arXiv subjects

Alina Czajka

Publications and source records attributed to Alina Czajka.

At least 19 recordsLinked to original sources

arXiv2026

Next-to-leading power gluon TMDs from back-to-back DIS dijets at next-to-eikonal accuracy at low x

We calculate next-to-leading power contributions to the gluon TMDs in DIS dijet production in the back-to-back limit at low x within the Color Glass Condensate (CGC) effective field theory at next-to-eikonal accuracy. We put a special emphasis on three-point correlation functions from CGC calculations, including their correspondence to an appropriately chosen definition of three- point TMDs within the aforementioned kinematical conditions. We also discuss importance of time ordering as well as momentum fraction space formulation of the correlators. Finally, we calculate the dijet cross section corresponding to the three-point CGC correlator as a combination of TMD functions.

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arXiv2026

Order-reversed Kubo formulas in relativistic kinetic theory

Using the stress-energy tensor response functions obtained in the Anderson-Witting model of kinetic theory with non-zero mass, we verify that these response functions satisfy the required analytic conditions and are fully consistent with the recently derived Kubo formulas in Ref.[1].

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arXiv2026

Analytic structure of stress-energy response functions and new Kubo formulae

Determining the transport properties of Quark-Gluon Plasma is one of the most important aspects of relativistic heavy ion collision studies. Field-theoretical calculations of the transport coefficients such as the shear and bulk viscosities require Kubo formulae which in turn require real-time correlation functions of stress-energy tensors. Consequently, knowing the analytic structure of these correlation functions is essential in any such studies. Using the energy-conservation laws and the results from the gravity-hydrodynamics analysis, we determine the low-frequency and low-wavenumber analytic structures of all stress-energy correlation functions in the rest frame of the medium. By comparing with the diffusion and sound spectra from the second-order and the third-order relativistic hydrodynamics, various new Kubo formulae are derived in the limit where the zero-frequency limit is taken first. We also show that the meaning of the Kubo formulae for relaxation times can change when higher-order terms are added to hydrodynamics. A subtle issue of taking the zero frequency and zero wavenumber limits when using skeleton diagrams is addressed as well.

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arXiv2026

Back-to-back dijet production in DIS with finite-energy corrections and twist-3 gluon TMDs

This work presents the summary of calculation of the cross section of the dijet production in deep inelastic scattering at small x at next-to-eikonal accuracy. The cross section is calculated in the back-to-back limit of the produced jets using results obtained in our previous works. The cross section is expressed via the transverse-momentum-dependent (TMD) parton distributions. Specifically, we show how the next-to-eikonal corrections are related to the $x$ dependent phase of twist-2 gluon TMD and to twist-3 unpolarized gluon TMDs.

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arXiv2024

Back-to-back dijet production in DIS at next-to-eikonal accuracy and twist-3 gluon TMDs

We consider dijet production in deep inelastic scattering at small $x$, on a purely gluonic unpolarized target. Starting from earlier results obtained at next-to-eikonal accuracy in the high-energy limit, we perform the expansion in the back-to-back dijet limit, at next-to-leading power accuracy. We rewrite our results in the language of transverse-momentum-dependent (TMD) factorization, in terms of twist-2 and twist-3 TMD gluon distributions (gluon TMDs). Among the next-to-eikonal corrections, we find in particular twist-2 contributions corresponding to the $x$ dependent phase of the twist-2 gluon TMDs. We also find two types of twist-3 unpolarized gluon TMDs, as well as correlators of three gluon field strength tensors.

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arXiv2023

DIS dijet production at next-to-eikonal accuracy in the CGC

We compute dijet production in Deep Inelastic Scattering at low $x$ in the dipole formalism at next-to-eikonal accuracy. We calculate the contributions induced by single photon exchange of either longitudinal or transverse polarization. We include all types of corrections to the eikonal approximation in the gluon background field: (i) finite longitudinal width of the target, (ii) interaction of the quark-antiquark pair with the subleading (transverse) component of the background field and (iii) dynamics of the target which is encoded in the $z^-$-coordinate dependence of the background field. The final expressions for the dijet cross section are written as sum of a "generalized eikonal" contribution (where longitudinal momentum $p^+$ exchange between the target and the incoming quark-antiquark pair is allowed since the average $z^-$ dependence of the background field is kept) and explicit next-to-eikonal corrections that involve decorated dipole and quadrupole operators.

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arXiv2023

DIS dijet production at next-to-eikonal accuracy in the CGC

In this work, we derive the cross-section for inclusive DIS dijet production at full next-to-eikonal order. We include the corrections that stem from taking a finite width of the target, the interaction of the quark with the transverse component of the background field and also the dynamics of the target.

