arXiv subjects

Tomasz Stebel

Publications and source records attributed to Tomasz Stebel.

At least 19 recordsLinked to original sources

arXiv2026

Simultaneous Color Glass Condensate fit to deep inelastic scattering and forward hadron production at HERA, RHIC, and the LHC

We present the first simultaneous fit to deep inelastic scattering (DIS) reduced cross sections from HERA and forward single inclusive hadron production (SIHP) from RHIC and the LHC in which the dipole amplitude is obtained from Balitsky--Kovchegov (BK) evolution within the Color Glass Condensate effective theory. We demonstrate that, using the LO BK equation with running coupling (with or without kinematical constraint) and a constant per-collider $K$-factor accounting for higher-order corrections, a global $χ^2/\mathrm{d.o.f.}$ close to unity is achieved in both schemes. The required $K$-factors are about a factor of two larger at RHIC than at the LHC, remarkably in agreement with threshold-resummed one-loop studies of forward production. In our setup and with the data available, we find the two observables to be complementary: the SIHP data tighten the constraint on the evolution speed of the dipole amplitude without introducing tension with the DIS description. We further quantify the dependence of the $K$-factors on the fragmentation-function set and the factorization scale, identifying these as the dominant systematic uncertainties to be addressed in future precision analyses of forward hadron production. We perform a full uncertainty analysis using the Hessian method, validated against a Monte Carlo Bayesian inference study.

hep-ph↗

arXiv2026

The eikonal spin-dependent Odderon and gluon Sivers function of a proton, and its small-$x$ evolution

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small $x_0 \sim 0.1$ and transverse momentum $k_\perp \lesssim 1$~GeV. The model light-cone (LC) wave function predicts the properties of $x f_{1T}^{\perp g}(x,k_\perp)$ such as its overall magnitude, the position of its peak in $k_\perp$, and its behavior at small $k_\perp$. We then compute numerically the BFKL anomalous dimension characterizing the power-law tail at $k_\perp \gtrsim 1.5$~GeV of the gluon Sivers function at small (but pre-asymptotic) LC momentum fractions, $α_s \log x_0/x = 1$: $x f_{1T}^{\perp g}(x,k_\perp) \sim k_\perp^{-3.3}$.

hep-ph↗

arXiv2026

Small-x TMD distributions initial condition: Nc-dependence and Gaussian approximations

We systematically derive expressions for ten small-$x$ Transverse Momentum Dependent (TMD) distributions in the Gaussian approximation, three in the quark-gluon sector and seven in the gluon-gluon sector; for the general $SU(N_c)$ gauge group. The derived formulae depend on the logarithm of the dipole amplitude. Using the McLerran-Venugopalan model for the initial condition, we simulate the dipole amplitude as well as estimate all ten TMD distributions for $N_c \in \{2,3,4,5\}$. We compare these explicit numerical results with the derived expressions and find very good agreement for all studied values of $N_c$. Consequently, we study the scaling with $N_c$ of the TMD distributions. Thanks to that, we are able to derive the large-$N_c$ limit of the Gaussian approximation results and show that they agree with expressions obtained in the mean-field approximation. By comparing with our numerical results, we are able to demonstrate the size, origin, and significance of subleading-$N_c$ corrections. This work sets the stage for a systematic study of subleading corrections induced by the JIMWLK evolution in the rapidity evolution of the TMD distributions. Interestingly, we find an exact sum rule that relates all seven gluon-gluon TMD operators at $N_c = 3$ and arbitrary $x$.

