arXiv subjects

E. Iancu

Publications and source records attributed to E. Iancu.

86 records · Page 5Linked to original sources

arXiv2002

Comparing different hard-thermal-loop approaches to quark number susceptibilities

We compare our previously proposed hard-thermal-loop (HTL) resummed calculation of quark number susceptibilities using a self-consistent two-loop approximation to the quark density with a recent calculation of the same quantity at the one-loop level in a variant of HTL-screened perturbation theory. Besides pointing out conceptual problems with the latter approach, we show that it severely over-includes the leading-order interaction effects while including none of the plasmon term which after all is the reason to construct improved resummation schemes.

hep-ph↗

arXiv2002

Froissart Bound from Gluon Saturation

We demonstrate that the dipole-hadron cross-section computed from the non-linear evolution equation for the Colour Glass Condensate saturates the Froissart bound in the case of a fixed coupling and for a small dipole (Q^2 >> Lambda_{QCD}^2). That is, the cross-section increases as the logarithm squared of the energy, with a proportionality coefficient involving the pion mass and the BFKL intercept (alpha_s N_c/pi)4 ln 2. The pion mass enters via the non-perturbative initial conditions at low energy. The BFKL equation emerges as a limit of the non-linear evolution equation valid in the tail of the hadron wavefunction. We provide a physical picture for the transverse expansion of the hadron with increasing energy, and emphasize the importance of the colour correlations among the saturated gluons in suppressing non-unitary contributions due to long-range Coulomb tails. We present the first calculation of the saturation scale including the impact parameter dependence. We show that the cross-section at high energy exhibits geometric scaling with a different scaling variable as compared to the intermediate energy regime.

hep-ph↗

arXiv2002

Non linear gluon evolution in path-integral form

We explore and clarify the connections between two different forms of the renormalisation group equations describing the quantum evolution of hadronic structure functions at small $x$. This connection is established via a Langevin formulation and associated path integral solutions that highlight the statistical nature of the quantum evolution, pictured here as a random walk in the space of Wilson lines. The results confirm known approximations, form the basis for numerical simulations and widen the scope for further analytical studies.

hep-ph↗

arXiv2002

Understanding Geometric Scaling at Small x

Geometric scaling is a novel scaling phenomenon observed in deep inelastic scattering at small x: the total virtual photon-proton cross section depends upon the two kinematical variables Q^2 and x only via their combination Q^2 R_0^2(x), with R_0^2(x) \propto x^λ. At sufficiently low Q^2, below the saturation scale Q_s^2(x) (a few GeV^2), this phenomenon finds a natural explanation as a property of the Color Glass Condensate, the high-density matter made of saturated gluons. To explain the experimental observation of geometric scaling up to much higher values of Q^2, of the order of 100 GeV^2, we study the solution to the BFKL equation subjected to a saturation boundary condition at Q^2\sim Q_s^2(x). We find that the scaling extends indeed above the saturation scale, within a window 1 < \ln(Q^2/Q_s^2) << \ln(Q_s^2/Λ^2_{\rm QCD}), which is consistent with phenomenology.

hep-ph↗

arXiv2002

Geometric Scaling above the Saturation Scale

We show that the evolution equations in QCD predict geometric scaling for quark and gluon distribution functions in a large kinematical window, which extends above the saturation scale up to momenta $Q^2$ of order $100 {\rm GeV}^2$. For $Q^2 < Q^2_s$, with $Q_s$ the saturation momentum, this is the scaling predicted by the Colour Glass Condensate and by phenomenological saturation models. For $1 \simle \ln(Q^2/Q_s^2) \ll \ln(Q_s^2/Λ^2_{\rm QCD})$, we show that the solution to the BFKL equation shows approximate scaling, with the scale set by $Q_s$. At larger $Q^2$, this solution does not scale any longer. We argue that for the intermediate values of $Q^2$ where we find scaling, the BFKL rather than the double logarithmic approximation to the DGLAP equation properly describes the dynamics. We consider both fixed and running couplings, with the scale for running set by the saturation momentum. The anomalous dimension which characterizes the approach of the gluon distribution function towards saturation is found to be close to, but lower than, one half.

hep-ph↗

arXiv2001

Quark number susceptibilities from HTL-resummed thermodynamics

We compute analytically the diagonal quark number susceptibilities for a quark-gluon plasma at finite temperature and zero chemical potential, and compare with recent lattice results. The calculation uses the approximately self-consistent resummation of hard thermal and dense loops that we have developed previously. For temperatures between 1.5 to 5 $T_c$, our results follow the same trend as the lattice data, but exceed them in magnitude by about 5-10%. We also compute the lowest order contribution, of order $α_s^3\log(1/α_s)$, to the off-diagonal susceptibility. This contribution, which is not a part of our self-consistent calculation, is numerically small, but not small enough to be compatible with a recent lattice simulation.

