arXiv subjects

Jean-Paul Blaizot

Publications and source records attributed to Jean-Paul Blaizot.

At least 37 records · Page 2Linked to original sources

arXiv2022

Effect of dipole size fluctuations on diffractive photo-production of vector mesons

We consider the diffractive photo-production of vector mesons on a proton, in the dipole model. We take into account the effect of the fluctuations of the the dipole size, whose magnitude is controlled by the overlap between the photon and the vector meson wave functions. Our predictions for the incoherent diffractive cross section, obtained within the Impact Parameter Saturation Model (IPSat), are shown to be in excellent agreement with the HERA data on $J/Ψ$ photo-production, down to very low momentum transfer, where the dipole size fluctuations are shown to play an essential role. This study complements, without introducing any additional parameter, previous treatments of incoherent diffractive processes in terms of fluctuations of the proton shape, by adding another source of ``geometrical'' fluctuations, namely those coming from the splitting of the photon into color dipoles of various sizes.

hep-ph↗

arXiv2021

S-wave pion-pion scattering lengths from nucleon-meson fluctuations

We present calculations of the $S$-wave isospin-zero and isospin-two pion-pion scattering lengths within a nucleon-meson model with parity doubling. Both scattering lengths are computed in various approximations, ranging from a mean-field (MF) calculation towards the inclusion of loop corrections by means of the functional renormalization group (FRG). The bosonic part of the investigated nucleon-meson model is formulated in terms of stereographic projections as a "natural" set of coordinates on the respective vacuum manifold. We thereby elucidate subtleties concerning the truncation of the effective action w.r.t. higher-derivative pion interactions and the "successful" computation of the scattering lengths. As the main result, we find simultaneous agreement for the isospin-zero and isospin-two scattering lengths with experimental data within the $\mathrm{LPA}^{\prime}$-truncation of the FRG, together with chiral symmetry breaking (roughly) occurring at the characteristic scale of $4πf_π$. The isoscalar $σ$-mass is dynamically generated by the FRG integration of momentum modes, and is a prediction of the model. It ends being of the order of $500\ \mathrm{MeV}$, i.e., much lower than the value ($> 1\ \mathrm{GeV}$) found in MF or one-loop treatment of this or related models. Finally, the convergence of the corresponding low-energy expansion of the quantum effective action in terms of pion momenta is discussed.

hep-ph↗

arXiv2021

Phenomenological study of quarkonium suppression and the impact of the energy gap between singlets and octets

The study of heavy quarkonium suppression in heavy-ion collisions represents an important source of information about the properties of the quark-gluon plasma produced in such collisions. In a previous paper, we have considered how to model the evolution of a quarkonium in such a way that the solution of the resulting equations evolves toward the correct thermal equilibrium distribution for an homogeneous and static medium. We found that it is crucial to take into account the energy gap between singlet and octet configurations when the temperature is not much greater than this energy gap. In this manuscript, we explore in more detail the phenomenological consequences of this observation in the more realistic situation of an expanding system. We consider two different scenarios, based on the same approximation scheme, but on different choices of parameters. In the first case, we rely on a Hard Thermal Loop approximation, while the second case is based on a recent determination of the static potential in lattice QCD. In both cases, we compute the decay width and the nuclear modification factor, both taking the energy gap into account and ignoring it. We find that the impact on the predictions is as large in the expanding medium as it is in the static case. Our conclusion is that this energy gap should be taken into account in phenomenological studies.

hep-ph↗

arXiv2021

Analytical attractor for Bjorken expansion

We present an analytic solution of a simple set of equations that govern the expansion of boost-invariant plasmas of massless particles. These equations describe, approximately, the early time, collisionless regime, and the transition to hydrodynamics at late time. Their mathematical structure encompasses all versions of second order hydrodynamics when applied to Bjorken flows. The analytic solution provides an explicit expression for the attractor solution that connects the collisionless regime to hydrodynamics. It also constitutes a neat example of an application of the theory of resurgence in asymptotic series.

nucl-th↗

arXiv2021

On attractor and fixed points in Bjorken flows

We consider a plasma of massless particles undergoing Bjorken expansion, mimicking the matter created in ultra-relativistic heavy ion collisions. We study the transition to hydrodynamics using kinetic theory in the relaxation time approximation. By allowing the relaxation time to depend on time, we can monitor the speed of the transition from the collisionless regime to hydrodynamics. By using a special set of moments of the momentum distribution, we reduce the kinetic equation to a coupled mode problem which encompasses all versions of second order viscous hydrodynamics for Bjorken flows. This coupled mode problem is analysed first using techniques of linear algebra. Then we transform this two mode problem into a single non linear differential equation and proceed to a fixed point analysis. We identify an attractor solution as the particular solution of this non linear equation that joins two fixed points: one corresponding to the collisionless, early time regime, the other corresponding to late time hydrodynamics. We exploit the analytic solution of this equation in order to test several approximations and to identify generic features of the transition to hydrodynamics. We argue that extending the accuracy of hydrodynamics to early time, i.e. to the region of large gradients, amounts essentially to improve the accuracy of the location of the collisionless fixed point. This is demonstrated by showing that a simple renormalisation of a second order transport coefficient puts the free streaming fixed point at the right location, and allows us to reproduce accurately the full solution of the kinetic equation within second order viscous hydrodynamics, even in regimes far from local equilibrium.

