arXiv subjects

B. Rezaei

Publications and source records attributed to B. Rezaei.

At least 19 recordsLinked to original sources

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 $R^{A}_{\sigma_{r}}$ 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 $R^{A}_{\sigma_{r}}$ 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 $R^{A}_{\sigma_{r}}$ 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.

hep-ph↗

arXiv2025

Nonlinear corrections to the nuclear heavy flavor structure functions

We study numerically the small-$x$ behaviour of the nuclear gluon distribution function $ G^A(x,Q^2)$ at next-to-leading order (NLO) approximation of the Gribov-Levin-Ryskin-Mueller-Qiu, Zhu-Ruan-Shen (GLR-MQ-ZRS) nonlinear equation and quantify the impact of gluon recombination in the kinematic range of $x \le 10^{-2}$ and $Q^2 \ge 5 \text{GeV}^2$ respectively. The results are comparable to the Rausch-Guzey-Klasen (RGK) [J.Rausch, V.Guzey and M.Klasen, Phys. Rev. D 107, 054003 (2023)] nuclear gluon distributions and the nCTEQ15 parametrization at the corresponding $Q^2$ values. Using the solutions of $ G^A(x,Q^2)$ in the framework of the nonlinear GLR-MQ-ZRS evolution equation, the linear and nonlinear behavior of the charm structure functions of nuclei per nucleon $F^{c\bar{c}-A}_2(x,Q^2)$ and $F^{c\bar{c}-A}_L(x,Q^2)$ are considered. The results reveal that nonlinear corrections play an important role in charm nuclear reduced cross sections at small-$ x$ and low $Q^2$ values. The computed results are compared with experimental data from the H1 and ZEUS Collaborations.

nucl-th↗

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 $\Psi(2s)$ and $J/\Psi$ on a lead nucleus.

hep-ph↗

arXiv2024

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

The nuclear reduced cross section $\sigma^{A}_{r}$, 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 $R^{A}_{\sigma}$ 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↗

arXiv2023

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↗

arXiv2023

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 $\mu^2$) is observable. The behavior of the nuclear ratio $\sigma^{A}_{\mathrm{dip}}/\sigma_{0}$ 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↗

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↗

arXiv2022

Higher order approximations to the longitudinal structure function $F_{L}$ from the parametrization of $F_{2}$ based on the Laplace transformation

We describe the determination of the longitudinal structure function $F_{L}$ at NLO and NNLO approximations, using Laplace transform techniques, into the parametrization of $F_{2}(x,Q^{2})$ and its derivative with respect to $\ln{Q^{2}}$ at low values of the Bjorken variable $x$. The obtained results are comparable with others by considering the effect of the charm quark mass to the longitudinal structure function, which leads to rescaling variable for $n_{f}=4$. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable $F_{L}(x,Q^{2})$ at small $x$ in a wide range of $Q^{2}$ values and can be applied as well in analyses of ultra-high energy processes with cosmic neutrinos. The obtained longitudinal structure functions with and without the LHeC simulated uncertainties [CERN-ACC-Note-2020-0002, LHeC Collaboration and FCC-he Study Group, P. Agostini et al., J. Phys. G: Nucl. Part. Phys. {\bf48}, 110501(2021).] are compared with the H1 Collaboration data [Eur.Phys.J.C{\bf74}, 2814(2014) and Eur.Phys.J.C{\bf71}, 1579 (2011)] and with the results from CT18 [Phys.Rev.D{\bf103}, 014013(2021)] parametrization model at NLO and NNLO approximations.

hep-ph↗

arXiv2021

The color dipole model bounds with the gluon-gluon recombination correction

We present nonlinear (NL) and higher twist (HT) corrections to the color dipole model (CDM) bounds at low values of $x$ and $Q^{2}$ using the parameterization method. Consistency between the bounds at this region describe that a transition from the linear to the nonlinear behavior is dependence on the behavior of the gluon distribution function. The parameters in the color dipole model are comparable with the color dipole bounds at low values of $Q^{2}$. Consequently, the obtained reduced cross sections at low and moderate $Q^{2}$ values due to the NL+HT effects show a good agreement with the H1 data.

