arXiv subjects

Eugene Levin

Publications and source records attributed to Eugene Levin.

At least 37 records · Page 2Linked to original sources

arXiv2023

Can $1/N_c$ corrections destroy the saturation of dipole densities?

In this paper we discuss a well known QCD result: the steep increase of Green's function for exchange of $n$ BFKL Pomerons $G_{n \pom}\Lb Y\Rb\propto \exp\Lb \frac{n^2}{N^2_c} Δ_{\mbox{\tiny BFKL}} Y\Rb$ where $N_c $ is the number of colours ,Y is the rapidity and $Δ_{\mbox{\tiny BFKL}}$ is the intercept of the BFKL Pomeron. We consider this problem in the framework of the simple Pomeon models in zero transverse dimensions, which have two advantages :(i) they allow to take into account all shadowing corrections, including the summation of the Pomeron loops and (ii) they have the same as in QCD striking increase of $G_{n \pom}\Lb Y\Rb $. We found that the strength of shadowing corrections is not enough to stop the increase of the scattering amplitude with energy in contradiction to the unitarity constraints. Hence, our answer to the question in the title is positive.We believe that we need to search an approach beyond of the BFKL Pomeron calculus to treat $1/N_c$ corrections in Colour Glass Condensate effective theory.

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arXiv2022

Soft Pomeron in the Colour Glass Condensate approach

In this paper we suggest a new approach to the structure of the soft Pomeron: based on the $t$-channel unitarity, we expressed the exchange of the soft Pomeron through the interaction of the dipole of small size of the order of $1/Q_s(Y)$ ($Q_s(Y)$ is the saturation momentum) with the hadrons. Therefore, it is shown that the typical distances in soft processes are small $r \sim 1/Q_s\Lb \h Y \Rb $, where $Y \,=\,ln s$. The saturation momentum, which determines the energy dependence of the scattering amplitude is proportional to $ Q^2_s\Lb \h Y \Rb \propto\,\exp\Lb\h λ\,Y\Rb$, with $λ\approx\,0.2$, and this behaviour is in perfect agreement with phenomenological Donnachie-Landshoff Pomeron. We demonstrate that the saturation models could describe the experimental data for $σ_{tot},σ_{el},σ_{diff} $ and $B_{el}$. Hence our approach is a good first approximation to start discussion of the soft processes in CGC approach on the solid theoretical basis.

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arXiv2021

Multiplicity distribution of dipoles in QCD from Le, Mueller and Munier equation

In this paper we derived in QCD the BFKL linear, inhomogeneous equation for the factorial moments of multiplicity distribution($M_k$) from LMM equation. In particular, the equation for the average multiplicity of the color-singlet dipoles($N$) turns out to be the homogeneous BFKL while $M_k \propto N^k$ at small $x$. Second, using the diffusion approximation for the BFKL kernel we show that the factorial moments are equal to: $M_k=k!N( N-1)^{k-1}$ which leads to the multiplicity distribution:$ \frac{σ_n}{σ_{in}}=\frac{1}{N} ( \frac{N\,-\,1}{N})^{n - 1}$. We also suggest a procedure for finding corrections to this multiplicity distribution which will be useful for descriptions of the experimental data.

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arXiv2021

Deep inelastic scattering as a probe of entanglement: confronting experimental data

Parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton. For very small $x$, the proton becomes a maximally entangled state. This approach leads to a simple relation $S = \ln N $ between the average number $N$ of color-singlet dipoles in the proton wave function and the entropy of the produced hadronic state $S$. At small $x$, the multiplicity of dipoles is given by the gluon structure function, $N = x G(x,Q^2)$. Recently, the H1 Collaboration analyzed the entropy of the produced hadronic state in DIS, and studied its relation to the gluon structure function; poor agreement with the predicted relation was found. In this letter we argue that a more accurate account of the number of color-singlet dipoles in the kinematics of H1 experiment (where hadrons are detected in the current fragmentation region) is given not by $xG(x,Q^2)$ but by the sea quark structure function $xΣ(x,Q^2)$. Sea quarks originate from the splitting of gluons, so at small $x$ $xΣ(x,Q^2)\,\sim\, xG(x,Q^2)$, but in the current fragmentation region this proportionality is distorted by the contribution of the quark-antiquark pair produced by the virtual photon splitting. In addition, the multiplicity of color-singlet dipoles in the current fragmentation region is quite small, and one needs to include $\sim 1/N$ corrections to $S= \ln N$ asymptotic formula. Taking both of these modifications into account, we find that the data from the H1 Collaboration in fact agree well with the prediction based on entanglement.

