arXiv subjects

Vladimir V. Skokov

Publications and source records attributed to Vladimir V. Skokov.

At least 37 records · Page 2Linked to original sources

arXiv2023

Entanglement entropy of the proton in coordinate space

We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region $\bar A$ of radius $L$, where $L$ is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in $\bar A$. For both, quarks and gluons we obtain the same simple result: $S_E =-\int\frac{dx}{Δx}\, N_{L^2}(x)\log[N_{a^2}(x)]$, where $a$ is the UV cutoff in coordinate space and $Δx$ is the longitudinal resolution scale. Here $N_{S}(x)$ is the number of partons (of the appropriate species) with longitudinal momentum fraction $x$ inside an area $S$. It is related to the standard parton distribution function (PDF) by $N_S(x)=\frac{S}{A_p}\, Δx\, F(x)$, where $A_p$ denotes the transverse area of the proton.

hep-ph↗

arXiv2023

Classical Entanglement and Entropy

Motivated by recent discussions of entanglement in the context of high energy scattering, we consider the relation between the entanglement entropy of a highly excited state of a quantum system and the classical entanglement entropy of the corresponding classical system. We show on the example of two weakly coupled harmonic oscillators, that the two entropies are equal. Quantum mechanically, the reduced density matrix which yields this entropy is close to the maximally entangled state. We thus observe that the nature of entanglement in this type of state is purely classical.

quant-ph↗

arXiv2022

CGC for Ultra-Peripheral Pb+Pb Collisions at the Large Hadron Collider: a more realistic calculation

We provide the first calculation of two-gluon production at mid-rapidity in ultra-peripheral collisions in the Color Glass Condensate framework. To estimate systematic uncertainty associated with poor understanding of the wave function of the nearly real photon, we consider two diametrically different models: the dilute quark-antiquark dipole approximation and a vector meson, in which color charge density is approximated by McLerran-Venugopalan model. In the experimentally relevant range, the target nucleus can be faithfully approximated by a highly saturated state. This simplification enables us to perform efficient numerical simulations and extract the two-gluon correlation functions and the associated azimuthal harmonics.

hep-ph↗

arXiv2022

Universal location of Yang-Lee edge singularity for a one-component field theory in $1\le d \le 4$

We determine the universal location of the Yang-Lee edge singularity in the entire relevant domain of spatial dimensions $1\le d \le 4$ for the Ising universality class. To that end, we present analytical results for $d=1,2,4$ and near four dimensions. For $d=3$ and a set of fractional dimensions, we perform numerical calculations using a systematic Functional Renormalization Group approach.

hep-ph↗

arXiv2022

Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model

For theories plagued with a sign problem at finite density, a Taylor expansion in the chemical potential is frequently used for lattice gauge theory based computations of the equation of state. Recently, in arXiv:2106.03165, a new resummation scheme was proposed for such an expansion that resums contributions of correlation functions of conserved currents to all orders in the chemical potential. Here, we study the efficacy of this resummation scheme using a solvable low energy model, namely the mean-field quark-meson model. After adapting the scheme for a mean-field analysis, we confront the results of this scheme with the direct solution of the model at finite density as well as compare with results from Taylor expansions. We study to what extent the two methods capture the analytical properties of the equation of state in the complex chemical potential plane. As expected, the Taylor expansion breaks down as soon as the baryon chemical potential reaches the radius of convergence defined by the Yang-Lee edge singularity. Encouragingly, the resummation not only captures the location of the Yang-Lee edge singularity accurately, but is also able to describe the equation of state for larger chemical potentials beyond the location of the edge singularity for a wide range of temperatures.

hep-ph↗

arXiv2022

A pedagagical introduction to the Lifshitz regime

We give an elementary and pedagogical review of the phase diagrams which are possible in Quantum ChromoDynamics (QCD). Currently, the emphasis is upon the appearance of a critical endpoint, where disordered and ordered phases meet. In many models, though, a Lifshitz point also arises. At a Lifshitz point, three phases meet: disordered, ordered, and one where spatially inhomogeneous phases arise. At the level of mean field theory, the appearance of a Lifshitz point does not dramatically affect the phase diagram. We argue, however, that fluctuations about the Lifshitz point are very strong in the infrared, and significantly alter the phase diagram. We discuss at length the analogy to inhomogenous polymers, where the Lifshitz regime produces a bicontinuous microemulsion. We briefly mention the possible relevance to the phase diagram of QCD.