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arXiv2022

Physical characteristics of glasma from the earliest stage of relativistic heavy ion collisions

We present analytic results that describe the gluon field, or glasma, at very early times after a collision of relativistic heavy ions at proper time $τ=0$. We use a Colour Glass Condensate approach, and perform an expansion in $τ$. The full details of our method are described in our previous paper [1]. In this paper we present an analysis of various physical quantities that can be obtained from the energy-momentum tensor. We show that the expansion to order $τ^6$ can be trusted to about $τ=0.05$ fm. For times small enough that the expansion converges, the transverse and longitudinal pressures move towards their equilibrium values of one third of the energy density. The Fourier coefficients of the azimuthal flow are larger than expected, which contradicts the usual assumption that anisotropy is mostly generated during the hydrodynamic evolution of the plasma. We find a significant correlation between the elliptic flow coefficient and the eccentricity, which indicates that the spatial asymmetry introduced by the initial geometry is effectively transmitted to the azimuthal distribution of the gluon momentum field, even at very early times. This result is interesting because correlations of this kind are characteristic of the onset of hydrodynamic behaviour. We show that the angular momentum of the glasma is orders of magnitude smaller than the angular momentum of the initial system of ions colliding with non-zero impact parameter. This indicates that most of the angular momentum carried by the valence quarks is not transmitted to the glasma, and contradicts the picture of a rapidly rotating initial glasma state that has been proposed by several authors, but agrees with the current lack of experimental evidence for a significant polarization effect of the hyperons and vector mesons produced in heavy ion collisions at the highest accessible energies.

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arXiv2022

Jet quenching in glasma

We discuss the transverse momentum broadening of hard probes traversing an evolving glasma, which is the earliest phase of the matter produced in relativistic heavy-ion collisions. The coefficient $\hat q$ is calculated using the Fokker-Planck equation, and an expansion in the proper time $τ$ which is applied to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision term, which in turn provides $\hat q$, are computed to fifth order in $τ$. The momentum broadening is shown to rapidly grow in time and reach a magnitude of several ${\rm GeV^2/fm}$. We show that the transient pre-equilibrium phase provides a contribution to the energy loss of hard probes which is comparable to that of the long lasting, hydrodynamically evolving, equilibrium phase.

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arXiv2022

Transport of hard probes through glasma

We calculate the transverse momentum broadening $\hat q$ and collisional energy loss $dE/dx$ of hard probes traversing an evolving glasma during the earliest phase of a relativistic heavy-ion collision. We use a Fokker-Planck equation and apply a proper time expansion to describe the temporal evolution of the glasma. The correlators of the chromodynamic fields that determine the Fokker-Planck collision terms, which in turn provide $\hat q$ and $dE/dx$, are computed to fifth order. Both transport coefficients are strongly dependent on time. The maximum values they acquire before the proper time expansion breaks down are large: $\hat q$ is of the order of a few ${\rm GeV^2/fm}$ and $dE/dx \sim 1~{\rm GeV/fm}$. Their precise values depend on the probe's velocity ${\bf v}$, the saturation momentum $Q_s$, and an IR regulator $m$ that is related to the confinement scale. We study the dependence of our results on these quantities. Different regularization procedures are analysed and shown to produce similar results. We also discuss the validity of the proper time expansion and the compatibility of the approximations that are inherent in the derivation of the Fokker-Planck equation. We show that hard probes lose a comparable amount of energy when they propagate through the short-lived glasma phase, and the long-lasting hydrodynamic phase. The conclusion is that the glasma plays an important role in jet quenching.

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arXiv2022

The energy-momentum tensor at the earliest stage of relativistic heavy ion collisions

Nuclear collisions at high energies produce a gluon field that can be described using the Colour Glass Condensate (CGC) effective theory at proper times $τ\lesssim 1$ fm/c. The theory can be used to calculate the gluon energy-momentum tensor, which provides information about the early time evolution of the chromo-electric and chromo-magnetic fields, energy density, longitudinal and transverse pressures, and other quantities. We obtain an analytic expression for the energy-momentum tensor using an expansion in the proper time, and working to sixth order. The calculation is technically difficult, in part because the number of terms involved grows rapidly with the order of the $τ$ expansion, but also because of several subtle issues related to the definition of event-averaged correlators, the method chosen to regulate these correlators, and the dependence of results on the parameters introduced by the regularization and nuclear density profile functions. All of these issues are crucially related to the important question of the extent to which we expect a CGC approach to be able to accurately describe the early stages of a heavy ion collision. We present some results for the evolution of the energy density and the longitudinal and transverse pressures. We show that our calculation gives physically meaningful results up to values of the proper time which are close to the regime at which hydrodynamic simulations are initialized. In a companion paper [1] we give a detailed analysis of several other experimentally relevant quantities that can be calculated from the energy-momentum tensor.

