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C. Alexandrou

Publications and source records attributed to C. Alexandrou.

At least 127 records · Page 7Linked to original sources
arXiv2001

The static three-quark SU(3) and four-quark SU(4) potentials

We present results on the static three- and four-quark potentials in SU(3) and SU(4) respectively within quenched lattice QCD. We use an analytic multi-hit procedure for the time links and a variational approach to determine the ground state. The three- and four-quark potentials extracted are consistent with a sum of two-body potentials, possibly with a weak many-body component. The results give support to the $Δ$ ansatz for the baryonic area law.

hep-lat↗
arXiv2001

The Gluon Propagator without lattice Gribov copies

We study the gluon propagator in quenched lattice QCD using the Laplacian gauge which is free of lattice Gribov copies. We compare our results with those obtained in the Landau gauge on the lattice, as well as with various approximate solutions of the Dyson Schwinger equations. We find a finite value $\sim (445 \rm{MeV})^{-2}$ for the renormalized zero-momentum propagator (taking our renormalization point at 1.943 GeV), and a pole mass $\sim 640 \pm 140$ MeV.

hep-lat↗
arXiv2000

What Can We Learn from QED at Large Couplings?

In order to understand QCD at the energies relevant to hadronic physics one requires analytical methods for dealing with relativistic gauge field theories at large couplings. Strongly coupled quenched QED provides an ideal laboratory for the development of such techniques, in particular as many calculations suggest that - like QCD - this theory has a phase with broken chiral symmetry. In this talk we report on a nonperturbative variational calculation of the electron propagator within quenched QED and compare results to those obtained in other approaches. We find surprising differences among these results.

hep-th↗
arXiv2000

Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach

Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the supersymmetry between bosonic and fermionic variables and the much more singular structure of a renormalizable gauge theory like QED in 3+1 dimensions. We take as trial action a general retarded quadratic action both for the bosonic and fermionic degrees of freedom and derive the variational equations for the corresponding retardation functions. We find a simple analytic, non-perturbative, solution for the anomalous mass dimension gamma_m(alpha) in the MS scheme. For small couplings we compare our result with recent four-loop perturbative calculations while at large couplings we find that gamma_m(alpha) becomes proportional to (alpha)^(1/2). The anomalous mass dimension shows no obvious sign of the chiral symmetry breaking observed in calculations based on the use of Dyson-Schwinger equations, however we find that a perturbative expansion of gamma_m(alpha) diverges for alpha > 0.7934. Finally, we investigate the behaviour of gamma_m(alpha) at large orders in perturbation theory.

hep-th↗
arXiv2000

One-loop renormalization of fermionic currents with the overlap-Dirac operator

We compute the one-loop lattice renormalization of the two-quark operators $\barψ Γψ$, where $Γ$ denotes the generic Dirac matrix, for the lattice formulation of QCD using the overlap-Dirac operator. We also study the renormalization of quark bilinears which are more extended and have better chiral properties. Finally, we present improved estimates of these renormalization constants, coming from cactus resummation and from mean field perturbation theory.

hep-lat↗
arXiv1999

Lambda-parameter of lattice QCD with the overlap-Dirac operator

We compute the ratio $Λ_L/Λ_{\bar{MS}}$ between the scale parameter $Λ_L$, associated with a lattice formulation of QCD using the overlap-Dirac operator, and $Λ_{\bar{MS}}$ of the $\bar{\rm MS}$ renormalization scheme. To this end, the necessary one-loop relation between the lattice coupling $g_0$ and the coupling renormalized in the $\bar{\rm MS}$ scheme is calculated, using the lattice background field technique.

hep-lat↗
arXiv1999

The Role of Center Vortices in QCD

Center vortices are unambiguously identified after Laplacian Center Gauge fixing and their influence on confinement and chiral symmetry breaking is investigated on a sample of SU(2) configurations at zero and finite temperature.

hep-lat↗
arXiv1999

Improved Multiboson Algorithm

We compare the performance of an UV-filtered Multiboson algorithm, including a global quasi-heatbath update, to the standard Hybrid Monte Carlo algorithm in full QCD with two flavours of Wilson fermions.

hep-lat↗
arXiv1999

The relevance of center vortices

We show remnants of chiral symmetry breaking in the center-projected theory. We construct and study an unambiguous definition of center vortices.

hep-lat↗
arXiv1999

Efficiency of the UV-filtered Multiboson algorithm

We study the efficiency of an improved Multiboson algorithm with two flavours of Wilson fermions in a realistic physical situation ($β= 5.60$, $κ= 0.156$ on a $16^3 \times 24$ lattice). The performance of this exact algorithm is compared with that of a state-of-the-art HMC algorithm: a considerable improvement is obtained for the plaquette auto-correlation time, while the two algorithms appear similarly efficient at decorrelating the topological charge.

