arXiv subjects

Margaret E. Carrington

Publications and source records attributed to Margaret E. Carrington.

At least 19 recordsLinked to original sources

arXiv2026

Gauge invariant momentum broadening of hard probes in glasma

We compute the transport coefficient $\hat q$ which quantifies the transverse momentum broadening of hard probes passing through the evolving glasma from the earliest stage of relativistic heavy-ion collisions. We use a proper-time expansion method which is designed to study the glasma at very early times. In our earlier calculations of $\hat q$ we used an approximation that greatly simplifies the complexity of the calculation but introduces a violation of gauge invariance. Based on these results we argued that the glasma plays an important role in jet quenching. In this paper we have used a gauge invariant formulation to calculate $\hat q$. The results for the momentum broadening coefficient are quantitatively very close to those of our previous simplified version of the calculation and confirm our earlier conclusion about the importance of the glasma contribution to jet quenching.

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arXiv2026

Angular momentum of glasma

The earliest phase of an ultrarelativistic heavy ion collision can be described as a highly populated system of gluons called glasma. We study some glasma characteristics related to the system's angular momentum. The first one is the global angular momentum perpendicular to the reaction plane, which is spanned by the beam axis and impact parameter vector. We show that only a small fraction of the enormous initial angular momentum of the colliding ultrarelativistic nuclei is transferred to the glasma. Our main focus is the glasma angular momentum directed along the beam axis. This quantity has a local character and results from the inhomogeneous velocity field generated in the glasma. We calculate the vorticity and local angular momentum which show noticeably different behaviour. The results are analyzed in detail and discussed in the context of existing experimental data. We argue that neither vorticity nor thermal vorticity but instead the local angular momentum controls the polarization of final-state hadrons.

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arXiv2026

${\cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $λ^{5/2}$

We calculate the resummed perturbative free energy of ${\cal N} = 4$ supersymmetric Yang-Mills in four spacetime dimensions (SYM$_{44}$) to order $λ^{5/2}$ in the 't Hooft coupling at finite temperature and zero chemical potential. All infrared divergences cancel when we include contributions from SYM$_{44}$ ring diagrams and the final result is both ultraviolet and infrared finite. Our result has special significance since order $λ^{5/2}$ is the highest order calculation that can be done with perturbation theory, because there are nonperturbative effects associated with the magnetic mass scale that come into play at order $λ^3$. We compare results obtained with regularization by dimensional reduction (RDR), which preserves supersymmetry, and canonical dimensional regularization (DR). We also compare with a generalized Padé approximant constructed by matching the weak coupling result at order $λ^2$ and the large $N_c$ strong coupling result at order $λ^{-3/2}$. Finally we make a comparison between our result and the QCD free energy and show that SYM$_{44}$ has better convergence properties.

hep-th↗

arXiv2025

The real-time QCD static potential at high temperature

We develop a procedure to analytically calculate higher-order contributions to the high-temperature real-time static potential in QCD. It is based on the introduction of a semi-hard external scale, which lies between the hard scale (the temperature) and the soft scale (the screening mass), and the method of integration by regions. We calculate the leading and next-to-leading corrections in the region where bound states transit from narrow resonances to wide ones. The calculation involves both loop diagrams calculated in the Hard Thermal Loop (HTL) effective theory and power corrections to the HTL Lagrangian calculated in QCD. We also calculate the thermal corrections to the heavy quarkonium spectrum, and estimate the dissociation temperatures. We compare our results with recent lattice data and discuss their usefulness to guide lattice inputs in inverse problems.

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arXiv2025

High-Temperature QCD Static Potential beyond Leading Order

We calculate the leading and next-to-leading corrections to the real-time QCD static potential in a high temperature medium in the region where bound states transit from narrow resonances to wide ones. We find sizable contributions to both the real and the imaginary part of the potential. The calculation involves both loop diagrams calculated in the Hard Thermal Loop (HTL) effective theory and power corrections to the HTL Lagrangian calculated in QCD. We compare our results with recent lattice data.

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arXiv2024

Hydrodynamic-like behaviour of glasma

At the earliest stage of ultrarelativistic heavy-ion collisions the produced matter is a highly populated system of gluons called glasma which can be approximately described in terms of classical chromodynamic fields. Although the system's dynamics is governed by Yang-Mills equations, glasma evolution is shown to strongly resemble hydrodynamic behaviour.

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arXiv2024

The earliest phase of relativistic heavy-ion collisions

According to the Color Glass Condensate approach to relativistic heavy-ion collisions, the earliest phase of the collision is a glasma which is made of highly populated gluon fields that can be treated classically. Using a proper time expansion we study analytically various properties of the glasma. In particular, we compute the glasma energy-momentum tensor which allows us to obtain the energy density, longitudinal and transverse pressure, collective flow, and angular momentum. We also study the role of the glasma in jet quenching by computing collisional energy loss and transverse momentum broadening.