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arXiv2021

Non-linear evolution in the re-summed next-to-leading order of perturbative QCD:\confronting the experimental data

In this paper we compare the experimental HERA data with the next-to-leading order approach (NLO) of Ref.[C.~Contreras, E.~Levin, R.~Meneses and M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029). This approach includes the re-summed NLO corrections to the kernel of the evolution equation, the correct asymptotic behaviour in the NLO at $τ= r^2 Q^2_s \,\gg\,1$; the impact parameter dependence of the saturation scale in accord with the Froissarrt theorem as well as the non-linear corrections. In this paper, we successfully describe the experimental data with the quality, which is not worse, than in the leading order fits with larger number of the phenomenological parameters. It is demonstrated, that the data could be described, taking into account both the diffusion on $\ln(k_T)$, which stems from perturbative QCD, and the Gribov's diffusion in impact parameters. It is shown an ability to describe the data at rather large values of $α_S$.

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arXiv2020

Reggeon Field Theory and Self Duality: Making Ends Meet

Motivated by the question of unitarity of Reggeon Field Theory, we use the effective field theory philosophy to find possible Reggeon Field Theory Hamiltonians $H_{RFT}$. We require that $H_{RFT}$ is self dual, reproduce all known limits (dilute-dense and dilute-dilute) and exhibits all the symmetries of the JIMWLK Hamiltonian. We find a family of Hamiltonians which satisfy all the above requirements. One of these is identical in form to the so called "diamond action" discussed in \cite{diamond,Balitsky05}. However we show by explicit calculation that the so called "diamond condition" is not satisfied beyond leading perturbative order.

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arXiv2020

The JIMWLK evolution and the s-channel unitarity

Further developing ideas set forth in \cite{KLL}, we discuss QCD Reggeon Field Theory (RFT) and formulate restrictions imposed on its Hamiltonian by the unitarity of underlying QCD. We identify explicitly the QCD RFT Hilbert space, provide algebra of the basic degrees of freedom (Wilson lines and their duals) and the algorithm for calculating the scattering amplitudes. We formulate conditions imposed on the "Fock states" of RFT by unitary nature of QCD, and explain how these constraints appear as unitarity constraints on possible RFT hamiltonians that generate energy evolution of scattering amplitudes. We study the realization of these constraints in the dense-dilute limit of RFT where the appropriate Hamiltonian is the JIMWLK Hamiltonian $H_{JIMWLK}$. We find that the action $H_{JIMWLK}$ on the dilute projectile states is unitary, but acting on dense "target" states it violates unitarity and generates states with negative probabilities through energy evolution.

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arXiv2020

Non-linear equation in the re-summed next-to-leading order of perturbative QCD: the leading twist approximation

In this paper, we use the re-summation procedure, suggested in Refs.\cite{DIMST,SALAM,SALAM1,SALAM2}, to fix the BFKL kernel in the NLO. However, we suggest a different way to introduce th non-linear corrections in the saturation region, which is based on the leading twist non-linear equation. In the kinematic region:$τ\,\equiv\,r^2 Q^2_s(Y)\,\leq\,1$ , where $r$ denotes the size of the dipole, $Y$ its rapidity and $Q_s$ the saturation scale, we found that the re-summation contributes mostly to the leading twist of the BFKL equation. Assuming that the scattering amplitude is small, we suggest using the linear evolution equation in this region. For $τ\,>\,1$ we are dealing with the re-summation of $\Lb \bas \,\ln τ\Rb^n$ and other corrections in NLO approximation for the leading twist.We find the BFKL kernel in this kinematic region and write the non-linear equation, which we solve analytically. We believe the new equation could be a basis for a consistent phenomenology based on the CGC approach.

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arXiv2020

QCD Odderon: non linear evolution in the leading twist

In the paper we propose and solve analytically the non-linear evolution equation in the leading twist approximation for the Odderon contribution. We found three qualitative features of this solution, which differs the Odderon contribution from the Pomeron one :(i) the behaviour in the vicinity of the saturation scale cannot be derived from the linear evolution in a dramatic difference with the Pomeron case; (ii) a substantial decrease of the Odderon contribution with the energy; and (iii) the lack of geometric scaling behaviour. The two last features have been seen in numerical attempts to solve the Odderon equation.

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arXiv2019

Multiplicity distributions as probes of quarkonia production mechanisms

In this paper we demonstrate that the vigorously growing multiplicity distributions measured by STAR and ALICE present a strong evidence in favor of multigluon fusion mechanisms of the quarkonia production in CGC approach. We analyze the contribution of 3-gluon fusion mechanism and demonstrate that it gives a sizeable contribution to quarkonia yields, as well as predicts correctly the multiplicity distributions for $J/ψ$ at RHIC and LHC. We also make predictions for other quarkonia states, such as $ψ(2S)$ and $Υ(1S)$, and find that the multiplicity dependence of these states should be comparable to similar dependence for $J/ψ$. Finally, we discuss an experimental setup in which very strong multiplicity dependence could be observed. This observation would be a strong evidence in favor of CGC approach.

