arXiv subjects

Krzysztof Kutak

Publications and source records attributed to Krzysztof Kutak.

At least 19 recordsLinked to original sources

arXiv2026

Deep inelastic scattering as a probe of entanglement: the complete QCD dipole cascade

We study entanglement entropy in Deep Inelastic Scattering (DIS) using the dipole formulation of the high-energy limit of QCD. We argue that a reduced density matrix arises in low $x$ DIS due to a trace over unobserved color degrees of freedom and we obtain entanglement entropy in terms of dipole multiplicities, directly from the von Neumann entropy. Dipole multiplicities are obtained from a solution to low $x$ evolution equations, which we solve numerically. Unlike previous studies, we take into account both transverse-size and azimuthal-angle dependence in the dipole evolution kernel. We study both the exact solution of the equation as well as its double leading-logarithmic approximation (DLLA). We find that for the same initial dipole size, the DLLA solution generates a larger entropy. Finally, we calculate the dipole multiplicities and entanglement entropy and compare our results to the Shannon entropy of hadron multiplicities, as measured by the H1 collaboration.

hep-ph↗

arXiv2026

Entanglement entropy, Monte Carlo event generators, and soft gluons DIScovery

We study entropy production in Deep Inelastic Scattering using Monte Carlo simulations. We show that the dominant contribution to entropy is due to soft gluons. This contribution is usually neglected in standard Monte Carlo approaches, since it does not affect hadronic spectra. However, it is relevant for entropy and multiplicity distributions, as we demonstrate with explicit calculations. We further show that as one includes soft gluons, making the Monte Carlo parton distributions closer to inclusive PDFs, the resulting entropy starts to grow with decreasing x. This provides further evidence that the bulk of the measured entropy originates from initial-state effects.

hep-ph↗

arXiv2026

Entropy and mean multiplicity from dipole models in the high energy limit

The 1D Mueller dipole model, its high energy limit, and its generalization were investigated. To address the ambiguity stemming from different definitions of the pseudorapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, $S(\ln\langle n\rangle$, as a universal observable. From the solutions of the models, we calculate both the entropy and the average charged particle multiplicity and compare to data measured in proton-proton collisions. We obtained these quantities directly from the measured charged particle multiplicity distributions and determine the model parameters via fits. We find that the generalized dipole model provides a significantly better description of the data than the 1D Mueller model.

hep-ph↗

arXiv2026

The Balitsky-Kovchegov equation for dipole gluon density in the momentum space

I present derivation the BK equation for the dipole gluon density in momentum space, starting from its standard formulation in coordinate space. I review the equation for both proton and nuclear targets, and I also discuss the resummed BK evolution.The purpose of this paper is to consolidate derivations and formulas scattered across the literature, to show in detail how the structure of the triple-Pomeron vertex emerges in the unfolded form of the nonlinear term, and to establish a consistent notation throughout.

hep-ph↗

arXiv2025

Cascades of gluons at high energies and their QI measures

In this contribution we report on recent extension of one dimensional dipole cascade models to account for saturation and transition to vacuum \cite{Kutak:2025syp}. We analyze properties of the models using Quantum Information tools. Furthermore, we present a description of the hadronic entropy measured by LHCb and predictions for the purity measurement. %we provide description of hadronic entropy as measured by LHCb and provide predictions for measurement of purity.

hep-ph↗

arXiv2025

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models

We investigate and compare QCD dipole cascade models, the 1D Mueller dipole model, its high energy limit and its generalization that follows from studies of 1D systems with conformal symmetry. To address the ambiguity stemming from different definitions of the rapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, $S(\ln\langle n \rangle)$, as a universal observable. From the solutions of the models, we calculate both the entropy and the average charged particle multiplicity and compare to data measured in proton-proton collisions. We obtained these quantities directly from the measured multiplicity distributions and determine the model parameters via fits. We find that the generalized dipole model provides a significantly better description of the data than the 1D Mueller model.

hep-ph↗

arXiv2025

Entropy, purity and gluon cascades at high energies with recombinations and transitions to vacuum