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arXiv2024

The effect of anisotropy on the formation of heavy quarkonium bound states

We study the real part of the static potential of a heavy quark-antiquark system in an anisotropic plasma medium. We use a quasi-particle approach where the collective dynamics of the plasma constituents is described using hard-loop perturbation theory. The parton distribution function is characterized by a set of parameters that can accurately describe the anisotropy of the plasma produced in a heavy ion collision. We calculate the potential numerically in strongly anisotropic systems and study the angular dependence of the distortion of the potential relative to the isotropic one. We obtain an analytic expression for the real part of the heavy quark potential in the limit of weak anisotropy using a model that expresses the potential in terms of effective screening masses that depend on the anisotropy parameters and the orientation of the quark-antiquark pair. A 1-dimensional potential is formulated in terms of angle averaged screening masses that incorporate the anisotropy of the medium into a radial coordinate. We solve the corresponding Schrödinger equation and show that the magnitude of the binding energy typically increases with anisotropy. Anisotropy can play an important role, especially in states with non-zero angular momentum. This means that the number of bound states that are formed could depend on specific characteristics of the anisotropy of the plasma. Our study suggests that plasma anisotropy plays an important role in the dynamics of heavy quarkonium and motivates further study.

hep-ph↗

arXiv2024

Evidence for universal flow and characteristics of early time thermalization in a scalar field model for heavy ion collisions

We study numerically the evolution of an expanding strongly self-coupled real scalar field. We use a conformally invariant action that gives a traceless energy-momentum tensor and is better suited to model the early time behaviour of a system such as QCD, whose action is also conformally invariant.We consider asymmetric initial conditions and observe that when the system is initialized with non-zero spatial eccentricity, the eccentricity decreases and the elliptic flow coefficient increases. We look at a measure of transverse pressure asymmetry that has been shown to behave similarly to the elliptic flow coefficient in hydrodynamic systems and show that in our system their behaviour is strikingly similar. We show that the derivative of the transverse velocity is proportional to the gradient of the energy in Milne coordinates and argue that this result means that transverse velocity initially develops in the same way that it does in hydrodynamic systems. We conclude that some aspects of the early onset of hydrodynamic behaviour that has been observed in quark-gluon plasmas are seen in our numerical simulation of strongly coupled scalar fields.

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arXiv2023

Glasma properties in small proper time expansion

In a series of works by two of us, various characteristics of the glasma from the earliest phase of relativistic heavy-ion collisions have been studied using a proper time expansion. These characteristics include: energy density, longitudinal and transverse pressures, collective flow, angular momentum and parameters of jet quenching. In this paper we extend the proper time interval where our results are reliable by working at higher order in the expansion. We also generalize our previous study of jet quenching by extending our calculations to consider inhomogeneous glasma. Inhomogeneities are an important aspect of physically realistic systems that are difficult to include in calculations and are frequently ignored.

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arXiv2023

Phase transitions in 3-dimensional Dirac semi-metals using Schwinger-Dyson equations

We study the semi-metal/insulator quantum phase transition in three-dimensional Dirac semi-metals by solving a set of Schwinger-Dyson equations. We study the effect of an anisotropic fermion velocity on the critical coupling of the transition. We consider the influence of several different approximations that are commonly used in the literature and show that results for the critical coupling change considerably when some of these approximations are relaxed. Most importantly, the nature of the dependence of the critical coupling on the anisotropy depends strongly on the approximations that are used for the photon polarization tensor. On the one hand, this means that calculations that include full photon dynamics are necessary to answer even the basic question of whether the critical coupling increases or decreases with anisotropy. On the other hand, our results mean that it is possible that anisotropy could provide a mechanism to promote dynamical gap generation in realistic three-dimensional Dirac semi-metallic materials.

cond-mat.str-el↗

arXiv2022

Isotropization of a rotating and longitudinally expanding $ϕ^4$ scalar system

We present numerical simulations for the evolution of an expanding system of massless scalar fields with quartic coupling. By setting a rotating, non-isotropic initial configuration, we compute the energy density, the transverse and longitudinal pressures and the angular momentum of the system. We compare the time scales associated with the isotropization and the decay of the initial angular momentum due to the expansion, and show that even for fairly large initial angular momentum, it decays significantly faster than the pressure anisotropy.

hep-th↗

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.

hep-ph↗

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.

hep-ph↗

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

Collective modes in anisotropic plasmas

We study collective modes in anisotropic plasmas of quarks and gluons using a quasi-particle picture and a hard loop approximation. We use a general class of anisotropic distribution functions, and we consider chirally asymmetric systems. We introduce a complete tensor basis to decompose the gluon polarization tensor into a set of nine scalar functions. We derive and solve the corresponding dispersion equations. Imaginary modes are particularly important because of their potential influence on plasma dynamics. We explore in detail their dependence on the chiral chemical potential and the parameters that characterise the anisotropy of the system. We show that our generalized distributions produce dispersion relations that are much richer in structure than those obtained with a simple one parameter deformation of an isotropic distribution. In addition, the size and domain of the imaginary solutions are enhanced, relative to those obtained with a one parameter deformation. Finally, we show that the influence of even a very small chiral chemical potential is significantly magnified when anisotropy is present.

hep-ph↗

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.

hep-ph↗

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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