hep-ph↗

arXiv2026

Variational Autoregressive Networks with probability priors

Monte Carlo methods are essential across diverse scientific fields, yet their efficiency is frequently hampered by critical slowing down-a sharp increase in autocorrelation times near phase transitions. Although deep learning approaches, such as neural-network-based samplers, have been proposed to alleviate this issue, they face another serious problem: the difficulty of training the models. This difficulty partially stems from the overly general nature of original machine-learning architectures, which often ignore underlying physical symmetries and force networks to relearn them from scratch. In this paper, we demonstrate that incorporating physical priors into the model significantly enhances performance. Building upon existing strategies that integrate spin-spin interactions, we propose a framework that utilizes a prior probability distribution as a starting point for training. Our results for the Ising model, as well as for the Edwards-Anderson spin glass model, suggest that moving away from `blank slate' models in favor of physics-informed priors reduces the training burden and facilitates the simulation of larger system sizes in discrete spin models.

cs.LG↗

arXiv2026

Sampling two-dimensional spin systems with transformers

Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be computationally inefficient. In this work, we propose a novel approach to transformer-based neural samplers in which we generate not a single spin per step but groups of spins. As an additional improvement, we construct a model of approximated probabilities, further improving the efficiency of the algorithm. Despite our approach being computationally heavier than dense networks or CNN-based approaches, we were able to sample larger systems of up to $180 \times 180$ spins in case of the Ising model. The Effective Sample Size of our sampler is $\sim 20$ times larger than that of the previous state-of-the-art neural sampler when trained for the $128 \times 128$ Ising model at critical temperature. Finally, we also test our algorithm on the 2D Edwards-Anderson model, where we train $64\times 64$ spin systems.

cond-mat.dis-nn↗

arXiv2025

Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions

We present a detailed numerical investigation of semi-inclusive forward di-hadron production in proton-nucleus collisions employing the Color Glass Condensate effective theory. We focus on the regime where di-hadrons are produced nearly back-to-back in the transverse plane, thereby justifying a transverse-momentum-dependent factorization approach in terms of small-$x$ gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky-Kovchegov equation with running coupling, ii) both perturbative and non-perturbative Sudakov resummation, and iii) a phenomenologically constrained model for the initial conditions for small-$x$ gluon distributions. We compare this phenomenological framework to experimental data from the STAR Collaboration on azimuthal correlations in forward di-pion production in both proton-proton and proton-gold collisions. We analyze the systematic theoretical uncertainties associated with the saturation scales of nuclei at the initial scale for rapidity evolution and with those associated with the hadronization process. Finally, we make predictions for the kinematics anticipated to be covered by the ALICE Forward Calorimeter (FoCal) upgrade at the Large Hadron Collider.

hep-ph↗

arXiv2025

Improving the solver for the Balitsky-Kovchegov evolution equation with Automatic Differentiation

The Balitsky-Kovchegov (BK) evolution equation is an equation derived from perturbative Quantum Chromodynamics that allows one to evolve with collision energy the scattering amplitude of a pair of quark and antiquark off a hadron target, called the dipole amplitude. The initial condition, being a non-perturbative object, usually has to be modeled separately. Typically, the model contains several tunable parameters that are determined by fitting to experimental data. In this contribution, we propose an implementation of the BK solver using differentiable programming. Automatic differentiation offers the possibility that the first and second derivatives of the amplitude with respect to the initial condition parameters are automatically calculated at all stages of the simulation. This fact should considerably facilitate and speed up the fitting step. Moreover, in the context of Transverse Momentum Distributions (TMD), we demonstrate that automatic differentiation can be used to obtain the first and second derivatives of the amplitude with respect to the quark-antiquark separation. These derivatives can be used to relate various TMD functions to the dipole amplitude. Our C++ code for the solver, which is available in a public repository, includes the Balitsky one-loop running coupling prescription and the kinematic constraint. This version of the BK equation is widely used in the small-$x$ evolution framework.

hep-ph↗

arXiv2025

Hierarchical autoregressive neural networks in three-dimensional statistical system