We study one dimensional dipole cascade models in the high-energy limit of QCD. Motivated by data on hadron multiplicities in the LHCb kinematical range, we generalize existing cascade models for splitting and recombination to account also for transitions to the vacuum. This modification allows us to describe the data. Furthermore, we perform both analytical and numerical studies of the cascades and find that the cascade including loop corrections, as well as the one accounting for transitions to the vacuum, can both be related to the Negative Binomial Distribution. In the latter case, however, one must properly normalize the cascade to account for transitions to the vacuum. We also study the scaling properties of the cascades and identify new regimes, which we call "focal" and "parallel." Finally, we investigate the Quantum Information (QI) measures of the cascades, which allow us to highlight their distinctive properties.

hep-ph↗

arXiv2025

Revisiting gluon density from the BK equation with kinematical constraint and large x terms

We perform analysis of the small x non-linear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in wide range of transverse momentum and longitudinal momentum fraction extending previous studies performed in \cite{Kutak:2003bd,Kutak:2004ym}. The linear part of the equation is motivated by the renormalization group improved small x approach which accounts for resummation of higher orders, and includes collinear splitting function and kinematical constraint. The solution to the equation is then used to perform the fit to Deep Inelastic Scattering reduced cross section data.

hep-ph↗

arXiv2025

Predictions for photon-jet correlations at forward rapidities in heavy-ion collisions

In this work, we study for the first time jet-medium interactions in heavy-ion collisions with introduction of saturation and Sudakov effects with parameters tuned for upcoming forward calorimeter acceptances in experiments, in particular the ALICE FoCal detector. We focus on $γ+$jet correlations by taking into account in-medium parton evolution using the BDIM equation that describes jet interactions with the quark-gluon plasma (QGP) combined with vacuum-like emissions (VLE). We systematically introduce the early time gluon saturation dynamics through the small-$x$ Improved Transverse Momentum Dependent factorization (ITMD). For our purpose, we use Monte Carlo programs KATIE and TMDICE to generate hard events and in-medium parton evolution, respectively. We present results of azimuthal correlations and nuclear modification ratios to gauge the impact of the gluon saturation effects at early time for the in-medium jet energy loss.

hep-ph↗

arXiv2024

QCD evolution of entanglement entropy

Entanglement entropy has emerged as a novel tool for probing nonperturbative quantum chromodynamics (QCD) phenomena, such as color confinement in protons. While recent studies have demonstrated its significant capability in describing hadron production in deep inelastic scatterings, the QCD evolution of entanglement entropy remains unexplored. In this work, we investigate the differential rapidity-dependent entanglement entropy within the proton and its connection to final-state hadrons, aiming to elucidate its QCD evolution. Our analysis reveals a strong agreement between the rapidity dependence of von Neumann entropy, obtained from QCD evolution equations, and the corresponding experimental data on hadron entropy. These findings provide compelling evidence for the emergence of a maximally entangled state, offering new insights into the nonperturbative structure of protons.

hep-ph↗

arXiv2024

Krylov complexity and gluon cascades in the high energy limit

We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high-energy QCD. In particular, we observe that the cascade equation of the dipole model is equivalent to the $SL(2,R)$ Schrodinger equation in the Krylov basis. Consequently, the Krylov complexity corresponds to the average distribution of partons and the Krylov entropy is the counterpart the entanglement entropy computations of \cite{Kharzeev:2017qzs}. Our work not only brings new tools for exploring quantum information and complexity in QCD, but also gives hope for experimental tests of some of the recent, physical probes of quantum complexity.

hep-ph↗

arXiv2024

Entanglement entropy of proton and its relation to thermodynamics entropy

I discuss the thermodynamics-based derivation of the formula for the entanglement entropy of a system of gluons. The derivation is based on an approach where saturation and the Unruh effect were used to obtain and discuss the entropy of gluons. The formula agrees, in the high-energy limit, up to a numerical factor, with more recent results, where arguments based on the density matrix and bipartition of the proton were used to obtain the formula. I also discuss the relation of entropy as obtained in BFKL in DLL approximation and with the application of the BK equation.

