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Eugene Levin

Publications and source records attributed to Eugene Levin.

At least 19 recordsLinked to original sources
arXiv2026

Dipole-dipole scattering at high energy in the Pomeron field theory with Braun Hamiltonian and beyond

In this paper we find that the scattering matrix for dipole-dipole interaction in the saturation region has the form: ${\cal S}^d_d \xrightarrow{z \,\gg\,1} \exp\Lb - C^d_d z^2\Rb \propto \Lb {\cal S}_{BK}\Rb^4 = \exp\Lb - 4\,C_{BK} z^2\Rb$, where $z = \bas \kappa Y\,+\,\ln\Lb \frac{r^2}{r'^2}\Rb$ for interaction of a dipole $r$ at rapidity $Y$ with dipole $r'$ at rest. $S_{BK}$ is the S-matrix for the Balitsky-Kovchegov amplitude. All constants are determined in the text. The proof is given in the same theoretical framework for both cases (${\cal S}^d_d$ and ${\cal S}_{BK}$): the Pomeron interaction which takes into account the Pomeron vertices in the leading $1/N_c$ approximation ($N_c$ is the number of colours). This result is in striking contradiction with 'rare' fluctuation approach as well as with summing the large Pomeron loops. These lead to ${\cal S}^d_d \propto \sqrt{{\cal S}_{BK}}$ at large $z$. In the paper we collect arguments supporting the idea that the sum of large Pomeron loops can be trusted in a wide region of energy: $Y \leq 1/\as^4$. In addition we discuss the influence of the structure of the Hamiltonian on the asymptotic behaviour of the scattering amplitudes using the exactly solvable one dimensional model as our theoretical ground.

hep-ph↗
arXiv2026

Multiplicity distribution of produced gluons in deep inelastic scattering: main equations and their homotopy solutions for heavy nuclei

In this paper we discuss the multiplicity distribution in the deep inelastic processes in the frame work of high energy QCD. We obtained three results. First, we get the new derivation of the equations for the cross sections of productions of $n$-cut Pomerons in the final states ($\sigma_n$). These equations coincide with the equations that have been derived using the Abramovsky, Gribov and Kancheli (AGK) cutting rules but based on the dipole approach to QCD. Second, we developed the homotopy approach for finding the solutions to these equations. It consists with the analytic solution for the first iteration and the converge procedure of calculating the next iterations using computing. Third, we found the analytical solution for $\sigma_n$ at large $n\,\gtrsim\,N(z) = 2 N_0 \,z\,\exp( z^2/(2 \kappa))$ with $z = \ln( r^2\,Q^2_s )$. Using this solution we calculate the entropy of the produced gluons at large $z$: $S_E = \ln \left( N(z)\right)$, where the saturation momentum $Q_s$ and all constants are discussed in the text.

hep-ph↗
arXiv2026

SentiFuse: Deep Multi-model Fusion Framework for Robust Sentiment Extraction

Sentiment analysis models exhibit complementary strengths, yet existing approaches lack a unified framework for effective integration. We present SentiFuse, a flexible and model-agnostic framework that integrates heterogeneous sentiment models through a standardization layer and multiple fusion strategies. Our approach supports decision-level fusion, feature-level fusion, and adaptive fusion, enabling systematic combination of diverse models. We conduct experiments on three large-scale social-media datasets: Crowdflower, GoEmotions, and Sentiment140. These experiments show that SentiFuse consistently outperforms individual models and naive ensembles. Feature-level fusion achieves the strongest overall effectiveness, yielding up to 4\% absolute improvement in F1 score over the best individual model and simple averaging, while adaptive fusion enhances robustness on challenging cases such as negation, mixed emotions, and complex sentiment expressions. These results demonstrate that systematically leveraging model complementarity yields more accurate and reliable sentiment analysis across diverse datasets and text types.

cs.CL↗
arXiv2026

CaST: Causal Discovery via Spatio-Temporal Graphs in Disaster Tweets

Understanding causality between real-world events from social media is essential for situational awareness, yet existing causal discovery methods often overlook the interplay between semantic, spatial, and temporal contexts. We propose CaST: Causal Discovery via Spatio-Temporal Graphs, a unified framework for causal discovery in disaster domain that integrates semantic similarity and spatio-temporal proximity using Large Language Models (LLMs) pretrained on disaster datasets. CaST constructs an event graph for each window of tweets. Each event extracted from tweets is represented as a node embedding enriched with its contextual semantics, geographic coordinates, and temporal features. These event nodes are then connected to form a spatio-temporal event graph, which is processed using a multi-head Graph Attention Network (GAT) \cite{gat} to learn directed causal relationships. We construct an in-house dataset of approximately 167K disaster-related tweets collected during Hurricane Harvey and annotated following the MAVEN-ERE schema. Experimental results show that CaST achieves superior performance over both traditional and state-of-the-art methods. Ablation studies further confirm that incorporating spatial and temporal signals substantially improves both recall and stability during training. Overall, CaST demonstrates that integrating spatio-temporal reasoning into event graphs enables more robust and interpretable causal discovery in disaster-related social media text.