hep-ph↗

arXiv2021

Nonlinear corrections on the parameterization methods

We present non-linear corrections (NLC) to the distribution functions at low values of $x$ and $Q^{2}$ using the parametrization $F_{2}(x,Q^{2})$ and $F_{L}(x,Q^{2})$. We use a direct method to extract non-linear corrections to the ratio of structure functions and the reduced cross section in the next-to-next-to-leading order (NNLO) approximation with respect to the parametrization method (PM). Comparison between the non-linear results with the bounds in color dipole model (CDM) and HERA data indicate the consistency of the non-linear behavior of the gluon distribution function at low-$x$ and low-$Q^{2}$. The non-linear longitudinal structure functions are comparable with the H1 Collaboration data in a wide range of $Q^{2}$ values. Consequently, the non-linear corrections at NNLO approximation to the reduced cross sections at low and moderate $Q^{2}$ values show good agreement with the HERA combined data. These results at low $x$ and low $Q^{2}$ can be applied to the LHeC region for analyses of ultra-high-energy processes.

hep-ph↗

arXiv2021

An Evaluation of The Proton Structure Functions $F_{2}$ and $F_{L}$ at Small $x$

We describe the determination of the DIS structure functions $F_{2}$ and $F_{L}$ by using the singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Altarelli-Martinelli equations at small values of $x$. The determination of the longitudinal structure function is presented as a parameterization of $F_{2}(x,Q^{2})$ and its derivative. Analytical expressions for $σ_{r}(x,Q^{2})$ in terms of the effective parameters of the parameterization of $F_{2}(x,Q^{2})$ and $F_{L}(x,Q^{2})$ are presented. This analysis is enriched by including the higher-twist effects in calculation of the reduced cross sections which is important at low-$x$ and low-$Q^{2}$ regions. Numerical calculations and comparison with H1 data demonstrate that the suggested method provides reliable $F_{L}(x,Q^{2})$ and $σ_{r}(x,Q^{2})$ at low $x$ in a wide range of the low absolute four-momentum transfers squared ($1.5~\mathrm{GeV}^{2}<Q^{2}<120~\mathrm{GeV}^{2}$) at moderate and high inelasticity. Expanding the method to low and ultra low values of $x$ can be considered in the process analysis of new colliders. We compare the obtained longitudinal structure function with respect to the LHeC simulated uncertainties [CERN-ACC-Note-2020-0002, arXiv:2007.14491 [hep-ex] (2020)] with the results from CT18 [Phys.Rev.D{\bf103}, 014013(2021)] parametrization model.

hep-ph↗

arXiv2021

Influence of gluon behavior on heavy-quark pair production

We check the impact of the gluon distribution due to the number of active flavor employed in the calculation of heavy-quark deep-inelastic scattering (DIS) electro-production on the reduced cross section and structure functions determined in the leading order (LO) and next-to-leading order (NLO) quantum chromodynamics (QCD) analysis using the Hadron Electron Ring Accelerator (HERA) combined data. The charm and beauty structure functions are determined and compared with the HERA combined data. The results are in good agreement with respect to the experimental data. We also compare the obtained charm and bottom structure functions with the results from CTEQ6.6 [Phys.Rev.D{\bf78}, 013004(2008)] and NNPDF3.1[Eur.Phys.J.C{\bf77}, 663(2017)] parameterization models. The effect of gluon density on these calculations depends on the number of active flavor at asymptotical values of the momentum transfer $Q^{2}$. Also, in the HERA kinematic range, the ratio of $F_{2}^{c\overline{c}}/F_{2}$ and $F_{2}^{b\overline{b}}/F_{2}$ are obtained. These results and comparison with the HERA combined data demonstrate that the suggested method can be applied in analysis of new colliders.

hep-ph↗

arXiv2020

The study of the gluon distribution function and reduced cross section behavior using the proton structure function