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arXiv2019

Lev Lipatov: my friend and renowned physicist

These notes are written for the book "From the past to the future: the legacy of Lev Lipatov", editors: Jochen Bartels et all, which will be published by WS. I tried to share with you the atmosphere and the flavour of everyday life in Gribov's theory department, where Lev matured as an independent researcher and wrote all his breakthrough papers.

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arXiv2019

BFKL equation in the next-to-leading order: solution at large impact parameters

In this paper, we show (i) that the NLO corrections do not change the power-like decrease of the scattering amplitude at large impact parameter ($b^2 \,>\,r^2 \exp\left( 2\bar(α}_S η(1 + 4 \barα_S)\right)$, where $r$ denotes the size of scattering dipole and $η\,=\,\ln(1/x_{Bj})$ for DIS), and, therefore, they do not resolve the inconsistency with unitarity; and (ii) they lead to an oscillating behaviour of the scattering amplitude atlarge $b$, in direct contradiction with the unitarity constraints. However, from the more practical point of view, the NLO estimates give a faster decrease of the scattering amplitude as a function of $b$, and could be very useful for description of the experimental data. It turns out, that in a limited range of $b$, the NLO corrections generates the fast decrease of the scattering amplitude with $b$, which can be parameterized as $N\, \propto\,\exp( -\,μ\,b)$ with $μ\,\propto \,1/r$ in accord with the numerical estimates in Ref.[1].

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arXiv2018

$J/ψ$ production in hadron scattering: three-pomeron contribution

In this paper we discuss the inclusive $J/ψ$ production in proton-proton collisions from fusion of three pomerons. We demonstrate that this mechanism gets dominant contribution from the region which can be theoretically described by CGC/Saturation approach. Numerically, it gives a substantial contribution to the $J/ψ$ production, and is able to describe the experimentally observable shapes of the rapidity, momenta and multiplicity distributions. The latter fact provides a natural explanation of the experimentally observed enhancement of multiplicity distribution in $J/ψ$ production.

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arXiv2018

DGLAP evolution for DIS diffraction production of high masses

In this paper we develop the DGLAP evolution for the system of produced gluons in the process of diffractive production in DIS, directly from the evolution equation in Color Glass Condensate approach. We are able to describe the available experimental data with small value of the QCD coupling ($\bar{α_S} \approx 0.1$). We conclude that in diffractive production, we have a dilute system of emitted gluons and in the order to describe them, we need to develop the next-to-leading order approach in perturbative QCD.

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arXiv2018

CGC/saturation approach: an impact-parameter dependent model for diffraction production in DIS

In the paper we discussed the evolution equations for diffractive production in the framework of CGC/saturation approach, and found the analytical solutions for several kinematic regions. The most impressive features of these solutions are, that diffractive production does not exibit geometric scaling behaviour i.e. being a function of one variable. Based on these solutions, we suggest an impact parameter dependent saturation model, which is suitable for describing diffraction production both deep in the saturation region, and in the vicinity of the saturation scale. Using the model we attempted to fit the combined data on diffraction production from H1 and ZEUS collaborations. We found that we are able describe both $x_\pom$ and $β$ dependence, as well as $Q$ behavior of the measured cross sections. In spite of the sufficiently large $χ^2/d.o.f.$ we believe that our description provides an initial impetus to find a fit of the experimental data, based on the solution of the CGC/saturation equation, rather than on describing the diffraction system in simplistic manner, assuming that only quark-antiquark pair and one extra gluons, are produced.

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arXiv2016

BFKL pomeron with massive gluons and running coupling

In this paper we proceed with the study of the Pomeron spectrum, by solving numerically the BFKL equation with massive gluons and running coupling. The spectrum of Regge singularities is discrete and the leading Pomeron has a considerable dependence on nonperturbative effects, for which we use Higgs mechanism as a model. We cross-checked this result with variational method and confirmed the infrared sensitivity of leading Pomeron. This fact is related to the infrared instability of the BFKL equation in QCD, with a running coupling. The subleading poles have a mild sensitivity to the soft physics, and are well described by known semiclassical methods. We also discuss the dependence on various prescriptions of the running coupling arguments.

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arXiv2016

QCD unitarity constraints on Reggeon Field Theory

We point out that the $s$-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.

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arXiv2016

On the energy spectrum of the electroweak Pomeron

In this paper we study the high energy behaviour of Electroweak Standard Model for a nonzero Weinberg angle $θ_{W}$. We evaluate the spectrum of the electroweak pomeron and demonstrate that the leading intercept is given by $α_{\rm e.w.}4 \ln 2$ and does not depend on the mixing angle $θ_{W}$. Due to its very small numerical value, we conclude that the high energy behaviour of electroweak theory cannot be discussed without including the QCD Pomeron which, at sufficiently large energies, will dominate.

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