Autoregressive Neural Networks (ANN) have been recently proposed as a mechanism to improve the efficiency of Monte Carlo algorithms for several spin systems. The idea relies on the fact that the total probability of a configuration can be factorized into conditional probabilities of each spin, which in turn can be approximated by a neural network. Once trained, the ANNs can be used to sample configurations from the approximated probability distribution and to explicitly evaluate this probability for a given configuration. It has also been observed that such conditional probabilities give access to information-theoretic observables such as mutual information or entanglement entropy. In this paper, we describe the hierarchical autoregressive network (HAN) algorithm in three spatial dimensions and study its performance using the example of the Ising model. We compare HAN with three other autoregressive architectures and the classical Wolff cluster algorithm. Finally, we provide estimates of thermodynamic observables for the three-dimensional Ising model, such as entropy and free energy, in a range of temperatures across the phase transition.

cond-mat.stat-mech↗

arXiv2025

State-of-the-art cross sections for ttH: NNLO predictions matched with NNLL resummation and EW corrections

We present new, state-of-the-art predictions for the associated production of the SM Higgs boson with top quarks, computed in accordance with the recommendations of the LHC Higgs Working Group. The NNLO QCD predictions, derived through suitable approximations of the two-loop virtual contribution, are supplemented with soft-gluon resummation up to NNLL accuracy. Two distinct resummation frameworks are employed - one based on direct QCD and the other on soft-collinear effective theory - and their features are compared in detail. These results are further combined with the complete-NLO corrections, yielding the most precise SM predictions for this process to date. The relevant sources of theoretical uncertainties are thoroughly estimated and discussed.

hep-ph↗

arXiv2025

Estimation of the reduced density matrix and entanglement entropies using autoregressive networks

We present an application of autoregressive neural networks to Monte Carlo simulations of quantum spin chains using the correspondence with classical two-dimensional spin systems. We use a hierarchy of neural networks capable of estimating conditional probabilities of consecutive spins to evaluate elements of reduced density matrices directly. Using the Ising chain as an example, we calculate the continuum limit of the ground state's von Neumann and Rényi bipartite entanglement entropies of an interval built of up to 5 spins. We demonstrate that our architecture is able to estimate all the needed matrix elements with just a single training for a fixed time discretization and lattice volume. Our method can be applied to other types of spin chains, possibly with defects, as well as to estimating entanglement entropies of thermal states at non-zero temperature.

quant-ph↗

arXiv2025

NeuMC -- a package for neural sampling for lattice field theories

We present the \texttt{NeuMC} software package, based on \pytorch, aimed at facilitating the research on neural samplers in lattice field theories. Neural samplers based on normalizing flows are becoming increasingly popular in the context of Monte-Carlo simulations as they can effectively approximate target probability distributions, possibly alleviating some shortcomings of the Markov chain Monte-Carlo methods. Our package provides tools to create such samplers for two-dimensional field theories.

hep-lat↗

arXiv2025

Gluon Sivers function from forward exclusive $χ_{c1}$ photoproduction on unpolarized protons

Exclusive production of a $χ_{c1}$ axial vector quarkonia in photon-proton scattering at high energies requires a $C$-odd $t$-channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as $t \to 0$. Alternatively, a $C$-odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the collinear trigluon correlator or the $k_\perp$-moment of the gluon Sivers function. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient $λ_θ$ governing the angular distribution of the $χ_{c1} \to J/ψ+ γ$ decay as functions of $x$. We point out that these observables constrain the magnitude of the gluon Sivers function at small $x$ which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions.

hep-ph↗

arXiv2024

Reconciling the kinematical constraint with the JIMWLK evolution equation: correlation functions non-local in rapidity

In the high-energy limit of DIS experiments the effective degrees of freedom of QCD are Wilson line operators. Their evolution in the rapidity variable is predicted by the set of Balitsky-JIMWLK evolution equations. We analyze a new class of two-point correlation functions of Wilson line operators where the Wilson lines are taken at different values of the rapidity variable. Such correlation functions can appear in the discussion of the kinematical constraint. We find that in the Langevin formulation of the JIMWLK equation, such correlation functions are affected by an infrared divergence. We discuss a possible regularization of this divergence and its consequences for the implementation of the kinematical constraint for the JIMWLK equation.

