arXiv subjects

Eugene Levin

Publications and source records attributed to Eugene Levin.

At least 55 records · Page 3Linked to original sources

arXiv2016

CGC/saturation approach: a new impact-parameter dependent model in the next-to-leading order of perturbative QCD

This paper is the first attempt to build CGC/saturation model based on the next-to-leading order corrections to linear and non-linear evolution in QCD. We assume that the renormalization scale is the saturation momentum and found that the scattering amplitude has geometric scaling behaviour deep in the saturation domain with the explicit formula of this behaviour at large $τ= r^2 Q^2_s$. We built a model that include this behaviour, as well as the ingredients that has been known: (i) the behaviour of the scattering amplitude in the vicinity of the saturation momentum, using the NLO BFKL kernel, (ii) the pre-asymptotic behaviour of $\ln\Lb Q^2_s\Lb Y \Rb\Rb$, as function of $Y$ and (iii) the impact parameter behaviour of the saturation momentum, which has exponential behaviour $\propto \exp\Lb -\, m\, b\Rb$ at large $b$.We demonstrated that the model is able to describe the experimental data for the deep inelastic structure function. Despite this, our model has difficulties that are related to the small value of the QCD coupling at $Q_s\Lb Y_0\Rb$ and the large values of the saturation momentum, which indicate the theoretical inconsistency of our description.

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arXiv2015

CGC/saturation approach: a new impact-parameter dependent model

{In this paper we propose a new impact-parameter dependent CGC/saturation model. We introduce two new features in the model that make it consistent with what we know theoretically about the deep inelastic scattering. They are: the use of the exact form of the solution to the non-linear (BK) equation, whereas in all previous attempts only the form of $r^2Q^2_s$ dependence, has been taken into account; and the large impact parameter dependence, through the $b$-dependence of the saturation momentum which reproduce the correct behaviour of the amplitude at large impact parameters $b$ ($A \propto \exp\Lb - μb\Rb$) as well as at large momentum transferred $Q_T$ ($A $ decreases as a power of $Q_T$ as it follows from perturbative QCD). These improvement compared to all previous attempts to build such models, allows us to claim, that the experimental data are in accord with the prediction of CGC/saturation approach while previously, based on similar models, we could only conclude that the DIS data, perhaps, can be described by introducing the shadowing corrections at small photon virtualities.

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arXiv2015

Semiclassical solution to the BFKL equation with massive gluons

In this paper we proceed to study the high energy behavior of a scattering amplitudes in the Yang-Mills theory with the Higgs mechanism for the gauge boson mass. The spectrum of the $j$-plane singularities of the $t$-channel partial waves, and corresponding eigenfunctions of the BFKL equation in leading log approximation (LLA), were previously calculated by us numerically in arXiv:1401.4671 . Here we develop a semiclassical approach and investigate the influence of the impact parameter exponential decrease, existing in this model, on the high energy asymptotic behaviour of the scattering amplitude. This approach is much simpler than the numerical calculations, and reproduces our earlier numerical results. The analytical (semianalytical) solutions which have been found in this paper, can be used to incorporate correctly the large impact parameter behavior in the framework of CGC/saturation approach. This behaviour is interesting as provides the high energy amplitude for the electroweak theory, which can be measured experimentally.

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arXiv2014

Large $\mathbf{b}$ behaviour in the CGC/saturation approach: BFKL equation with pion loops

In this paper we proposed a solution to the longstanding problem of the CGC/saturation approach: the power-like fall of the scattering amplitudes at large $b$. This decrease leads to the violation of the Froissart theorem and makes the approach theoretically inconsistent. We showed in the paper that sum of the pion loops results in the exponential fall of the scattering amplitude at large impact parameters and in the restoration of the Froissart theorem.

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arXiv2014

Azimuthal angle correlations in hadron-nucleus scattering: enhanced diagrams

In this paper we calculate the contribution to rapidity and angular correlations of the first Pomeron loop diagram in the dense partonic environment. This diagram is expected to give the largest contribution to the density variation mechanism of the angular correlations. We show that this diagrams leads to sizable contributions to the rapidity correlation functions of the order of $σ_{in} /\Lb πR^2\Rb$ where $σ_{in}$ is the inelastic cross section and $R$ is the size of the typical dipole inside the proton saturation scale. Therefore, the correlations do not depend on the saturation scale. We demonstrated that density variation mechanism does not lead to suppression of the angular dependance of the double inclusive cross section generating the coefficient in front of $\cos^2 φ$ in $A^{1/3}$ larger in the case of hadron-nucleus collision than in hadron-hadron interaction. The angular correlations are suppressed in comparison with the rapidity ones but only due to large multiplicity of the produced gluons. We consider this paper as the first attempt of quantitative description of the density variation mechanism in CGC/saturation approach.

