arXiv subjects

Ismail Zahed

Publications and source records attributed to Ismail Zahed.

At least 217 records · Page 12Linked to original sources

arXiv1999

Generalized Pions in Dense QCD

QCD superconductors in the color-flavor-locked (CFL) phase sustain light Goldstone modes (that will be referred to as generalized pions) that can be described as pairs of particle and/or hole excitations around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy, their form factor, mass and decay constant can be evaluated exactly. These modes are found to satisfy an axial-Ward-identity, constraining the mass of the Goldstone modes in the CFL phase.

hep-ph↗

arXiv1999

U(1) Problem at Finite Temperature

We model the effects of a large number of zero and near-zero modes in the QCD partition function by using sparse chiral matrix models with an emphasis on the quenched topological susceptibility in the choice of the measure. At finite temperature, the zero modes are not affected by temperature but are allowed to pair into topologically neutral near-zero modes which are gapped at high temperature. In equilibrium, chiral and U(1) symmetry are simultaneously restored for total pairing, evading mean-field arguments. We analyze a number of susceptibilities versus the light quark masses. At the transition point the topological susceptibility vanishes, and the dependence on the vacuum angle $θ$ drops out. Our results are briefly contrasted with recent lattice simulations.

hep-lat↗

arXiv1999

Dense QCD : Overhauser or BCS Pairing ?

We discuss the Overhauser effect (particle-hole pairing) versus the BCS effect (particle-particle or hole-hole pairing) in QCD at large quark density. In weak coupling and to leading logarithm accuracy, the pairing energies can be estimated exactly. For a small number of colors, the BCS effect overtakes the Overhauser effect, while for a large number of colors the opposite takes place, in agreement with a recent renormalization group argument. In strong coupling with large pairing energies, the Overhauser effect may be dominant for any number of colors, suggesting that QCD may crystallize into an insulator at a few times nuclear matter density, a situation reminiscent of dense Skyrmions. The Overhauser effect is dominant in QCD in 1+1 dimensions, although susceptible to quantum effects. It is sensitive to temperature in all dimensions.

hep-ph↗

arXiv1999

Chiral Disorder in Two-Color QCD with Abelian External Fluxes

We investigate the effects of several Abelian external fluxes $ϕ$, on the Euclidean Dirac spectrum of light quarks in QCD with two colors. Our results provide for a novel way of assessing the pion weak decay constant directly from spectral fluctuations, and discriminating a flux-rich from a flux-poor vacuum, using QCD lattice simulations.

hep-lat↗

arXiv1999

Green's Functions in Non-hermitian Random Matrix Models

We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The results are illustrated in terms of the eigenvalue distribution, eigenvector statistics and addition laws.

cond-mat.dis-nn↗

arXiv1999

Elastic Parton-Parton Scattering from AdS/CFT

Using the AdS/CFT correspondence and the eikonal approximation, we evaluate the elastic parton-parton scattering amplitude at large $N$ and strong coupling $g^2N$ in N=4 SYM. We obtain a scattering amplitude with a Regge behavior that unitarizes at large $\sqrt{s}$.

hep-th↗

arXiv1999

Qualitons At High Density

In the color-flavor-locked (CFL) phase of the QCD superconductor we show that baryons behave as qualitons (called "superqualitons") with quantum numbers $B=(1 {\rm mod} 2)/3$, S=1/2 and Y=B. An intriguing possibility implied by this identification is that light baryonic modes in the form of superqualitons could be excited below the (color) superconducting gap in the CFL phase, a novel phenomenon foreign to normal superconductors.

hep-ph↗

arXiv1999

Zero Color Magnetization in QCD Matter

We show that all spatial gluon connected correlation functions in SU(N) or SO(N) QCD vanish at finite temperature and zero momentum in lattice Landau or Coulomb gauges, due to the proximity of the Gribov horizon. These observations also apply to QCD with two colors and an even number of flavors at large chemical potential. These nonperturbative results may have consequences on the nature of the thermal magnetic mass and the character of the magnetic color superconductivity.

hep-th↗

arXiv1999

$θ$ Vacuum in a Random Matrix Model

Inspired by recent lattice calculations, we model certain aspects of the $θ$-vacuum using a matrix model with gaussian weights. The vacuum energy exhibits a cusp at $θ<π$ that is sensitive to both the accuracy of the numerical analysis and the maximum density of winding modes present in a finite volume.

hep-ph↗

arXiv1999

Chiral Disorder and Diffusion in The QCD Vacuum

In this talk, which popularizes some of our recent work, we provide novel insights into the bulk properties of light chiral quarks in a fixed Euclidean volume (e.g. lattice QCD). We show that the spontaneous breakdown of chiral symmetry results into diffusing quarks with a vacuum diffusion constant $D=2F_π^2/|<\bar{q}q>|$ $\approx 0.22$ fm, in striking analogy to diffusing electrons in disordered metals in one-, two- and three-dimensions.