hep-ph↗

arXiv2024

Photon-Odderon interference in exclusive $χ_{c}$ charmonium production at the Electron-Ion Collider

Exclusive $C=+1$ scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a $C$-odd $t$-channel exchange of a photon or a three gluon ladder. We derive the expressions for the corresponding amplitudes. The relative phase of the photon vs. three gluon exchange amplitudes is determined by the sign of the light-front matrix element of the eikonal color current operator $d^{abc}J^{+a}J^{+b}J^{+c}$ at moderate $x$, and is not affected by small-$x$ QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer $|t|\sim 1$~GeV$^2$ where the cross section for $χ_{cJ}$ production exceeds that for pure photon exchange by up to a factor of 4. We find that exclusive $χ_{cJ}$ electroproduction at the Electron-Ion Collider should occur with well measurable rates and measurements of these processes should allow to find an evidence of the perturbative Odderon exchange. We also compute the total electroproduction cross section as a function of energy and provide first estimates of the number of $χ_{cJ}$ events per month at the Electron-Ion Collider design luminosity.

hep-ph↗

arXiv2024

Rényi entanglement entropy of spin chain with Generative Neural Networks

We describe a method to estimate Rényi entanglement entropy of a spin system, which is based on the replica trick and generative neural networks with explicit probability estimation. It can be extended to any spin system or lattice field theory. We demonstrate our method on a one-dimensional quantum Ising spin chain. As the generative model, we use a hierarchy of autoregressive networks, allowing us to simulate up to 32 spins. We calculate the second Rényi entropy and its derivative and cross-check our results with the numerical evaluation of entropy and results available in the literature.

cond-mat.stat-mech↗

arXiv2024

Training normalizing flows with computationally intensive target probability distributions

Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of lattice field theories (LFT) the target distribution is given by the exponential of the action. The common loss function's gradient estimator based on the "reparametrization trick" requires the calculation of the derivative of the action with respect to the fields. This can present a significant computational cost for complicated, non-local actions like e.g. fermionic action in QCD. In this contribution, we propose an estimator for normalizing flows based on the REINFORCE algorithm that avoids this issue. We apply it to two dimensional Schwinger model with Wilson fermions at criticality and show that it is up to ten times faster in terms of the wall-clock time as well as requiring up to $30\%$ less memory than the reparameterization trick estimator. It is also more numerically stable allowing for single precision calculations and the use of half-float tensor cores. We present an in-depth analysis of the origins of those improvements. We believe that these benefits will appear also outside the realm of the LFT, in each case where the target probability distribution is computationally intensive.

cs.LG↗

arXiv2024

Back-to-back inclusive dijets in DIS at small $x$: Complete NLO results and predictions

We compute the back-to-back dijet cross-section in deep inelastic scattering (DIS) at small $x$ to next-to-leading order (NLO) in the Color Glass Condensate effective field theory. Our result can be factorized into a convolution of the Weizsäcker-Williams gluon transverse momentum dependent distribution function (WW gluon TMD) with a universal soft factor and an NLO coefficient function. The soft factor includes both double and single logarithms in the ratio of the relative transverse momentum $P_\perp$ of the dijet pair to the dijet momentum imbalance $q_\perp$; its renormalization group (RG) evolution is resummed into the Sudakov factor. Likewise, the WW TMD obeys a nonlinear RG equation in $x$ that is kinematically constrained to satisfy both lifetime and rapidity ordering of the projectile. Exact analytical expressions are obtained for the NLO coefficient function of transversely and longitudinally polarized photons. Our results allow for the first quantitative separation of the dynamics of Sudakov suppression from that of gluon saturation. They can be extended to other final states and provide a framework for precision tests of novel QCD many-body dynamics at the Electron-Ion Collider.

hep-ph↗

arXiv2023

Mutual information of spin systems from autoregressive neural networks

We describe a new direct method to estimate bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It allows studying arbitrary geometries of subsystems and can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply-connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.

cond-mat.stat-mech↗