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arXiv2014

Non linear evolution: revisiting the solution in the saturation region

In this paper we revisit the problem of the solution to Balitsky-Kovchegov equation deeply in the saturation domain. We find that solution has the form of Levin-Tuchin solution but it depends on variable $\bar{z} = \ln(r^2 Q^2_s) + \mbox{Const}$ and the value of $\mbox{Const}$ is calculated in this paper. We propose the solution for full BFKL kernel at large $z$ in the entire kinematic region that satisfies the McLerram-Venugopalan initial condition

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arXiv2014

KLWMIJ Reggeon Field Theory beyond the large $N_c$ limit

We extend the analysis of KLWMIJ evolution in terms of QCD Reggeon fields beyond leading order in the $1/N_c$ expansion. We show that there is only one type of corrections to the leading order Hamiltonian discussed in \cite{last}. These are terms linear in original Reggeons and quadratic in conjugate Reggeon operators. All of these have the interpretation as vertices of the "`merging"' type $2\rightarrow 1$, where two Reggeons merge into one. Importantly, the triple Pomeron merging vertex does not emerge from the KLWMIJ Hamiltonian. We show that, although in the range of applicability of the KLWMIJ Hamiltonian these merging terms are subleading in $N_c$, in the dense-dense regime they all become of the same (leading) order in $N_c$. In this regime vertices involving higher Reggeons are enhanced by inverse powers of the coupling constant.

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arXiv2014

Reggeon Field Theory for Large Pomeron Loops

We analyze the range of applicability of the high energy Reggeon Field Theory $H_{RFT}$ derived in [1]. We show that this theory is valid as long as at any intermediate value of rapidity $η$ throughout the evolution at least one of the colliding objects is dilute. Importantly, at some values of $η$ the dilute object could be the projectile, while at others it could be the target, so that $H_{RFT}$ does not reduce to either $H_{JIMWLK}$ or $H_{KLWMIJ}$. When both objects are dense, corrections to the evolution not accounted for in [1] become important. The same limitation applies to other approaches to high energy evolution available today, such as for example [3] and [4]. We also show that, in its regime of applicability $H_{RFT}$ can be simplified. We derive the simpler version of $H_{RFT}$ and in the large $N_c$ limit rewrite it in terms of the Reggeon creation and annihilation operators. The resulting $H_{RFT}$ is explicitly self dual and provides the generalization of the Pomeron calculus developed in [4] by including higher Reggeons in the evolution. It is applicable for description of `large' Pomeron loops, namely Reggeon graphs where all the splittings occur close in rapidity to one dilute object (projectile), while all the merging close to the other one (target). Additionally we derive, in the same regime expressions for single and double inclusive gluon production (where the gluons are not separated by a large rapidity interval) in terms of the Reggeon degrees of freedom.

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arXiv2014

BFKL Pomeron with massive gluons

We solve the BFKL equation in the leading logarithmic approximation numerically in the Yang-Mills theory with the Higgs mechanism for the vector boson mass generation. It can be considered as a model for the amplitude with the correct behavior of the $s$-channel partial waves at large impact parameters. The Pomeron spectrum of the massive BFKL kernel in the $ω$-space for $t=0$ coincides with the continuous spectrum for the massless case although the density of its eigenvalues is two times smaller for $ω>ω_0$, where $ω_0$ is a negative number. We find a simple parametrization for the corresponding eigenfunctions. Because the leading singularity in the $ω$-plane in this Higgs model for $t=0$ is a fixed cut, the Regge pole contributions could be only for non-physical positive $t$. Hence we can state that the correct behaviour at large $b$ does not influence the main properties of the BFKL equation.

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arXiv2013

Dipole-dipole scattering in CGC/saturation approach at high energy: summing Pomeron loops

In this paper we demonstrate that the dense system of partons (gluons) can be produced in dilute-dilute system scattering, using the example of dipole-dipole collisions. This increase in density stems from the intensive gluon cascades that can be described by the enhanced BFKL Pomeron diagrams (Pomeron loops). For the first time we found the analytical solution to the equation for diffraction production in the dipole-dense parton system scattering, using the simplified BFKL kernel. Having this solution as well as the solution to Balitsky- Kovchegov equation we developed technique that allowed us to calculate the total cross section, cross sections for single and double diffractions in the MPSI approximation. Calculating inclusive production and two gluon correlations we see that the dense and strongly correlated system of gluons can be produced at high energy in the dipole-dipole scattering.

