arXiv subjects

Ph. de Forcrand

Publications and source records attributed to Ph. de Forcrand.

At least 19 recordsLinked to original sources

arXiv2009

Dimensional reduction and the phase diagram of 5d Yang-Mills theory

We present a non-perturbative study of the phase diagram of 5d SU(2) Yang-Mills theory with one compact extra dimension on the lattice. Assuming at least a modest scale separation between the cutoff and the compactification scales leads to an exponential separation between the compactification scale and the four-dimensional correlation length. While we demonstrate that it is not possible to take a full five-dimensional continuum limit, this dynamical generation of scale hierarchy opens up the possibility for us to make limited, but non-perturbative, predictions about continuum theories whose low-energy sector is described by an effective 5d Yang-Mills theory.

hep-lat↗

arXiv2008

Revisiting strong coupling QCD at finite temperature and baryon density

The strong coupling limit ($β_{gauge}=0$) of lattice QCD with staggered fermions enjoys the same non-perturbative properties as continuum QCD, namely confinement and chiral symmetry breaking. In contrast to the situation at weak coupling, the sign problem which appears at finite density can be brought under control for a determination of the full (mu,T) phase diagram by Monte Carlo simulations. Further difficulties with efficiency and ergodicity of the simulations, especially at the strongly first-order, low-T, finite-mu transition, are addressed respectively with a worm algorithm and multicanonical sampling. Our simulations reveal sizeable corrections to the old results of Karsch and Muetter. Comparison with analytic mean-field determinations of the phase diagram shows discrepancies of O(10) in the location of the QCD critical point.

hep-lat↗

arXiv2008

Towards a controlled study of the QCD critical point

The phase diagram of QCD, as a function of temperature T and quark chemical potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative nature makes it a natural object of lattice studies. However, the sign problem prevents the application of standard Monte Carlo techniques at non-zero baryon density. We have been pursuing an approach free of the sign problem, where the chemical potential is taken as imaginary and the results are Taylor-expanded in mu/T about mu=0, then analytically continued to real mu. Within this approach we have determined the sensitivity of the critical chemical potential mu_E to the quark mass, d(μ_E)^2/dm_q|_{μ_E=0}. Our study indicates that the critical point moves to {\em smaller} chemical potential as the quark mass {\em increases}. This finding, contrary to common wisdom, implies that the deconfinement crossover, which takes place in QCD at mu=0 when the temperature is raised, will remain a crossover in the mu-region where our Taylor expansion can be trusted. If this result, obtained on a coarse lattice, is confirmed by simulations on finer lattices now in progress, then we predict that no {\em chiral} critical point will be found for mu_B \lesssim 500 MeV, unless the phase diagram contains additional transitions.

hep-lat↗

arXiv2008

Center-Symmetric Effective Theory for High-Temperature SU(2) Yang-Mills Theory

We construct and study a dimensionally reduced effective theory for high-temperature SU(2) Yang-Mills theory that respects all the symmetries of the underlying theory. Our main motivation is to study, whether the correct treatment of the center symmetry can help extend the applicability of the dimensional reduction procedure towards the confinement transition. After performing perturbative matching to the full theory at asymptotically high temperatures, we map the phase diagram of the effective theory using non-perturbative lattice simulations. We find that at lower temperature the theory undergoes a second order confining phase transition, in complete analogy with the full theory, which is a direct consequence of having incorporated the center symmetry.

hep-ph↗

arXiv2007

On the phase diagram of QCD at finite isospin density

Using a canonical formalism, we determine the equation of state and the phase diagram of eight-flavour QCD, as a function of temperature and isospin density. Two mechanisms are at work: Bose condensation of pions at high density, and deconfinement at high temperature. We study their interplay and find that on our small and coarse lattice the first order deconfinement transition appears to end at a critical point at finite density. We investigate the strength of the overlap and of the sign problems and discuss implications for the baryonic density case.

hep-lat↗

arXiv2006

Evidence for diquarks in lattice QCD

Diquarks may play an important role in hadron spectroscopy, baryon decays and color superconductivity. We investigate the existence of diquark correlations in lattice QCD by considering systematically all the lowest energy diquark channels in a color gauge-invariant setup. We measure mass differences between the various channels and show that the positive parity scalar diquark is the lightest. Quark-quark correlations inside the diquark are clearly seen in this channel, and yield a diquark size of order 1 fm.

hep-lat↗

arXiv2006

Screening of Z(N) monopole pairs in gauge theories

The screening of magnetic Z(N)-monopoles and the associated screening length in SU(N) gauge theories are analyzed theoretically, and computed numerically in the 3d SU(2) theory. The nature of the screening excitations as well as their mass have so far remained inconclusive in the literature. Here we show that the screening mass is identical to the lowest J^{PC}_R=0^{++}_+ excitation of the Yang-Mills Hamiltonian with one compact direction with period 1/T, the subscript R referring to parity in this direction. We extend the continuum formulation to one on the lattice, and determine the transfer matrix governing the decay of the spatial monopole correlator at any finite lattice spacing. Our numerical results for SU(2) for the screening mass in the dimensionally reduced (high temperature) theory are compatible with the 0^{++} glueball mass in 3d SU(2).