hep-ph↗

arXiv2022

Probing gluon Bose correlations in DIS

We study correlations originating from the quantum nature of gluons in a hadronic wave function. Bose-Einstein correlation between identical particles lead to the enhancement in the number of pairs of gluons with the same quantum numbers and small relative momentum. We show that these preexisting correlations can be probed in Deep Inelastic Scattering experiments at high energy. Specifically, we consider diffractive dijet plus a third jet production. The azimuthal dependence displays a peak at the zero relative angle between the transverse momentum imbalance of the photon-going dijet and the transverse momentum of the hadron-going jet. Our calculations explicitly show that the peak originates from Bose enhancement. Comparing electron-proton to electron-nucleus collisions, we demonstrate that the nuclear target enhances the relative strength of the peak. With the future high luminosity Electron-Ion Collider the proposed measurements of gluon Bose enhancement become experimentally feasible.

hep-ph↗

arXiv2021

First saturation correction in high energy proton-nucleus collisions: Part III. Ensemble averaging

In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtained. In this paper, we perform ensemble averaging in the McLerran-Venugopalan model and the Dipole Approximation. We find that, in the saturation correction, the effects of the initial state interactions are negligible while the final state interactions play most important role and give a positive-valued contribution to the semi-hard gluon spectrum. Furthermore, we show that the single gluon spectrum scales approximately $1/k_{\perp}^{4}$ at small $k_{\perp}$, suggesting that a resummation of higher order saturation corrections is required to regulate the infrared region of the gluon spectrum.

hep-ph↗

arXiv2021

Gluon Quasi Particles and the CGC Density Matrix

We revisit and extend the calculation of the density matrix and entanglement entropy of a Color Glass Condensate by including the leading saturation corrections in the calculation. We show that the density matrix is diagonal in the quasi particle basis, where it has the Boltzmann form. The quasi particles in a wide interval of momenta behave as massless two-dimensional bosons with the temperature proportional to the typical semi-hard scale $T=Q_s/\sqrt{α_sN_c}$. Thus the semi-hard momentum region $Q_s<k<Q_s/\sqrt{α_sN_c}$ arises as a well-defined intermediate regime between the perturbatively hard momenta and the nonperturbative soft momenta $k<Q_s$ in the CGC description of a hadronic wave function.

hep-ph↗

arXiv2021

Correlations between azimuthal asymmetries and multiplicity and mean transverse momentum in small collisions systems in the CGC

Considering a dilute-dense situation suitable for pA collisions, we compute in the Color Glass Condensate the correlation between azimuthal asymmetries, specifically the squared second Fourier coefficient $v_2^2$, and the total multiplicity in the event. We also analyse the correlation between $v_2^2$ and the mean squared transverse momentum of particles in the event. In both cases, we find that the correlations are generally very small, consistent with the observations. We also note an interesting sharp change in the value of $v_2^2$ and its correlations as a function of the width of the transverse momentum bin, related with a change of the dominance of Bose and HBT quantum correlations.

hep-ph↗

arXiv2021

First Saturation Correction in High Energy Proton-Nucleus Collisions: II. Single Inclusive Semi-Hard Gluon Production

Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive semi-hard gluon production in high energy proton-nucleus collisions by applying the Lehmann-Symanzik-Zimmermann reduction formula. We thus finalize the program started by Balitsky (see Ref.~\cite{Balitsky:2004rr}) and independently by Chirilli, Kovchegov and Wertepny (see Ref.~\cite{Chirilli:2015tea}) albeit using a very different approach to carry out our calculations. We extracted the functional dependence of gluon spectrum on the color charge densities of the colliding objects; thus our results can be used to evaluate complete first saturation correction to the double/multiple inclusive gluon productions.

hep-ph↗

arXiv2021

First Saturation Correction in High Energy Proton-Nucleus Collisions: I. Time evolution of classical Yang-Mills fields beyond leading order

In high energy proton-nucleus collisions, the single- and double-inclusive soft gluon productions at the leading order have been calculated and phenomenologically studied in various approaches for many years. These studies do not take into account the saturation and multiple rescatterings in the field of the proton. The first saturation correction to these leading order results (the terms that are enhanced by the combination $α_s^2 μ^2$, where $μ^2$ is the proton's color charge squared per unit transverse area) has not been completely derived despite recent attempts using a diagrammatic approach. This paper is the first in a series of papers towards analytically completing the first saturation correction to physical observables in high energy proton-nucleus collisions. Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime using the Color Glass Condensate effective theory and compute physical observables constructed from classical gluon fields. In the current paper, the Yang-Mills equations are solved perturbatively in the field of the dilute object (the proton). Next-to-leading order and next-to-next-to-leading order analytic solutions are explicitly constructed. A systematic way to obtain all higher order analytic solutions is outlined

hep-ph↗

arXiv2020

Angular correlations in pA collisions from CGC: multiplicity and mean transverse momentum dependence of $v_2$

Within the dense-dilute Color Glass Condensate approach, and using the Golec-Biernat-Wuesthoff model for the dipole scattering amplitude, we calculate $v_2^2$ as well as the correlations between $v_2^2$ and both the total multiplicity and the mean transverse momentum of produced particles. We find that the correlations are generally very small consistent with the observations. We note an interesting sharp change in the value of $v^2_2$ as well as of its correlations as a function of the width of the transverse momentum bin. This crossover is associated with the change from Bose enhancement dominance of the correlation for narrow bin to HBT dominated correlations for larger bin width.

