arXiv subjects

Jean-Paul Blaizot

Publications and source records attributed to Jean-Paul Blaizot.

At least 109 records · Page 6Linked to original sources

arXiv2005

The Kosterlitz-Thouless-Berezinskii transition of homogeneous and trapped Bose gases in two dimensions

We derive the scaling structure of the Kosterlitz-Thouless-Berezinskii (KTB) transition temperature of a homogeneous Bose gas in two dimensions within diagrammatic perturbation theory. Approaching the system from above the transition, we calculate the critical temperature, $T_{KT}$, and show how the superfluid mass density emerges from Josephson's relation as an interplay between the condensate density in a finite size system, and the infrared structure of the single particle Green's function. We then discuss the trapped two-dimensional Bose gas, where the interaction changes the transition qualitatively from Bose-Einstein in an ideal gas to a KTB transition in the thermodynamic limit. We show that the transition temperature lies below the ideal Bose-Einstein transition temperature, and calculate the first correction in terms of the interparticle interactions. The jump of the total superfluid mass at the transition is suppressed in a trapped system.

cond-mat.other↗

arXiv2005

Photon and dilepton production in the Quark-Gluon plasma: perturbation theory vs lattice QCD

This talk reviews the status of QCD calculations of photon and dilepton production rates in a Quark-Gluon plasma. Theses rates are known to order ${\cal O}(α_s)$. Their calculations involve various resummations to account for well identified physical effects that are briefly described. Lattice calculations of the spectral functions give also access to the dilepton rates. Comparison with perturbative results points to inconsistencies in both approaches when the dilepton energy becomes small.

hep-ph↗

arXiv2004

Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas

We propose a new approximation scheme to solve the Non Perturbative Renormalization Group equations and obtain the full momentum dependence of $n$-point functions. This scheme involves an iteration procedure built on an extension of the Local Potential Approximation commonly used within the Non Perturbative Renormalization Group. Perturbative and scaling regimes are accurately reproduced. The method is applied to the calculation of the shift $ΔT_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity which is very sensitive to all momenta intermediate between these two regions. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%. The next-to-leading order differs by about 10% from the best accepted result.

cond-mat.stat-mech↗

arXiv2004

Searching Evidence for the Color Glass Condensate at RHIC

This contribution discusses the phenomenon of parton saturation, the color glass picture of hadronic wavefuntions, and their relevance in the early stages of nucleus-nucleus collisions. Evidence for the color glass condensate in the presently available RHIC data is critically reviewed.

hep-ph↗

arXiv2004

Isolating vacuum amplitudes in quantum field calculations at finite temperature

In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved easily by exploiting a simple method, due to M. Gaudin, to perform the sum over the Matsubara frequencies. In order to manipulate freely contributions which may be individually singular, a regularization has to be introduced. We show that, in some cases, it is possible to choose this regularization in such a way that the isolated subdiagrams can be identified with analytical continuations of vacuum n-point functions. As an aside illustration of Gaudin's method, we use it to prove the main part of a recent conjecture concerning the relation which exists in the imaginary time formalism between the expressions of a Feynman diagram at zero and finite temperature.

hep-ph↗

arXiv2003

Renormalization of Φ-derivable approximations in scalar field theories

We discuss the renormalization of Φ-derivable approximations for scalar field theories. In such approximations, the self-energy is obtained as the solution of a self-consistent equation which effectively resums infinite subsets of diagrams of perturbation theory. We show that a consistent renormalization can be carried out, and we provide an explicit construction of the counterterms needed to eliminate the subdivergences. The counterterms are calculated from the solution of an auxiliary gap equation which determines the leading asymptotic part of the self-energy. This auxiliary gap equation may be chosen as the gap equation of the massless theory at zero temperature. We verify explicitly that the counterterms determined at zero temperature are sufficient to eliminate the divergences which occur in finite temperature calculations.

hep-ph↗

arXiv2003

Renormalizability of Phi-derivable approximations in scalar phi^4 theory

We discuss the renormalizability of Phi-derivable approximations in scalar phi^4 theory in four dimensions. The formalism leads to self-consistent equations for the 2-point and the 4-point functions which are plagued by ultraviolet divergences. Through a detailed analysis of the one and two-loop self-energy skeletons, we show that both equations can be renormalized simultaneously and determine the corresponding counterterms. These insure the elimination of ultraviolet divergences both at zero and finite temperature.

hep-ph↗

arXiv2001

The Entropy of the Quark-Gluon Plasma

The entropy of the quark-gluon plasma can be calculated from QCD using (approximately) self-consistent approximations. Lattice results for pure gauge theories are accurately reproduced down to temperatures of the order of 2.5$T_c$. Comparisons with other approaches to the thermodynamics of the quark-gluon plasma are briefly discussed.

hep-ph↗

arXiv2001

Bose-Einstein transition in a dilute interacting gas

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include the dynamic correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, $a$, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates.