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arXiv2013

BFKL equation with running QCD coupling and HERA data

In this paper we developed approach based on the BFKL evolution in $\ln\Lb Q^2\Rb$. We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good $χ^2/d.o.f. \approx 1.3$. From our description of the experimental data we learned several lessons; (i) the non-perturbative physics at long distances started to show up at $Q^2 = 0.25\,GeV^2$; (ii) the scattering amplitude at $Q^2 = 0.25\,GeV^2$ cannot be written as sum of soft Pomeron and the secondary Reggeon but the Pomeron interactions should be taken into account; (iii) the Pomeron interactions can be reduced to the enhanced diagrams and, therefore, we do not see any needs for the shadowing corrections at HERA energies; and (iv) we demonstrated that the shadowing correction could be sizable at higher than HERA energies without any contradiction with our initial conditions.

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arXiv2013

BFKL Pomeron: modeling confinement

In this paper we introduce the confinement into the kernel of the BFKL equation,assuming that the sizes of produced dipoles cannot be large. The goal of this paper is to find how this assumption, which leads to a correct exponential decrease of the amplitude at large impact parameters, affects the main properties of the BFKL Pomeron. We solve the equations for total cross section and $\ <| b^2 |\ >$ numerically and developed some methods of analytical solutions. The main result is that the modified BFKL Pomeron has the same intercept and $α'_\pom = 0$ as the BFKL Pomeron.It gives us a hope that the unknown confinement will change only slightly the equations of the CGC/saturation approach

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arXiv2013

BFKL Pomeron calculus: solution to equations for nucleus-nucleus scattering in the saturation domain

In this paper we solve the equation for nucleus-nucleus scattering in the BFKL Pomeron calculus, suggested by Braun. We find these solutions analytically at high energies as well as numerically in the entire region of energies inside the saturation region. The semi-classical approximation is used to select out the infinite set of the parasite solutions. The nucleus-nucleus cross sections at high energy are estimated and compared with the Glauber-Gribov approach. It turns out that the exact formula gives the estimates that are very close to the ones based on Glauber-Gribov formula which is important for the practical applications

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arXiv2012

Nuclear modification factor for gluon jets

It is shown that the nuclear modification factor can be smaller that unity for jet production at small $x$ and at large transverse momentum without any violation of the factorization theorem and the initial state effects is able to explain the nuclear modification factor of the order of the one measured by ATLAS. In other word, initial state effects are able to describe the jet quenching for the gluon jet production.

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arXiv2012

Gluon saturation: survival probability for leading neutrons in DIS

In this paper we discuss the example of one rapidity gap process: the inclusive cross sections of the leading neutrons in deep inelastic scattering with protons (DIS). The equations for this process are proposed and solved, giving the example of theoretical calculation of the survival probability for one rapidity gap processes. It turns out that the value of the survival probability is small and it decreases with energy

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arXiv2011

BFKL Pomeron calculus: nucleus-nucleus scattering

In this paper the action of the BFKL Pomeron calculus is re-written in momentum representation, and the equations of motion for nucleus-nucleus collisions are derived, in this representation. We found the semi-classical solutions to these equations, outside of the saturation domain. Inside this domain these equations reduce to the set of delay differential equations, and their asymptotic solutions are derived.

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arXiv2011

The Ridge from the BFKL evolution and beyond

We show that the long-range rapidity correlations between the produced charged-hadron pairs from two BFKL parton showers generate considerable azimuthal angle correlations. These correlations have no 1/N_c suppression. The effect of gluon saturation on these correlations are discussed and we show that it is important. We show that a pronounced ridge-like structure emerges by going from the BFKL to the saturation region. We show that the ridge structure at high-energy proton-proton and nucleus-nucleus collisions has the same origin and its main feature can be understood due to initial-state effects. Although the effects of final-state interactions in the latter case can be non-negligible.

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arXiv2011

High density QCD and nucleus-nucleus scattering deeply in the saturation region

In this paper we solve the equations that describe nucleus nucleus scattering, in high density QCD,in the framework of the BFKL Pomeron calculus. We found that (i) the contribution of short distances to the opacity for nucleus-nucleus scattering dies at high energies, (ii) the opacity tends to unity at high energy, and (iii) the main contribution that survives comes from soft (long distance) processes for large values of the impact parameter. The corrections to the opacity $Ω\Lb Y,b\Rb = 1$ were calculated and it turns out that they have a completely different form, namely($1 - Ω\to \exp\Lb - Const\,\sqrt{Y}\Rb$) than the opacity that stems from the Balisky-Kovchegov equation, which is($1 - Ω\to \exp\Lb - Const\,Y^2\Rb$). We reproduce the formula for the nucleus-nucleus cross section that is commonly used in the description of nucleus-nucleus scattering, and there is no reason why it should be correct in the Glauber-Gribov approach

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