hep-lat↗
arXiv1999

Worldline path integral for the massive Dirac propagator : A four-dimensional approach

We simplify and generalize an approach proposed by Di Vecchia and Ravndal to describe a massive Dirac particle in external vector and scalar fields. Two different path integral representations for the propagator are derived systematically without the usual five-dimensional extension and shown to be equivalent due to the supersymmetry of the action. They correspond to a projection on the mass of the particle either continuously or at the end of the time evolution. It is shown that the supersymmetry transformations are generated by shifting and scaling the supertimes and the invariant difference of two supertimes is given for the general case. A nonrelativistic reduction of the relativistic propagator leads to a three-dimensional path integral with the usual Pauli Hamiltonian. By integrating out the photons we obtain the effective action for quenched QED and use it to derive the gauge-transformation properties of the general Green function of the theory.

hep-th↗
arXiv1998

The Feynman Variational Principle in the Worldline Representation of Field Theory

Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in terms of particle trajectories (worldlines) instead of field operators. The Green functions of the theory are then approximated variationally on the pole of the external particles by using a retarded quadratic trial action. Application to a scalar theory gives non-perturbative, covariant results for vertex functions and scattering processes. Recent progress in dealing with the spin degrees of freedom in fermionic systems, in particular Quantum Electrodynamics, is discussed. We evaluate the averages needed in the Feynman variational principle for a general quadratic trial action and study the structure of the dressed fermion propagator.

hep-th↗
arXiv1998

Thermodynamics of One-flavour QCD

We give a brief introduction on finite temperature phase transitions in lattice QCD including a discussion on the identification of first order transitions. We present a study of the deconfinement phase transition of one-flavour QCD, using the multiboson algorithm on lattice of sizes $8^3$, $12^3$ and $16^3\times 4$. For heavy quarks our results are characteristic of a first order phase transition which gets weaker as the quark mass decreases and ends at a critical value of $κ\sim 0.1$ or in physical units at about 1.6 GeV.

hep-lat↗
arXiv1997

One-flavour QCD at finite temperature

We present results, for heavy to moderate quark masses, of a study of thermodynamic properties of 1-flavour QCD, using the multiboson algorithm. Finite-size scaling behaviour is studied on lattices of size $8^3\times 4$, $12^3\times 4$ and $16^3\times 4$. It is shown that, for heavy quarks, the peak of the Polyakov loop susceptibility grows linearly with the spatial volume, indicating a first order phase transition. The deconfinement ratio and the distribution of the norm of the Polyakov loop corroborate this result. For moderately heavy quarks the first-order transition weakens and becomes a crossover. We estimate the end point of the first-order phase transition to occur at a quark mass of about 1.6 GeV.

hep-lat↗
arXiv1997

Variational treatment of quenched QED using the worldline technique

There has been growing interest in studying the behaviour of QED in its strong coupling limit. The reason for this is not only that it serves as a simple prototype gauge theory for testing nonperturbative calculational techniques which one then goes on to apply to QCD, but also because the theory exhibits interesting behaviour in its own right. In particular, it now appears to be quite well established that QED breaks chiral symmetry dynamically as long as the coupling is sufficiently large. In this contribution we describe the progress made in applying the polaron variational approach to quenched QED within the context of the worldline formulation of field theory. Although it is too early for quantitative results, qualitatively the approach seems promising: The method is formulated covariantly in Minkowski space-time, the Ward-Takahashi identities are satisfied, the connection between the bare- and pole-masses of the electron is gauge independent, the known exact result for the infrared dependence of the on-shell renormalized propagator is reproduced and corrections to the variational approximation can be calculated systematically.

nucl-th↗
arXiv1997

Variational Field Theoretic Approach to Relativistic Scattering

Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of the variational calculation are that it is a controlled approximation scheme valid for arbitrary coupling strengths, the Green functions have all the cuts and poles expected for the exact result at any order in perturbation theory and that the variational parameters are simultaneously sensitive to the infrared as well as the ultraviolet behaviour of the theory. We generalize the previously used quadratic trial action by allowing more freedom for off-shell propagation without a change in the on-shell variational equations and evaluate the scattering amplitude at first order in the variational scheme. Particular attention is paid to the $s$-channel scattering near threshold because here non-perturbative effects can be large. We check the unitarity of a our numerical calculation and find it greatly improved compared to perturbation theory and to the zeroth order variational results.

nucl-th↗
arXiv1996

Thermodynamics of 1-flavor QCD

We present first results, for heavy to moderate quark masses, of a study of thermodynamic properties of 1-flavor QCD, using the multiboson algorithm.

hep-lat↗