The behavior of the gluon distribution function and the reduced cross section considered from the proton structure function and its derivatives at low values of $x$. These behaviors studied and compared with the experimental data. These results are augmented by including an additional higher-twist term in the description of the nonlinear correction. This additional term, modified nonlinear correction, improves the description of the reduced cross sections significantly at low values of $Q^{2}$. We discuss, furthermore, how this behavior can be determine the reduced cross section with respect to the proton parameterization at high-y values. The resulting predictions for $σ_{r}$ suggest that further corrections are required for $Q^{2}$ less than about $3~\mathrm{GeV}^{2}$.

hep-ph↗

arXiv2020

Longitudinal structure function from the parton parameterization

We present a set of formulas to extract the longitudinal structure function from the proton structure function and its derivatives with respect to lnQ2 in the next-to-next-to-leading order of the perturbative theory at low x based on a hard poemron exchange. The behavior of the DIS cross section ratio R(x;Q2) and the ratio FL(x;Q2)=F2(x;Q2) studied and compared with the experimental data, also these behaviors controlled by the color dipole model bound. These results show a good agreement with the DIS experimental data throughout the low values of x. These results within the next-to-next-to-leading order approximation at very low x can be applied in the LHeC region for analyses of ultra-high energy processes.

hep-ph↗

arXiv2020

Searching for top quark pair production cross section at LHeC and FCC-eh

The deep inelastic scattering mode of $t\overline{t}$ pair production at the proposed LHeC and FCC-eh is considered. We present a method to extract the top reduced cross section related to the transversal structure function $F_{2}(x,Q^{2})$ parameterization. Numerical calculations with known kinematics of the LHeC and FCC-eh colliders are demonstrated. The results obtained for charm and beauty pair production are comparable with the experimental data. We show that for a wide range of the momentum transfer into the top quark pair, the reduced cross section is well described by center-of-mass energies.

hep-ph↗

arXiv2020

The Color Dipole Picture and extracting the ratio of structure functions at small $x$

We present a set of formulas to extract the ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ and $R(x,Q^{2})$ from the proton structure function parameterized in the next-to-next-to-leading order of the perturbative theory at low $x$ values. The behavior of these ratios are considered with respect to the power-law behavior of the proton structure function. The results are compared with experimental data and the color dipole model bounds. These ratios are in good agreement with the HERA data throughout the fixed value of the invariant mass. The behavior of these ratios controlled by the nonlinear corrections at low values of $Q^{2}$. These results and comparison with HERA data demonstrate that the suggested method for the ratio of structure functions can be applied in analyses of the LHeC and FCC-eh projects.

hep-ph↗

arXiv2019

Ratio of the structure functions and the color dipole model bound

We observe that the DGLAP evolution equations at NNLO analysis predicts a ratio of the structure functions in region of small Bjorken variable $x$. The ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ is obtained and compared with the prediction of the dipole model and HERA data. In particular we show that this ratio is lower than dipole model bound at high-$Q^{2}$ values and it is higher at low-$Q^{2}$ values . Then the effect of adding a higher twist term to the description of the ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ for $Q^{2}< 20~GeV^{2}$ is investigated. Also the bounds are discussed by including charm distribution on $F_{L}/F_{2}$. We discuss, furthermore, how this ratio can be determine the proton structure function with respect to the reduced cross section at high-$y$ values.

hep-ph↗

arXiv2019

The behavior of the structure function by using the effective exponent at low-x

An analytical solution of the QCD evolution equations for the singlet and gluon distribution is presented. We decouple DGLAP evolution equations into the initial conditions by using a Laplace transform method at $N^{n}LO$ analysis. The relationship between the nonlinear behavior and color dipole model is considered based on an effective exponent behavior at low-$x$ values. We obtain the effective exponent at NLO analysis from the decoupled behavior of the distribution functions. The proton structure function compared with H1 data from the inclusive structure function $F_{2}(x,Q^{2})$ for $x {\leq}~ 10^{-2}$ and $5 {\leq} Q^{2} {\leq} 250~GeV^{2}$.

hep-ph↗