cs.SI↗
arXiv2025

Dipole-dipole scattering: summing large Pomeron loops in non-linear evolution with leading twist kernel

It is shown in this paper that the QCD equations for dipole density have the natural solution: the 'fan' diagrams of the Pomeron calculus. We found the dipole densities comparing the analytic solution to the Balitsky-Kovchegov (BK) equation for the simplified leading twist kernel with the $t$ channel unitarity. Using these densities we calculate the contributions of large Pomeron loops to dipole-dipole scattering at high energies. Applying the Abramovsky,Gribov and Kancheli cutting rules we found that the produced gluons are distributed accordingly the KNO (Koba, Nielsen and Olesen) law which leads to the entropy $S_E = \ln(x G(x,Q^2))$ in an agreement with Kharzeev - Levin predictions.

hep-ph↗
arXiv2025

Homotopy approach for scattering amplitude for running QCD coupling

In this paper we proposed the homotopy approach for solving the nonlinear Balitsky-Kovchegov (BK) evolution equation with running QCD coupling. The approach consists of two steps. First, is the analytic solution to the nonlinear evolution equation for the simplified, leading twist kernel. Second, is the iteration procedure that allow us to calculate corrections analytically or semi-numerically. For the leading twist kernel it is shown that the first iteration leads to $\leq 1\%$ accuracy. The $\zeta = -\frac{4N_c}{b_0}Y \ln\Lb \bas (1/Q^2_s(Y))/\bas\Lb r^2\Rb\Rb$ ($r$ is the dipole size, $Q_s$ is the saturation scale) and geometric scaling behaviour of the scattering amplitude are discussed as well as the dependence on the value of the infrared cutoff.

hep-ph↗
arXiv2025

Modified Homotopic approach for diffractive production

We review the recent developments of the use of the homotopy method for solving the non-linear evolution equation for the diffractive production in deep inelastic scattering. We introduce part of the non-linear corrections in the linear term. This simplified non-linear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. It turns out that these corrections are rather small and can be estimated in the regular iterative procedure.

hep-ph↗
arXiv2025

Summing large Pomeron loops in the saturation region: dipole-nucleus collision beyond nonlinear equations

In this paper we found the dipole-nucleus scattering amplitude at high energies by summing large Pomeron loops. It turns out that the energy dependence of this amplitude is the same as for dipole-dipole scattering. It means that the Balitsky-Kovchegov (BK) equation, which has been derived to describe this scattering, can be trusted only in the limited range of energies: $z \,\leq\, \sqrt{2\,\kappa\,C}A^{1/6} $

hep-ph↗
arXiv2024

Particle production in the toy world: multiplicity distribution and entropy

In this paper we found the multiplicity distribution of the produced dipoles in the final state for dipole-dipole scattering in the zero dimension toy models. This distribution shows the great differences from the distributions of partons in the wave function of the projectile. However, in spite of this difference the entropy of the produced dipoles turns out to be the same as the entropy of the dipoles in the wave function. This fact is not surprising since in the parton approach only dipoles in the hadron wave function which can be produced at $t = +\infty$ and measured by the detectors. We can also confirm the result of Kharzeev and Levin that this entropy is equal to $S_E = \ln\bigl(xG(x)\bigr)$, where we denote by $xG$ the mean multiplicity of the dipoles in the deep inelastic scattering. The evolution equations for $\sigma_n$ are derived.

hep-ph↗
arXiv2024

Can $1/N_c$ corrections be treated in the Pomeron calculus?

The main goal of the paper is to show that we can treat the $1/N_c$ QCD corrections in the Pomeron calculus. We develop the one dimensional model which is a simplification of the QCD approach that includes $\pom \to 2 \pom$, $2 \pom \to \pom$ and $ 2 \pom \to 2 \pom$ vertices and gives the description of the high energy interaction, both in the framework of the parton cascade and in the Pomeron calculus. In this model we show that the scattering amplitude can be written as the sum of Green's function of $n$ Pomeron exchanges $G_{n \pom} \propto e^{ \omega_n \Y}$ with $\omega_n =\kappa\,n^2$ at $\kappa \ll 1$. This means that choosing $\kappa = 1/N^2_c$ we can reproduce the intercepts of QCD in $1/N_c$ order. The scattering amplitude is an asymptotic series that cannot be sum using Borel approach. We found a general way of summing such series. In addition to the positive eigenvalues we found the set of negative eigenvalues which corresponds to the partonic description of the scattering amplitude. Using Abramowsky, Gribov and Kancheli cutting rules we found the multiplicity distributions of the produced dipoles as well as their entropy $S_E$.

hep-ph↗
arXiv2024

Summing large Pomeron loops in the saturation region: amplitude and multiplicity distributions for dipole-dipole scattering