hep-ph↗

arXiv2024

Probing the onset of maximal entanglement inside the proton in diffractive DIS

It has been proposed that at small Bjorken $x$, or equivalently at high energy, hadrons represent maximally entangled states of quarks and gluons. This conjecture is in accord with experimental data from the electron-proton collider HERA at the smallest accessible $x$. In this Letter, we propose to study the onset of the maximal entanglement inside the proton using Diffractive Deep Inelastic Scattering. It is shown that the data collected by the H1 Collaboration at HERA allows to probe the transition to the maximal entanglement regime. By relating the entanglement entropy to the entropy of final state hadrons, we find a good agreement with the H1 data using both the exact entropy formula as well as its asymptotic expansion which indicates the presence of a nearly maximally-entangled state. Finally, future opportunities at the Electron Ion Collider are discussed.

hep-ph↗

arXiv2023

Evidence for the maximally entangled low $x$ proton in Deep Inelastic Scattering from H1 data

We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low $x$ and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low $x$, which we obtain from an unintegrated gluon distribution subject to next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both next-to-next-to-leading order and next-to-next-to-leading with small $x$ resummation, where the latter provides an acceptable description of data.

hep-ph↗

arXiv2023

Forward $γ$+jet production in proton-proton and proton-lead collisions at LHC within the FoCal calorimeter acceptance

Using the small-$x$ Improved Transverse Momentum Dependent factorization (ITMD), which, for a general two-to-two massless scattering can be proved within the Color Glass Condensate (CGC) theory for transverse momenta of particles greater than the saturation scale, we provide predictions for isolated forward photon and jet production in proton-proton and proton-nucleus collisions within the planned ALICE FoCal detector acceptance. We study azimuthal correlations, $p_T$ spectra, as well as normalized ratios of proton-proton cross sections for different energies. The only TMD distribution needed for that process is the "dipole" TMD gluon distribution, which in our computations is based on HERA data and undergoes momentum space BK evolution equation with DGLAP corrections and Sudakov resummation. We conclude, that the process provides an excellent probe of the dipole TMD gluon distribution in saturation regime.

hep-ph↗

arXiv2023

Transverse momentum broadening of medium-induced cascades in expanding media

In this work, we explore the features of gluonic cascades in static and Bjorken expanding media by numerically solving the full BDIM evolution equations in longitudinal momentum fraction $x$ and transverse momentum $\boldsymbol{k}$ using the Monte Carlo event generator MINCAS. Confirming the scaling of the energy spectra at low-$x$, discovered in earlier works, we use this insight to compare the amount of broadening in static and expanding media. We compare angular distributions for the in-cone radiation for different medium profiles with the effective scaling laws and conclude that the out-of-cone energy loss proceeds via the radiative break-up of hard fragments, followed by an angular broadening of soft fragments. While the dilution of the medium due to expansion significantly affects the broadening of the leading fragments, we provide evidence that in the low-$x$ regime, which is responsible for most of the gluon multiplicity in the cascade, the angular distributions are very similar when comparing different medium profiles at an equivalent, effective in-medium path length. This is mainly due to the fact that in this regime, the broadening is dominated by multiple splittings. Finally, we discuss the impact of our results on the phenomenological description of the out-of-cone radiation and jet quenching.

hep-ph↗

arXiv2023

Effects of gluon kinematics and the Sudakov form factor on the dipole amplitude

We investigate effects of exact gluon kinematics on the parameters of the Golec-Biernat-Wüsthoff, and Bartels-Golec-Biernat-Kowalski saturation models. The resulting fits show some differences, particularly, in the normalization of the dipole cross section $σ_0$. The refitted models are used for the dijet production process in DIS to investigate effects of the Sudakov form factor at Electron Ion Collider energies.

hep-ph↗

arXiv2023

Sudakov effects and the dipole amplitude

In this study we incorporate the Sudakov form factor into the dipole factorization formula, where the hard scale of the former is provided by the photon virtuality $Q^2$. We obtain a general formula which we then apply to the well-known GBW and BGK saturation models. Parameters of the above Sudakov-improved models are successfully fitted to the $F_2$ data from HERA. We observe, in particular, that inclusion of the Sudakov factor on top of the GBW model improves description of data at large $Q^2$.

hep-ph↗