nucl-th↗

arXiv2021

Functional renormalization group and 2PI effective action formalism

We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, the other on the functional renormalization group (fRG), in an effort to develop new non-perturbative approximations for the field theoretical description of strongly coupled systems. In particular, we exploit the exact 2PI relations between the two-point and four-point functions in order to truncate the infinite hierarchy of equations of the functional renormalization group. The truncation is "exact" in two ways. First, the solution of the resulting flow equation is independent of the choice of the regulator. Second, this solution coincides with that of the 2PI equations for the two-point and the four-point functions, for any selection of two-skeleton diagrams characterizing a so-called $Φ$-derivable approximation. The transformation of the equations of the 2PI formalism into flow equations offers new ways to solve these equations in practice, and provides new insight on certain aspects of their renormalization. It also opens the possibility to develop approximation schemes going beyond the strict $Φ$-derivable ones, as well as new truncation schemes for the fRG hierarchy.

hep-th↗

arXiv2019

Angular mode expansion of the Boltzmann equation in the small-angle approximation

We use an expansion in angular mode functions in order to solve the Boltzmann equation for a gluon plasma undergoing longitudinal expansion. By comparing with the exact solution obtained numerically by other means we show that the expansion in mode functions converges rapidly for all cases of practical interest, and represents a substantial gain in numerical effort as compared to more standard methods. We contrast the cases of a non expanding plasma and of longitudinally expanding plasmas, and follow in both cases the evolutions towards thermalization. In the latter case, we observe that, although the spherical mode function appears to be well reproduced after some time by a local equilibrium distribution function depending on slowly varying temperature and chemical potential, thereby suggesting thermalization of the system, the longitudinal and transverse pressures take more time to equilibrate. This is because the expansion hinders the relaxation of the first angular mode function. This feature was also observed in a simpler context where the Boltzmann equation is solved in terms of special moments within the relaxation time approximation, and attributed there to the particular coupling between the first two moments of the distribution function. The present analysis confirms this observation in a more realistic setting.

hep-ph↗

arXiv2019

Emergence of hydrodynamical behavior in expanding quark-gluon plasmas

We use a set of simple angular moments to solve the Boltzmann equation in the relaxation time approximation for a boost invariant longitudinally expanding gluonic plasma. The transition from the free streaming regime at early time to the hydrodynamic regime at late time is well captured by the first two-moments, corresponding to the monopole and quadrupole components of the momentum distribution, or equivalently to the energy density and the difference between the longitudinal and the transverse pressures. We relate this property to the existence of fixed points in the infinite hierarchy of equations satisfied by the moments. These fixed points are already present in the two-moment truncations and are only moderately affected by the coupling to higher moments. Collisions contribute to a damping of all the non trivial moments. At late time, when the hydrodynamic regime is entered, only the monopole and quadrupole moments are significant and remain strongly coupled, the decay of the quadrupole moment being delayed by the expansion, causing in turn a delay in the full isotropization of the system. The two-moment truncation contains second order viscous hydrodynamics, in its various variants, and third order hydrodynamics, together with explicit values of the relevant transport coefficients, can be easily obtained from the three-moment truncation.

nucl-th↗

arXiv2019

Diffractive incoherent vector meson production off protons: a quark model approach to gluon fluctuation effects

Fluctuations play an important role in diffractive production of vector mesons. It was in particular recently suggested, based on the Impact-Parameter dependent Saturation model (IPSat), that geometrical fluctuations triggered by the motion of the constituent quarks within the protons could explain incoherent diffractive processes observed at HERA. We propose a variant of the IPSat model which includes spatial and symmetry correlations between constituent quarks, thereby reducing the number of parameters needed to describe diffractive vector meson production to a single one, the size of the gluon cloud around each valence quark. The application to $J/Ψ$, $ρ$ and $ϕ$ diffractive electron and photon production cross sections reveal the important role of geometrical fluctuations in incoherent channels, while other sources of fluctuations are needed to fully account for electroproduction of light mesons, as well as photo production of $J/Ψ$ mesons at small momentum transfer.

