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L. Giusti

Publications and source records attributed to L. Giusti.

At least 37 records · Page 2Linked to original sources
arXiv2002

Numerical techniques for lattice QCD in the $ε$--regime

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $ε$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.

hep-lat↗
arXiv2002

Numerical Exploration of the RI/MOM Scheme Gauge Dependence

The gauge dependence of some fermion bilinear RI/MOM renormalization constants is studied by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is below the statistical errors of our data sample which is of the order of (1-1.5)%.

hep-lat↗
arXiv2002

Remarks on the Gauge Dependence of the RI/MOM Renormalization Procedure

The RI/MOM non-perturbative renormalization scheme is studied on the lattice in SU(3) quenched QCD with Wilson fermions. The gauge dependence of some fermion bilinear renormalization constants is discussed by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is moderate and below the statistical errors.

hep-lat↗
arXiv2002

Fermions on tori in uniform abelian fields

We study Fermi fields defined on tori in the presence of gauge backgrounds carrying non-trivial topology. We show that 2k dimensional field space can alternatively be described by fields over a k-dimensional space. This dual description is particularly natural when the background is uniform and abelian. The reduction in number of dimensions carries over to the lattice. The lattice ultraviolet regularization induces an infrared regularization of the lower dimensional representations. We focus on k=1,2.

hep-lat↗
arXiv2002

A Study of the 't Hooft Model with the Overlap Dirac Operator

We present the results of an exploratory numerical study of two dimensional QCD with overlap fermions. We have performed extensive simulations for U(N_c) and SU(N_c) color groups with N_c=2, 3, 4 and coupling constants chosen to satisfy the 't Hooft condition g^2 N_c =const=4/3. We have computed the meson spectrum and decay constants, the topological susceptibility and the chiral condensate. For U(N_c) gauge groups, our results indicate that the Witten-Veneziano relation is satisfied within our statistical errors and that the chiral condensate for N_f=1 is compatible with a non-zero value. Our results exhibit universality in N_c and confirm once more the excellent chiral properties of the overlap-Dirac operator.

hep-lat↗
arXiv2001

Quenched Results for Light Quark Physics with Overlap Fermions

We present results of a quenched QCD simulation with overlap fermions on a lattice of volume V = 16^3X32 at beta=6.0, which corresponds approximatively to a lattice cutoff of 2 GeV and an extension of 1.4 fm. From the two-point correlation functions of bilinear operators we extract the pseudoscalar meson masses and the corresponding decay constants. From the GMOR relation we determine the chiral condensate and, by using the K-meson mass as experimental input, we compute the sum of the strange and average up-down quark masses (m_s + \hat m). The needed logarithmic divergent renormalization constant Z_S is computed with the RI/MOM non-perturbative renormalization technique. Since the overlap preserves chiral symmetry at finite cutoff and volume, no divergent quark mass and chiral condensate additive renormalizations are required and the results are O(a) improved.

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arXiv2001

The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions

We show how it is possible to give a precise and unambiguous implementation of the Witten--Veneziano formula for the eta' mass on the lattice, which looks like the formal continuum one, if the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg--Wilson relation, is employed. By using recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions, one obtains values for the mass of the lightest pseudo-scalar flavour-singlet state that agree within errors with theoretical expectations and experimental data, respectively.

hep-lat↗
arXiv2001

Quark and Gluon Propagators in Covariant Gauges

We present data for the gluon and quark propagators computed in the standard lattice Landau's gauge and for three values of the covariant gauge-fixing parameter lambda=0,8,16. Our results are obtained using the SU(3) Wilson action in the quenched approximation at beta=6.0 and volume=16^3x32.

hep-lat↗
arXiv2001

The $U_A(1)$ Problem on the Lattice

If the expression of the topological charge density operator, suggested by fermions obeying the Ginsparg--Wilson relation, is employed, it is possible to prove on the lattice the validity of the Witten--Veneziano formula for the $η'$ mass. Recent numerical results from simulations with overlap fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions give values for the mass of the lightest pseudo-scalar flavour-singlet state that agree with theoretical expectations and/or experimental data.

