Leonardo Giusti

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.

Chiral symmetry breaking and the Banks-Casher relation in lattice QCD with Wilson quarks

The Banks-Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in a given energy interval are renormalizable and can therefore be computed using the Wilson formulation of lattice QCD even though the latter violates chiral symmetry at energies on the order of the inverse lattice spacing. Using numerical simulations, we find (in two-flavour QCD) that the low quark modes do condense in the expected way. In particular, the chiral condensate can be accurately calculated simply by counting the low modes on large lattices. Other spectral observables can be considered as well and have a potentially wide range of uses.

Delta M(K) and epsilon(K) in SUSY at the next-to-leading order

We perform a Next-to-Leading order analysis of ?S = 2 processes beyond the Standard Model. Combining the recently computed NLO anomalous dimensions and the B parameters of the most general ?S = 2 effective Hamiltonian, we give an analytic formula for ?MK and ?K in terms of the Wilson coefficients at the high energy scale. This expression can be used for any extension of the Standard Model with new heavy particles. Using this result, we consider gluino-mediated contributions to ?S = 2 transitions in general SUSY models and provide an improved analysis of the constraints on off-diagonal mass terms between the first two generations of down-type squarks. Finally, we improve the constraints on R-violating couplings from ?MK and ?K.

Stability of lattice QCD simulations and the thermodynamic limit

We study the spectral gap of the Wilson-Dirac operator in two-flavour lattice QCD as a function of the lattice spacing a, the space-time volume V and the current-quark mass m. It turns out that the median of the probability distribution of the gap scales proportionally to m and that its width is practically equal to a/V1/2. In particular, numerical simulations are safe from accidental zero modes in the large-volume regime of QCD.

Light quenched hadron spectrum and decay constants on different lattices

In this paper we study O(2000) (quenched) lattice configurations from the APE collaboration, for different lattice volumes and for 6.0 \le beta \le 6.4 using both the Wilson and the SW-Clover fermion actions. We determine the light hadronic spectrum and meson decay constants and study the mesonic dispersion relation. We extract the hadronic variable J and the strange quark mass in the continuum at the next-to-leading order obtaining m_s^{MSbar}(mu=2 GeV) = 122 +/- 20 MeV. A study is made of their dependence on lattice spacing. We implement a newly developed technique to extract the inverse lattice spacing using data at the simulated values of the quark mass (i.e. at masses around the strange quark mass).In this paper we study (2000) (quenched) lattice configurations from the APE collaboration, for different lattice volumes and for 6.0 ⩽ β ⩽ 6.4 using both the Wilson and the SW-Clover fermion actions. We determine the light hadronic spectrum and meson decay constants and study the mesonic dispersion relation. We extract the hadronic variable J and the strange quark mass in the continuum at the next-to-leading order obtaining msMS(μ = 2 GeV) = 122 ± 20 MeV. A study is made of their dependence on lattice spacing. We implement a newly developed technique to extract the inverse lattice spacing using data at the simulated values of the quark mass (i.e. at masses around the strange quark mass).

QCD with light Wilson quarks on fine lattices (I): first experiences and physics results

In this second report on our recent numerical simulations of two-flavour QCD, we provide further technical details on the simulations and describe the methods we used to extract the meson masses and decay constants from the generated ensembles of gauge fields. Among the topics covered are the choice of the DD-HMC parameters, the issue of stability, autocorrelations and the statistical error analysis. Extensive data tables are included as well as a short discussion of the quark-mass dependence in partially quenched QCD, supplementing the physics analysis that was presented in the first paper in this series.Recent conceptual, algorithmic and technical advances allow numerical simulations of lattice QCD with Wilson quarks to be performed at significantly smaller quark masses than was possible before. Here we report on simulations of two-flavour QCD at sea-quark masses from slightly above to approximately 1/4 of the strange-quark mass, on lattices with up to 64×32 3 points and spacings from 0.05 to 0.08 fm. Physical sea-quark effects are clearly seen on these lattices, while the lattice effects appear to be quite small, even without O(a) improvement. A striking result is that the dependence of the pion mass on the sea-quark mass is accurately described by leading-order chiral perturbation theory up to meson masses of about 500 MeV.

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 η ′ 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.

QCD with light Wilson quarks on fine lattices (II): DD-HMC simulations and data analysis

In this second report on our recent numerical simulations of two-flavour QCD, we provide further technical details on the simulations and describe the methods we used to extract the meson masses and decay constants from the generated ensembles of gauge fields. Among the topics covered are the choice of the DD-HMC parameters, the issue of stability, autocorrelations and the statistical error analysis. Extensive data tables are included as well as a short discussion of the quark-mass dependence in partially quenched QCD, supplementing the physics analysis that was presented in the first paper in this series.

The QCD chiral condensate from the lattice

Abstract We determine the chiral condensate from simulations of quenched lattice QCD with Wilson fermions. Our measurements have been obtained with high statistics at three values of the gauge coupling, corresponding to UV cutoffs in the range 2–4 GeV. Several improvements have been made with respect to earlier lattice computations. The most important are the non-perturbative renormalization of the condensate, the use of the tree-level improved Clover action and the reduction of the systematic error due to uncertainties in the lattice calibration. Our result for the chiral condensate in the MS scheme is 〈 ψ ψ〉 MS (μ = 2 GeV ) = −0.0147(8)(16)(12) GeV 3 = −[245(4)(9)(7) MeV ] 3 , where the first error is statistical, the second is due to the non-perturbative renormalization and the third due to the lattice calibration.

Lattice QCD in the epsilon-regime and random matrix theory

In the -regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5?fm4.