hep-ph↗

arXiv2019

Radiative corrections to the jet quenching parameter in dilute and dense media

We extend the calculation of radiative corrections to momentum broadening in a QCD medium to include processes where single scattering dominates over multiple soft scatterings. Our analysis focusses on processes that are enhanced by a potentially large double logarithmic contribution. We demonstrate that such double logarithmic contributions emerge in calculations of momentum broadening in dilute systems where only single scattering occurs. We show how the different regimes, multiple versus single scattering, constrain different parts of the phase space.

hep-ph↗

arXiv2018

Fluid dynamics of out of equilibrium boost invariant plasmas

We establish a set of equations for moments of the distribution function. In the relaxation time approximations, these moments obey a coupled set of equations that can be truncated order-by-order. Solving the equations of moments, we are able to identify an attractor solution that controls a transition from a free streaming fixed point to a hydrodynamic fixed point. In particular, this attractor solution provides a renormalization of the effective value of the shear viscosity to entropy density ratio, $η/s$, taking into account off-equilibrium effects.

nucl-th↗

arXiv2018

The approach to equilibrium of a quarkonium in a quark-gluon plasma

We derive equations of motion for the reduced density matrix of a heavy quarkonium in contact with a quark-gluon plasma in thermal equilibrium. These equations allow in particular a proper treatment of the regime when the temperature of the plasma is comparable to the binding energy of the quarkonium. These equations are used to study how the quarkonium approaches equilibrium with the plasma, and we discuss the corresponding entropy increase, or free energy decrease, depending on the temperature regime. The effect of collisions can be accounted for by the generalization of the imaginary potential introduced in previous studies, and from which collision rates are derived. An important outcome of the present analysis is that this imaginary potential has a sizeable dependence on the energy of the relevant transitions.

hep-ph↗

arXiv2017

Goldstino in supersymmetric Bose-Fermi mixtures in the presence of Bose Einstein condensate

We analyze the spectral properties of the Goldstino excitation in a Bose-Fermi mixture of cold atoms, whose masses and interaction strengths are tuned so that the hamiltonian is supersymmetric. We consider systems at zero temperature and assume that, in the weak coupling regime, the fermions form a Fermi sea, while the bosons form a Bose-Einstein condensate. We study the excitation spectrum within a simple extension of the random phase approximation, taking into account the mixing between the supercharge and the fermion caused by the condensate. This mixing affects the fermion spectrum strongly. We argue that the corresponding modification of the fermion spectrum, and the associated fermion distribution in momentum space, could be accessible experimentally, and potentially allow for a determination of the Goldstino properties.

cond-mat.quant-gas↗

arXiv2017

Fluid dynamics of out of equilibrium boost invariant plasmas

By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.

nucl-th↗

arXiv2017

Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma

We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate strategies to solve numerically the resulting equations in the case of a quark-antiquark pair. One involves Langevin equations with additional random color forces, the other treats the transition between the singlet and octet color configurations as collisions in a Boltzmann equation which can be solved with Monte Carlo techniques.

hep-ph↗

arXiv2017

Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions

The pre-equilibrium evolution of a quark-gluon plasma produced in a heavy-ion collision is studied in the framework of kinetic theory. We discuss the approach to local thermal equilibrium, and the onset of hydrodynamics, in terms of a particular set of moments of the distribution function. These moments quantify the momentum anisotropies to a finer degree than the commonly used ratio of longitudinal to transverse pressures. They are found to be in direct correspondence with viscous corrections of hydrodynamics, and provide therefore an alternative measure of these corrections in terms of the distortion of the momentum distribution. As an application, we study the evolution of these moments by solving the Boltzmann equation for a boost invariant expanding system, first analytically in the relaxation time approximation, and then numerically for a quark-gluon plasma within the small angle approximation to the collision kernel.

nucl-th↗

arXiv2017

Thermalization of overpopulated systems in the 2PI formalism

Based on the two-particle irreducible (2PI) formalism to next-to-leading order in the $1/N$ expansion, we study the thermalization of overpopulated systems in scalar $O(N)$ theories with moderate coupling. We focus in particular on the growth of soft modes, and examine whether this can lead to the formation of a transient Bose-Einstein condensate (BEC) when the initial occupancy is high enough. For the value of the coupling constant used in our simulations, we find that while the system rapidly approaches the condensation threshold, the formation of a BEC is eventually hindered by particle number changing processes.

hep-ph↗

arXiv2016

Non-Gaussian eccentricity fluctuations

We study the fluctuations of the anisotropy of the energy density profile created in a high-energy collision at the LHC. We show that the anisotropy in harmonic $n$ has generic non-Gaussian fluctuations. We argue that these non-Gaussianities have a universal character for small systems such as p+Pb collisions, but not for large systems such as Pb+Pb collisions where they depend on the underlying non-Gaussian statistics of the initial density profile. We generalize expressions for the eccentricity cumulants $\varepsilon_2\{4\}$ and $\varepsilon_3\{4\}$ previously obtained within the independent-source model to a general fluctuating initial density profile.

nucl-th↗