hep-ph↗

arXiv2006

QCD at Zero Baryon Density and the Polyakov Loop Paradox

We compare the grand canonical partition function at fixed chemical potential mu with the canonical partition function at fixed baryon number B, formally and by numerical simulations at mu=0 and B=0 with four flavours of staggered quarks. We verify that the free energy densities are equal in the thermodynamic limit, and show that they can be well described by the hadron resonance gas at T < T_c and by the free fermion gas at T>T_c. Small differences between the two ensembles, for thermodynamic observables characterising the deconfinement phase transition, vanish with increasing lattice size. These differences are solely caused by contributions of non-zero baryon density sectors, which are exponentially suppressed with increasing volume. The Polyakov loop shows a different behaviour: for all temperatures and volumes, its expectation value is exactly zero in the canonical formulation, whereas it is always non-zero in the commonly used grand-canonical formulation. We clarify this paradoxical difference, and show that the non-vanishing Polyakov loop expectation value is due to contributions of non-zero triality states, which are not physical, because they give zero contribution to the partition function.

hep-lat↗

arXiv2005

The 3-state Potts model as a heavy quark finite density laboratory

The 3-D Z(3) Potts model is a model for finite temperature QCD with heavy quarks. The chemical potential in QCD becomes an external magnetic field in the Potts model. Following Alford et al.\cite{Alford_et_al}, we revisit this mapping, and determine the phase diagram for an arbitrary chemical potential, real or imaginary. Analytic continuation of the phase transition line between real and imaginary chemical potential can be tested with precision. Our results show that the chemical potential weakens the heavy-quark deconfinement transition in QCD.

hep-lat↗

arXiv2005

More evidence of localization in the low-lying Dirac spectrum

We have extended our computation of the inverse participation ratio of low-lying (asqtad) Dirac eigenvectors in quenched SU(3). The scaling dimension of the confining manifold is clearer and very near 3. We have also computed the 2-point correlator which further characterizes the localization.

hep-lat↗

arXiv2005

Algorithm Shootout: R versus RHMC

We present initial results comparing the RHMC and R algorithms on large lattices with small quark masses using chiral fermions. We also present results concerning staggered fermions near the deconfinement/chiral phase transition. We find that the RHMC algorithm not only eliminates the step-size error of the R algorithm, but is also considerably more efficient. We discuss several possibilities for further improvement to the RHMC algorithm.

hep-lat↗

arXiv2005

Monte Carlo overrelaxation for SU(N) gauge theories

The standard approach to Monte Carlo simulations of SU(N) Yang-Mills theories updates successive SU(2) subgroups of each SU(N) link. We follow up on an old proposal of Creutz, to perform overrelaxation in the full SU(N) group instead, and show that it is more efficient.

hep-lat↗

arXiv2005

The baryon static potential from lattice QCD

Lattice QCD simulations offer the possibility of determining the potential between three static quarks from first principles. We review the status of such simulations, and the relative standing of the two theoretical proposals for the baryonic potential: the Delta law (sum of two-body terms) and the Y law (length of three flux strings joined together at a junction). We also present new results on the leading Luscher-like corrections to the asymptotic linear potential.

hep-ph↗

arXiv2005

Properties of hadron screening masses at small baryonic density

The properties of hadron screening masses around the deconfinement phase transition at finite baryonic density can be studied by evaluating the Taylor coefficients with respect to the iso-scalar and iso-vector chemical potentials. We simulate 2-flavour lattice QCD with staggered fermions on a 12*12*24*6 lattice with ma = 0.05 and 0.10 and report investigations of nucleon, pseudo-scalar and vector mesons. We present new, strong evidence that in the confining phase, the screening masses at vanishing chemical potential have significant temperature dependence, but the effect of the iso-scalar chemical potential is very small. Above the critical temperature, the second derivative terms of mesons rapidly increase as contrasted to the case of baryon. We also study the responses of the screening masses to an iso-vector chemical potential and discuss some of the issues related to the properties of hadron masses at finite density.

hep-lat↗

arXiv2004

Momentum dependence of the N to Delta transition form factors

We present a new method to determine the momentum dependence of the N to Delta transition form factors and demonstrate its effectiveness in the quenched theory at $β=6.0$ on a $32^3 \times 64$ lattice. We address a number of technical issues such as the optimal combination of matrix elements and the simultaneous overconstrained analysis of all lattice vector momenta contributing to a given momentum transfer squared, $Q^2$.

hep-lat↗

arXiv2004

The scaling dimension of low lying Dirac eigenmodes and of the topological charge density

As a quantitative measure of localization, the inverse participation ratio of low lying Dirac eigenmodes and topological charge density is calculated on quenched lattices over a wide range of lattice spacings and volumes. Since different topological objects (instantons, vortices, monopoles, and artifacts) have different co-dimension, scaling analysis provides information on the amount of each present and their correlation with the localization of low lying eigenmodes.

hep-lat↗

arXiv2004

The N to Delta electromagnetic transition form factors from Lattice QCD

The magnetic dipole, the electric quadrupole and the Coulomb quadrupole amplitudes for the transition γN\to Δare calculated in quenched lattice QCD at β=6.0 with Wilson fermions. Using a new method combining an optimal combination of interpolating fields for the $Δ$ and an overconstrained analysis, we obtain statistically accurate results for the dipole form factor and for the ratios of the electric and Coulomb quadrupole amplitudes to the magnetic dipole amplitude, R_{EM} and R_{SM}, up to momentum transfer squared 1.5 GeV^2. We show for the first time using lattice QCD that both R_{EM} and R_{SM} are non-zero and negative, in qualitative agreement with experiment and indicating the presence of deformation in the N- Delta system.

hep-lat↗

arXiv2004

QCD Phase Diagram at small Baryon Densities from Imaginary mu: Status Report

We summarize our recent results for the (T,mu)-phase diagram of N_f=3 QCD. Finding a strong variation of the critical endpoint mu_c with the quark mass m, we point out that an endpoint within reach of experiment requires fine-tuned quark masses. We further discuss the strategy and first data towards extending our results to the physical N_f=2+1 theory.

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