The gluon distributions can be obtained directly in terms of the proton structure functions and the running coupling and compared with the results from the GJR and MSTW parametrizations.

hep-ph↗