cond-mat.stat-mech↗

arXiv2001

Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$.

cond-mat.stat-mech↗

arXiv2001

Theory of the Quark-Gluon Plasma

These lectures are an introduction to recent developments in the study of the high temperature phase of QCD by using weak coupling techniques. After a brief introduction to some techniques of quantum field theory at finite temperature, I proceed to an analysis of the various important scales and degrees of freedom of the quark-gluon plasma and focus on the effective theory for the collective modes which develop at the particular momentum scale $gT$, where $g$ is the gauge coupling and $T$ the temperature. A powerful technique to construct the effective theory is based on kinetic equations which govern the dynamics of the hard degrees of freedom. Some of the collective phenomena that are described by this effective theory are briefly mentioned. Then I turn to the calculation of the entropy of the quark-gluon plasma and show how the information coded in the effective theory can be exploited in (approximately) self-consistent calculations.

hep-ph↗

arXiv2001

Theoretical Conference Summary

This talk reviews progress reported at Quark-Matter 2001 on various theoretical aspects of the quark-gluon plasma and discusses how the new results obtained at RHIC change the standard picture of ultrarelativistic nucleus-nucleus collisions.

nucl-th↗

arXiv2001

J/Psi suppression in central Pb-Pb collisions

We discuss the recent NA50 J/Psi production data in Pb--Pb collisions, in particular the second drop at high transverse energies which correspond to the most central collisions. Using a model which relates the J/Psi suppression to the local energy density, we show that the data can be explained by taking into account transverse energy fluctuations at a given impact parameter. Predictions of this model for RHIC are briefly discussed.

nucl-th↗

arXiv2001

The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops

We present a unified description of the high temperature phase of QCD, the so-called quark-gluon plasma, in a regime where the effective gauge coupling $g$ is sufficiently small to allow for weak coupling calculations. The main focuss is the construction of the effective theory for the collective excitations which develop at a typical scale $gT$, which is well separated from the typical energy of single particle excitations which is the temperature $T$. We show that the plasma particles provide a source for long wavelength oscillations of average fields which carry the quantum numbers of the plasma constituents, the quarks and the gluons. To leading order in $g$, the plasma particles obey simple gauge-covariant kinetic equations, whose derivation from the general Dyson-Schwinger equations is outlined. As a by-product, the ``hard thermal loops'' emerge naturally in a physically transparent framework. We show that the collective excitations can be described in terms of classical fields, and develop for these a Hamiltonian formalism. The effect of collisions among the hard particles is also studied, in particular in relation with the effective theory for ultrasoft excitations, with momenta $\sim g^2T$.

hep-ph↗

arXiv2000

Transverse energy fluctuations and the pattern of J/Psi suppression in Pb-Pb collisions

The NA50 collaboration has recently observed that the J/psi production rate in Pb-Pb collisions decreases more rapidly as a function of the transverse energy for the most central collisions than for less central ones. We show that this phenomenon can be understood as an effect of transverse energy fluctuations in central collisions. A good fit of the data is obtained using a model which relates J/psi suppression to the local energy density. Our results suggest that the J/psi is completely suppressed at the highest densities achieved in Pb-Pb collisions.

nucl-th↗

arXiv1999

Ultrasoft Amplitudes in Hot QCD

By using the Boltzmann equation describing the relaxation of colour excitations in the QCD plasma, we obtain effective amplitudes for the ultrasoft colour fields carrying momenta of order $g^2 T$. These amplitudes are of the same order in $g$ as the hard thermal loops (HTL), which they generalize by including the effects of the collisions among the hard particles. The ultrasoft amplitudes share many of the remarkable properties of the HTL's: they are gauge invariant, obey simple Ward identities, and, in the static limit, reduce to the usual Debye mass for the electric fields. However, unlike the HTL's, which correspond effectively to one-loop diagrams, the ultrasoft amplitudes resum an infinite number of diagrams of the bare perturbation theory. By solving the linearized Boltzmann equation, we obtain a formula for the colour conductivity which accounts for the contributions of the hard and soft modes beyond the leading logarithmic approximation.

hep-ph↗

arXiv1999

A Boltzmann Equation for the QCD Plasma

We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on the gauge coupling assumed to be small. We point out a limitation of the gradient expansion arising when the range of the interactions becomes comparable with that of the space-time inhomogeneities of the system. The method is first applied to the case of scalar electrodynamics, and then to the description of long wavelength colour fluctuations in the QCD plasma. In the latter case, we recover Bödeker's effective theory and its recent reformulation by Arnold, Son and Yaffe. We discuss interesting cancellations among various collision terms, which occur in the calculation of most transport coefficients, but not in that of the quasiparticle lifetime, or in that of the relaxation time of colour excitations.

hep-ph↗

arXiv1999

The transition temperature of the dilute interacting Bose gas

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

cond-mat.stat-mech↗