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M. -P. Lombardo

Publications and source records attributed to M. -P. Lombardo.

18 recordsLinked to original sources
arXiv2004

Lattice QCD at finite density

QCD at finite density presents specific challenges to lattice gauge theory. Nonetheless, a region of the QCD phase diagram up to moderately large baryon chemical potentials has been successfully explored on the lattice and new results and idea are continuously emerging. I will outline the lattice formulation of QCD, introduce the calculational schemes currently used to treat a nonzero baryon density, and mention lattice methods alternative to MonteCarlo, including the strong coupling expansion which might give access to the the superconducting phase of QCD. The results for the critical line, and the different phases will be discussed highlighting the strength of the different methods, as well as the possible comparisons with phenomenological models.

hep-lat↗
arXiv2003

SU(2) Glueballs, diquarks and mesons in dense matter

We present preliminary results from a high statistics study of 2-color QCD at low temperature and non-zero baryon density. The simulations are carried out on a 6^3*12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. Observables include glueball correlators evaluated via a multi-step smearing procedure as well as scalar and vector mesons and diquarks.

hep-lat↗
arXiv2002

Vector spectrum and color screening in two color QCD at nonzero T and μ

We discuss a few aspects of the phase diagram of two color lattice QCD: we investigate the long distance screening analyzing the behavior of the interquark potential at large distances; we present a first set of results for vector mesons and diquarks; we note similarities and differences between features at high temperature and high baryon density.

hep-lat↗
arXiv2002

Finite density QCD via imaginary chemical potential

We study QCD at nonzero temperature and baryon density in the framework of the analytic continuation from imaginary chemical potential. We carry out simulations of QCD with four flavor of staggered fermions, and reconstruct the phase diagram in the temperature-imaginary μplane. We consider ansätze for the analytic continuation of the critical line and other observables motivated both by theoretical considerations and mean field calculations in four fermion models and random matrix theory. We determine the critical line, and the analytic continuation of the chiral condensate, up to μ_B approx. 500 MeV. The results are in qualitative agreement with the predictions of model field theories, and consistent with a first order chiral transition. The correlation between the chiral transition and the deconfinement transition observed at μ=0 persists at nonzero density.

hep-lat↗
arXiv2001

Finite temperature field theory

These lectures review phases and phase transitions of the Standard Model, with emphasis on those aspects which are amenable to a first principle study. Model calculations and theoretical ideas of practical applicability are discussed as well. Contents: 1.Overview; 2. Field Theory at Finite Temperature and Density; 3.Critical Phenomena; 4.Electroweak Interactions at Finite Temperature; 5. Thermodynamics of Four Fermions models; 6.The Phases of QCD; 7.QCD at Finite Temperature, $μ_B = 0$; 8.QCD at Finite Temperature, $μ_B \ne 0$.

hep-ph↗
arXiv2000

On the Triviality of Textbook Quantum Electrodynamics

By adding a small, irrelevant four fermi interaction to the action of lattice Quantum Electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. This allows an ab initio high precision, controlled study of the existence of "textbook" Quantum Electrodynamics with several species of fermions. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial. The logarithms of triviality, which modify mean field scaling laws, are pinpointed in several observables. The result supports Landau's contention that perturbative QED suffers from complete screening and would have a vanishing fine structure constant in the absence of a cutoff.

hep-lat↗
arXiv2000

Universality and Chaos in Quantum Field Theories

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution, $P(s)$. We further study two-color QCD at nonzero chemical potential, $μ$, by constructing the spacing distribution of adjacent eigenvalues in the complex plane. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior.

hep-lat↗
arXiv1999

Finite density (might well be easier) at finite temperature

Experiments with imaginary chemical potential and Glasgow method carried out in two interrelated models - four dimensional QCD in the infinite coupling limit, and one dimensional QCD - support the point of view expressed by the title.

hep-lat↗
arXiv1999

Interquark potential, susceptibilities and particle density of two color QCD at finite chemical potential and temperature

We explore the phase diagram of SU(2) Lattice Gauge Theory with dynamical fermions in the temperature, mass, chemical potential space. We observe qualitative changes of the dependence of the particle density on $μ$ and $T$, which is compatible with that expected of a gas of free massless quarks $n \propto μ^3$ only for $T \simeq T_c$. At the onset for thermodynamics the interquark potential flattens at large separations, indicating enhanced fermion screening and the transition to a deconfined phase. Temporal and spatial Polyakov loops behave in different ways, the latter being nearly insensitive to the chemical potential. The rotation of the chiral condensate to a baryonic condensate, as inferred from the susceptibilities, might occur together with a reduction of its magnitude in the chiral limit, possibly leading to a critical temperature for diquark condensation smaller than the deconfinement temperature. We further asses the rôle of the chemical potential into the gauge dynamics by carrying out a partial quenched calculation. We speculate on the relevance, or lack thereof, of our findings to real QCD.