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arXiv2021

Quarks at next-to-eikonal accuracy in the CGC I: Forward quark-nucleus scattering

We derive Next-to-Eikonal (NEik) corrections to the background quark propagator, which stem from (i) considering a finite longitudinal width target instead of an infinitely thin shockwave and (ii) including the interaction of the quark with the transverse components of the background field. These two different corrections to the eikonal approximation combine together and provides a gauge covariant expression for the quark propagator at NEik accuracy. We then apply our results to quark (or antiquark) scattering on a nucleus at NEik accuracy, considering both unpolarized cross section and helicity asymmetry.

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arXiv2020

Heavy Quarks Embedded in Glasma

Heavy quarks, which are produced at the earliest stage of relativistic heavy-ion collisions, probe the entire history of the quark-gluon plasma that is created in the collision. Initially the plasma is populated with chromodynamic fields which can be treated as classical. We study the transport of heavy quarks across such a system, which is called glasma, using a Fokker-Planck equation where the quarks interact with long wavelength chromodynamic fields. We compute field correlators which are used to calculate the collision terms of the transport equation. Finally, the energy loss and momentum broadening of heavy quarks in the glasma are studied. Both of these quantities are sizable and strongly directionally dependent.

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arXiv2020

Effects of the mean field on fluid dynamics in the relaxation time approximation

In this paper the nonequilibrium correction to the distribution function containing a time and space dependent mass is obtained. Given that, fully consistent fluid dynamic equations are formulated. Then, the physics of the bulk viscosity is elaborated for Boltzmann and Bose-Einstein gases within the relaxation time approximation. It is found that the parametric form of the ratio $ζ/τ_R$ for the quantum gas is affected by the infrared cut-off. This may be an indication that the relaxation time approximation is too crude to obtain a reliable form of bulk viscosity.

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arXiv2019

Bulk Viscosity at Extreme Limits: From Kinetic Theory to Strings

In this paper we study bulk viscosity in a thermal QCD model with large number of colors at two extreme limits: the very weak and the very strong 't Hooft couplings. The weak coupling scenario is based on kinetic theory, and one may go to the very strong coupling dynamics via an intermediate coupling regime. Although the former has a clear description in terms of kinetic theory, the intermediate coupling regime, which uses lattice results, suffers from usual technical challenges that render an explicit determination of bulk viscosity somewhat difficult. On the other hand, the very strong 't Hooft coupling dynamics may be studied using string theories at both weak and strong string couplings using gravity duals in type IIB as well as M-theory respectively. In type IIB we provide the precise fluctuation modes of the metric in the gravity dual responsible for bulk viscosity, compute the speed of sound in the medium and analyze the ratio of the bulk to shear viscosities. In M-theory, where we uplift the type IIA mirror dual of the UV complete type IIB model, we study and compare both the bulk viscosity and the sound speed by analyzing the quasi-normal modes in the system at strong IIA string coupling. By deriving the spectral function, we show the consistency of our results both for the actual values of the parameters involved as well for the bound on the ratio of bulk to shear viscosities.

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arXiv2018

Consequences of conformal anomaly on fluid dynamics

We review a recent progress on fluid dynamics applied to strongly interacting nuclear matter. The efforts are made to highlight consequences of scale invariance breaking on the hydrodynamic description of a nuclear medium. Both phenomenological and analytical findings are summarized.

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arXiv2018

On Bulk Viscosity at Weak and Strong 't Hooft Couplings

Bulk viscosity is an important transport coefficient that exists in the hydrodynamical limit only when the underlying theory is non-conformal. One example being thermal QCD with large number of colors. We study bulk viscosity in such a theory at low energies and at weak and strong 't Hooft couplings when the temperature is above the deconfinement temperature. The weak coupling analysis is based on Boltzmann equation from kinetic theory whereas the strong coupling analysis uses non-conformal holographic techniques from string and M-theories. Using these, many properties associated with bulk viscosity may be explicitly derived. This is a shortened companion paper that summarizes some of the results of our longer paper arXiv:1807.04713.

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arXiv2018

Bulk viscosity of strongly interacting matter in the relaxation time approximation

This paper presents how thermal mean field effects are incorporated consistently in the hydrodynamical modelling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity over its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the $β_λ$-function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cut-off. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of $ζ/τ_R$ for gases obeying Bose-Einstein statistics.

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