hep-ph↗

arXiv1999

$θ$ Vacuum: A Matrix Model

We model the effects of a large number of zero modes for $N_f$ species of quarks at finite vacuum angle $θ$, using a matrix model with gaussian weights constrained by the topological susceptibility and compressibility. The quenched free energy exhibits a cusp at $θ<π$ that is sensitive to the accuracy of the numerical analysis and the maximum density of winding modes. Our results bear much in common with recent lattice simulations by Schierholtz and others. The unquenched free energy exhibits similar sensitivities, but for small quark masses or a large density of zero modes the results are in agreement with those derived using chiral effective Lagrangians.

hep-ph↗

arXiv1999

The Role of Nucleons in Electromagnetic Emission Rates

Electromagnetic emission rates from a thermalized hadronic gas are important for the interpretation of dilepton signals from heavy-ion collisions. Although there is a consensus in the literature about rates for a pure meson gas, qualitative differences appear with a finite baryon density. We show this to be essentially due to the way in which the pi-N background is treated in regards to the nucleon resonances. Using a background constrained by unitarity and broken chiral symmetry, it is emphasized that the thermalized hadronic gas can be considered dilute.

hep-ph↗

arXiv1998

Chiral Random Matrix Models in QCD

We review some motivation behind the introduction of chiral random matrix models in QCD, with particular emphasis on the importance of the Gell-Mann-Oakes (GOR) relation for these arguments. We show why the microscopic limit is universal in power counting, and present arguments for why the macroscopic limit is generic for a class of problems that defy power counting, examples being the strong CP and U(1) problems. Some new results are discussed in light of recent lattice simulations.

hep-ph↗

arXiv1998

A Simple Derivation of the Hard Thermal Loop Effective Action

We use the background field method along with a special gauge condition, to derive the hard thermal loop effective action in a simple manner. The new point in the paper is to relate the effective action explicitly to the S-matrix from the onset.

hep-th↗

arXiv1998

Chiral Disorder and QCD Phase Transitions

If QCD is to undergo a second order phase transition, the light quark return probability is universal for large times at the critical point. We show that this behavior is distinct from the one expected at the mobility edge of a metal-insulator transition or a percolation transition in d$\leq 4$. Our results are accessible to current lattice QCD simulations.

hep-ph↗

arXiv1998

Two-Color QCD and Aharonov-Bohm Fluxes

We investigate the effects of several Abelian Aharonov-Bohm fluxes $ϕ$ on the Euclidean Dirac spectrum of light quarks in QCD with two colors. A quantitative change in the quark return probability is caused by the fluxes, resulting into a change of the spectral correlations. These changes are controlled by a universal function of $σ_L ϕ^2$ where $σ_L$ is the pertinent Ohmic conductance. The quark return probability is sensitive to Abelian flux-disorder but not to $Z_2$ flux-disorder in the ergodic and diffusive regime, and may be used as a probe for the nature of the confining fields in the QCD vacuum.

hep-ph↗

arXiv1998

Chiral Disorder and Diffusion of Light Quarks in the QCD Vacuum

We give a pedagogical introduction to the concept that light quarks diffuse in the QCD vacuum following the spontaneous breaking of chiral symmetry. By analogy with disordered electrons in metals, we show that the diffusion constant for light quarks in QCD is $D=2F_π^2/|\la\bar{q}q\to|$ which is about 0.22 fm. We comment on the correspondence between the diffusive phase and the chiral phase as described by chiral perturbation theory, as well as the cross-over to the ergodic phase as described by random matrix theory. The cross-over is identified with the Thouless energy $E_c=D/\sqrt{V_4}$ which is the inverse diffusion time in an Euclidean four-volume $V_4$.

hep-ph↗

arXiv1998

Chiral Disorder and QCD at Finite Chemical Potential

We investigate the effects of a finite chemical potential $μ$ in QCD viewed as a disordered medium. In the quenched approximation, $A_4=iμ$ induces a complex electric Aharonov-Bohm effect that causes the diagonal contribution to the quark return probability to vanish at $μ=m_π/2$ (half the pion mass). In two-color QCD, the weak-localization contribution to the quark return probability remains unaffected causing a mutation in the spectral statistics. In full QCD, the complex electric flux is screened and the light quarks are shown to diffuse asymmetrically with a substantial decrease in the conductivity along the `spatial' directions. Mean-field arguments suggest that a d=1 percolation transition may take place in the range $1.5ρ_0<ρ<3ρ_0$, where $ρ_0$ is nuclear matter density.

hep-ph↗