hep-lat↗
arXiv1999

Deconfinement and non-zero baryon density

I discuss a few issues related with deconfinement at finite baryon density by considering lattice results for two colors QCD and ``toy'' studies of three colors QCD.

hep-lat↗
arXiv1997

Results on Finite Density QCD

A brief summary of the formulation of QCD at finite chemical potental, $μ$, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential $\approx { {m_π} \over 2}$. However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, ($e^{μ/T}$), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when $μ$ passed through the value $m_π/2}$.

hep-lat↗
arXiv1997

The Critical Points of Strongly Coupled Lattice QCD at Nonzero Chemical Potential

We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point μ_c in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations. We observe, however, two unphysical critical points: the onset for the number density μ_o, and μ_s the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point μ_c, and offers a new intepretation of μ_o, which confirms its unphysical nature. The perspectives for future lattice QCD calculations of the properties of dense baryonic matter are briefly discussed.

hep-lat↗
arXiv1996

The critical points of lattice QCD with a non--zero quark density

We study the interplay of quark number density and chiral symmetry in lattice QCD. We suggest that both are controlled by the eigenvalue spectrum of the fermionic propagator matrix, which shapes the pattern of zeros of the partition function. The onset of the quark current would be triggered by the lowest lying eigenvalue, the chiral transition by the density of zeros, the two critical points being distinct in full QCD, and coincident in the quenched approximation. Our preliminary estimate for the critical point in full QCD in the infinite couling limit compares favourably with the predictions of the strong coupling expansions and of numerical simulations based on exact, alternative representations of the partition function. Several reasons of perplexity however remain, which are briefly discussed.

hep-lat↗
arXiv1995

Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential

We simulate lattice QCD at non--zero baryon density and zero temperature in the quenched approximation, both in the scaling region and in the infinite coupling limit. We investigate the nature of the forbidden region -- the range of chemical potential where the simulations grow prohibitively expensive, and the results, when available, are puzzling if not unphysical. At weak coupling we have explored the sensitivity of these pathologies to the lattice size, and found that using a large lattice ($64 \times 16^3$) does not remove them. The effective potential sheds considerable light on the problems in the simulations, and gives a clear interpretation of the forbidden region. The strong coupling simulations were particularly illuminating on this point.

hep-lat↗
arXiv1992

Universal Properties of Chiral Simmetry Breaking

We discuss chiral symmetry breaking critical points from the perspective of PCAC, correlation length scaling and the chiral equation of state. A scaling theory for the ratio $R_π$ of the pion to sigma masses is presented. The Goldstone character of the pion and properties of the longitudinal and transverse chiral susceptibilities determine the ratio $R_π$ which can be used to locate critical points and measure critical indices such as $δ$. We show how PCAC and correlation length scaling determine the pion mass' dependence on the chiral condensate and lead to a practical method to measure the anomalous dimension $η$. These tools are proving useful in studies of the chiral transition in lattice QED and the quark-gluon plasma transition in lattice QCD.

hep-lat↗
arXiv1992

Lattice QCD Spectroscopy with an Improved Wilson Fermion Action

We study the hadronic spectrum in quenched lattice QCD using an improved Wilson fermion action (Hamber-Wu(1983),Eguchi-Kawamoto(1984)) at $β= 5.7$ and $β=6.0$. We find a systematic reduction of the finite spacing effects compared to the results obtained by using the standard Wilson action.

hep-lat↗
arXiv1992

Spectroscopy, Scaling and Critical Indices in Strongly Coupled Quenched QED

The interplay of spectroscopy, scaling laws and critical indices is studied in strongly coupled quenched QED. Interpreted as a model of technicolor having strong interactions at short distances, we predict the techni-meson mass spectrum in a simplified model of a dynamically generated top quark mass $M_f$. Our results support the strict inequality that the techni-sigma mass $M_σ$ is less than twice the dynamical quark mass $M_f$, and confirm that the techni-pion is a Nambu-Goldstone boson. The level ordering $0 = M_π< M_σ< 2M_f < M_ρ< M_{a1} $ is found.An equation of state, and scaling laws are derived for the techni-meson masses by exploiting correlation length scaling. The resulting universality relations are confirmed by simulations on $16^4$, $32\times 16^3$ and $32^4$ lattices. The anomalous dimension $η$ is measured to be approximatively $0.50$ in good agreement with past lattice simulations and hyperscaling relations, as well as with the analytic solution of the quenched, planar gauged Nambu-Jona Lasinio model solved by continuum Schwinger-Dyson equation techniques.

hep-lat↗