hep-ph↗

arXiv2020

Conundrum for the free energy of a holonomous gluonic plasma at cubic order

We compute the term $\sim g^3$ in the free energy for a $SU(N)$ gauge theory with nonzero holonomy at nonzero temperature. If the holonomy is generated kinematically by the introduction of gauge invariant sources coupled to Polyakov loops, the contribution of charged (off-diagonal) gluons to the free energy at order $g^3$, ${\cal F}^{\left( 3\rm{:c.g.} \right)}$, is singular: ${\cal F}^{\left( 3\rm{:c.g.} \right)} \neq 0 $ without holonomy, but ${\cal F}^{\left( 3 \rm{:c.g.} \right)}= 0$ when the holonomy is nonzero, even infinitesimally. We show that the absence of the charged gluon contribution is required by gauge invariance alone and is therefore a universal feature.

hep-th↗

arXiv2020

Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model

We define the "entropy of ignorance" which quantifies the entropy associated with ability to perform only a partial set of measurement on a quantum system. For a parton model the entropy of ignorance is equal to a Boltzmann entropy of a classical system of partons. We analyze a calculable model used for describing low x gluons in Color Glass Condensate approach, which has similarities with the parton model of QCD. In this model we calculate the entropy of ignorance in the particle number basis as well as the entanglement entropy of the observable degrees of freedom. We find that the two are similar at high momenta, but differ by a factor of order unity at low momenta. This holds for the Renyi as well as von Neumann entropies. We conclude that the entanglement does not seem to play an important role in the context of the parton model.

hep-ph↗

arXiv2020

Free energy of a Holonomous Plasma

At a nonzero temperature T, a constant field $\overline{A}_0 \sim T/g$ generates nontrivial eigenvalues of the thermal Wilson line. We discuss contributions to the free energy of such a holonomous plasma when the coupling constant, $g$, is weak. We review the computation to $\sim g^2$ by several alternate methods, and show that gauge invariant sources, which are nonlinear in the gauge potential $A_0$, generate novel contributions to the gluon self energy at $\sim g^2$. These ensure the gluon self energy remains transverse to $\sim g^2$, and are essential in computing contributions to the free energy at $\sim g^3$ for small holonomy, $\overline{A}_0 \sim T$. We show that the contribution $\sim g^3$ from off-diagonal gluons is discontinuous as the holonomy vanishes. The contribution from diagonal gluons is continuous as the holonomy vanishes, but sharply constrains the possible sources which generate nonzero holonomy, and must involve an infinite number of Polyakov loops.

hep-ph↗

arXiv2019

Initial state description of azimuthally collimated long range correlations in ultrarelativistic light-heavy ion collisions

It was argued in arXiv:1805.09342 and arXiv:1807.00825 that the systematics of the azimuthal anisotropy coefficients $v_{2,3}$ measured in ultrarelativistic light-heavy ion collisions at RHIC and the LHC can be described in an initial state dilute-dense Color Glass Condensate (CGC) framework. We elaborate here on the discussion in these papers and provide further novel results that strengthen their conclusions. The underlying mathematical framework and numerical techniques employed are very similar to those in the CGC based IP-Glasma model used previously as initial conditions for heavy-ion collisions. The uncertainties in theory/data comparisons for small systems are discussed, with unknowns that are specific to the model distinguished from those that are generic to all models. We present analytical arguments that demonstrate that quantum interference effects such as Bose enhancement and Hanbury-Brown-Twiss correlations of gluons, as well as coherent multiple scattering of gluons in the projectile off color domains in the target, are enhanced in rare events. The quantum origins of the large anisotropies in small systems are corroborated by numerical results for deuteron-gold collisions that show that large anisotropies in rare configurations can occur when the nucleons in the projectile overlap significantly. This is at variance with the classical intuition of hydrodynamical models. We also comment on the consequences of ignoring the many-body color charge correlations of gluons in models that only consider geometrical fluctuations in the energy density.

hep-ph↗

arXiv2019

Bose enhancement, the Liouville effective action and the high multiplicity tail in p-A collisions

In the framework of dense-dilute CGC approach we study fluctuations in the multiplicity of produced particles in p-A collisions. We show that the leading effect that drives the fluctuations is the Bose enhancement of gluons in the proton wave function. We explicitly calculate the moment generating function that resums the effects of Bose enhancement. We show that it can be understood in terms of the Liouville effective action for the composite field which is identified with the fluctuating density, or saturation momentum of the proton. The resulting probability distribution turns out to be very close to the gamma-distribution. We also calculate the first correction to this distribution which is due to pairwise Hanbury Brown-Twiss correlations of produced gluons.

hep-ph↗