hep-ph↗

arXiv2001

The Renormalization Group Equation for the Color Glass Condensate

We present an explicit and simple form of the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate (CGC). This is a functional Fokker-Planck equation for the probability density of the color field which describes the CGC in the covariant gauge. It is equivalent to the Euclidean time evolution equation for a second quantized current-current Hamiltonian in two spatial dimensions. The quantum corrections are included in the leading log approximation, but the equation is fully non-linear with respect to the generally strong background field. In the weak field limit, it reduces to the BFKL equation, while in the general non-linear case it generates the evolution equations for Wilson-line operators previously derived by Balitsky and Kovchegov within perturbative QCD.

hep-ph↗

arXiv2001

The thermodynamics of the quark-gluon plasma: Self-consistent resummations vs. lattice data

We discuss a recent approach for overcoming the poor convergence of the perturbative expansion for the thermodynamic potential of QCD. This approach is based on self-consistent approximations which allow for a gauge-invariant and manifestly ultraviolet-finite resummation of the essential physics of the hard thermal/dense loops. The results thus obtained are in good agreement with available lattice data down to temperatures of about twice the critical temperature. Calculations for a plasma with finite quark density (i.e., with a non-zero chemical potential $μ$) are no more difficult than at $μ=0$.

hep-ph↗

arXiv2000

Approximately self-consistent resummations for the thermodynamics of the quark-gluon plasma. I. Entropy and density

We propose a gauge-invariant and manifestly UV finite resummation of the physics of hard thermal/dense loops (HTL/HDL) in the thermodynamics of the quark-gluon plasma. The starting point is a simple, effectively one-loop expression for the entropy or the quark density which is derived from the fully self-consistent two-loop skeleton approximation to the free energy, but subject to further approximations, whose quality is tested in a scalar toy model. In contrast to the direct HTL/HDL-resummation of the one-loop free energy, in our approach both the leading-order (LO) and the next-to-leading order (NLO) effects of interactions are correctly reproduced and arise from kinematical regimes where the HTL/HDL are justifiable approximations. The LO effects are entirely due to the (asymptotic) thermal masses of the hard particles. The NLO ones receive contributions both from soft excitations, as described by the HTL/HDL propagators, and from corrections to the dispersion relation of the hard excitations, as given by HTL/HDL perturbation theory. The numerical evaluations of our final expressions show very good agreement with lattice data for zero-density QCD, for temperatures above twice the transition temperature.

hep-ph↗

arXiv1999

Variational calculations with improved energy functionals in gauge theories

For a SU(N) Yang-Mills theory, we present variational calculations using gaussian wave functionals combined with an approximate projection on gauge invariant states. The projection amounts to correcting the energy of the gaussian states by substracting the spurious energy associated with gauge rotations. Based on this improved energy functional, we perform variational calculations of the interaction energy in the presence of external electric and magnetic fields. We verify that the ultraviolet behaviour of our approximation scheme is consistent, as it should, with that expected from perturbation theory. In particular, we recover in this variational framework the standard one-loop beta function, with a transparent interpretation of the screening and anti-screening contributions.

hep-ph↗

arXiv1999

Self-consistent hard-thermal-loop thermodynamics for the quark-gluon plasma

Self-consistent approximations allowing the calculation of the entropy and the baryon density of a quark-gluon plasma are presented. These approximations incorporate the essential physics of the hard thermal loops, involve only ultraviolet-finite quantities, and are free from overcounting ambiguities. While being nonperturbative in the strong coupling constant $g$, agreement with ordinary perturbation theory is achieved up to and including order $g^3$. It is shown how the pressure can be reconstructed from the entropy and the baryon density taking into account the scale anomaly. The results obtained are in good agreement with available lattice data down to temperatures of about twice the critical temperature.

hep-ph↗

arXiv1999

The entropy of the QCD plasma

Self-consistent approximations in terms of fully dressed propagators provide a simple expression for the entropy of an ultrarelativistic plasma, which isolates the contribution of the elementary excitations as a leading contribution. Further approximations, whose validity is checked on a soluble model involving a scalar field, allow us to calculate the entropy of the QCD plasma. We obtain an accurate description of lattice data for purely gluonic QCD, down to temperatures of about twice the transition temperature.

hep-ph↗

arXiv1998

Variational calculations in gauge theories with approximate projection on gauge invariant states

Variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states are presented. We find that the energy exhibits a minimum for a wave functional centered around a non vanishing background magnetic field. We show that divergences can be removed by a renormalization of the coupling constant. The resulting expectation value of the gluon condensate is found to be in qualitative agreement with phenomenological estimates.

hep-th↗

arXiv1995

Non-perturbative aspects of screening phenomena in abelian and non abelian gauge theories

When computed to one-loop order in resummed perturbation theory, the non-abelian Debye mass appears to be logarithmically sensitive to the magnetic scale $g^2T$. More generally, we show that in higher orders power-like infrared divergences forbid the use of perturbation theory to calculate the corrections to Debye screening. A similar infrared problem occurs in the determination of the mass-shell for the scalar propagator in 2+1-dimensional scalar electrodynamics. In this context, we provide a non-perturbative approach which solves the infrared problems and allows for an accurate calculation of the scalar propagator in the vicinity of the mass-shell.

hep-ph↗