hep-lat↗
arXiv2001

Light Quark Masses with Overlap Fermions in Quenched QCD

We present the results of a computation of the sum of the strange and average up-down quark masses with overlap fermions in the quenched approximation. Since the overlap regularization preserves chiral symmetry at finite cutoff and volume, no additive quark mass renormalization is required and the results are O(a) improved. Our simulations are performed at beta=6.0 and volume V=16^3X32, which correspond to a lattice cutoff of ~2 GeV and to an extension of ~1.4 fm. The logarithmically divergent renormalization constant has been computed non-perturbatively in the RI/MOM scheme. By using the K-meson mass as experimental input, we obtain (m_s + m_l)^RI(2 GeV) = 120(7)(21) MeV, which corresponds m_s^MS (2 GeV) = 102(6)(18) MeV if continuum perturbation theory and ChiPT are used. By using the GMOR relation we also obtain ^MS(2 GeV)/N_f = - 0.0190(11)(33) GeV^3 = - [267(5)(15) MeV]^3.

hep-lat↗
arXiv2001

Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions

We study the renormalization of the DeltaS=1 effective weak Hamiltonian with overlap fermions. The mixing coefficients among dimension-six operators are computed at one loop in perturbation theory. As a consequence of the chiral symmetry at finite lattice spacing and of the GIM mechanism, which turns out to be quadratic in the masses, the K-->pi pi and K -->pi matrix elements relevant for the Delta I =1/2 rule can be computed without any power subtractions. The analogous amplitudes for e'/e require one divergent subtraction only, which can be performed non-perturbatively using K-->0 matrix elements.

hep-lat↗
arXiv2000

Results on the Gluon Propagator in Lattice Covariant Gauges

We illustrate preliminary results on the gluon propagator computed in generic covariant lattice gauges in the quenched approximation with the Wilson action. We have applied a recently proposed procedure to fix a generic covariant gauge on the lattice. We make a comparison among results obtained at two different values of the gauge parameter and in the standard Landau's gauge.

hep-lat↗
arXiv2000

Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator

We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the results are very promising. We also present a detailed computation of the spectrum and chiral properties of the Schwinger Model in the overlap lattice formulation.

hep-lat↗
arXiv2000

RI/MOM Renormalization Window and Goldstone Pole Contamination

We perform a comparative study of the ratio of lattice (Wilson fermion) renormalization constants Z_P/Z_S, obtained non-perturbatively from the RI/MOM renormalization conditions and from Ward Identities of on- and off-shell Green's functions. The off-shell Ward Identity used in this work relies on correlation functions with non-degenerate quark masses. We find that, due to discretization effects, there is a 10-15% discrepancy between the two Ward Identity determinations at current bare couplings (beta values). The RI/MOM result is in the same range and has a similar systematic error of 10-15%. Thus, contrary to a previous claim, the contamination of the RI/MOM result from the presence of a Goldstone pole at scales of about 2 GeV is subdominant, compared to finite cutoff effects.

hep-lat↗
arXiv2000

Perturbative Renormalization of Weak-Hamiltonian Four-Fermion Operators with Overlap Fermions

The renormalization of the most general dimension-six four-fermion operators without power subtractions is studied at one loop in lattice perturbation theory using overlap fermions. As expected, operators with different chirality do not mix among themselves and parity-conserving and parity-violating multiplets renormalize in the same way. The renormalization constants of unimproved and improved operators are also the same. These mixing factors are necessary to determine physical matrix elements relevant to many phenomenological applications of weak interactions. The most important are the K0-K0bar and B0-B0bar mixings in the Standard Model and beyond, the Delta I =1/2 rule and epsilon'/epsilon.

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