In this paper we found the parton densities at high energies. Their expressions stems from our attempts to reconcile the exact solution to the Balitsky-Kovchegov (BK) equation, which describes the rare fluctuation in the dipole-target scattering, with the fact that this equation sums the 'fan' Pomeron diagrams. Using these densities we can calculate the contributions of large Pomeron loops to dipole-dipole scattering at high energies. We detected that the scattering matrix for this process has the same suppression as was predicted by Iancu and Mueller from their estimates of the 'rare' fluctuation in QCD. Applying the Abramovsky,Gribov and Kancheli cutting rules we found that the produced gluons are distributed accordingly the KNO (Koba, Nielsen and Olesen) law which leads to the entropy $S_E = \ln(x G(x,Q^2))$. $xG$ has to be in the saturation region at high energies.

hep-ph↗
arXiv2024

High energy scattering in the Unitary Toy Model

We continue exploring the Unitary Toy Model (UTM) as a playground for high energy collisions in QCD. Our new approach is based on the diagonalization of the evolution Hamiltonian. Part of the spectrum can be identified with intercepts of dressed Pomerons. Analogously to QCD, a multi-Pomeron expansion of the $S$-matrix is badly divergent asymptotic series. Yet we succeeded to establish resummation procedures resulting in a well behaved $S$-matrix. In addition the Hamiltonian possesses negative eigenvalues, which dominate the approach of the $S$-matrix to saturation. We are hopeful that important lessons about BFKL-based Pomeron calculus could be taken from the toy world to real QCD.

hep-ph↗
arXiv2024

Modified homotopy approach for diffractive production in the saturation region

In this paper we continue to develop the homotopy method for solving of the non linear evolution equation for the diffractive production in deep inelastic scattering(DIS). We introduce part of the nonlinear corrections as a first step of this approach. This simplified nonlinear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. At the second step of our approach we demonstrated that the perturbative procedure can be used for the remaining parts of the non-linear corrections. It turns out that these corrections are small and can be estimated in the regular iterative procedure.

hep-ph↗
arXiv2024

Scattering amplitude in QCD: summing large Pomeron loops

In this paper we show that the sum of enhanced BFKL Pomeron loop diagrams generates the scattering amplitude, which turns out to be much smaller, than in the case of deep inelastic scattering. We use the simplified BFKL kernel in the leading twist approximation, which reproduces the main features of the scattering amplitude in the deep inelastic scattering(DIS). For such kernel the results are highly unexpected and they contradict (i) the solution to the Balitsky- Kovchegov(BK) equation for the scattering amplitude; (ii) the idea that the scattering amplitude stems from rare fluctuation and it has the same form as in DIS ; and (iii) the numerical simulations. We sincerely hope, that we made a mistake, which we failed to note, and which our reader will find. If not , we need to reconsider our view on the sum of the BFKL Pomeron loops and accept that their summing will lead to large contribution of the rare configurations in CGC approach to the scattering amplitude.

hep-ph↗
arXiv2023

Multiplicity distribution and entropy of produced gluons in deep inelastic scattering at high energies

In this paper we found the multiplicity distribution of the produced gluons in deep inelastic scattering at large $z=\ln\LbQ^2_s/Q^2\Rb\,\,\gg\,\,1$ where $ Q_s $ is the saturation momentum and $Q^2$ is the photon virtuality. It turns out that this distribution at large $n > \bar{n}$ almost reproduces the KNO scaling behaviour with the average number of gluons $ \bar{n} \propto \exp\Lb z^2/2 \kappa\Rb$, where $\kappa = 4.88 $ in the leading order of perturbative QCD. TheKNO function $\Psi\Lb \frac{n}{\bar{n}}\Rb = \exp\Lb -\,n/\bar{n}\Rb$. For $n < \bar{n}$ we found that $\sigma_n \propto\Big( z - \sqrt{2 \,\kappa\,\ln (n-1)}\Big)/(n-1)$. Such small $n$ determine the value of entropy of produced gluons $S_E = 0.3\, z^2/(2\,\kappa)$ at large $z$. The factor $0.3$ stems from the non-perturbative corrections that provide the correct behaviour of the saturation momentum at large $b$.

hep-ph↗
arXiv2023

Homotopy solution to non-linear evolution for heavy nuclei

In the paper we suggest the homotopy method for solving of the non linear evolution equation. This method consists of two steps. First is the analytical solution for the linearized version of the non-linear evolution deep in the saturation region. Second, the perturbative procedure is suggested to take into account the remaining parts of the non-linear corrections. It turns out that these corrections are rather small and can be estimated in the regular iterative procedure.

hep-ph↗
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 $G_{n \pom}\Lb Y\Rb\propto \exp\Lb \frac{n^2}{N^2_c} \Delta_{\mbox{\tiny BFKL}} Y\Rb$ where $N_c $ is the number of colours ,Y is the rapidity and $\Delta_{\mbox{\tiny BFKL}}$ 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.

hep-ph↗