Stanislav Shcheredin

Spectral properties of the overlap Dirac operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 84 , 104 and 124 at β = 5.85 and β = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the -expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)4 . For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered.

Axial correlation functions in the epsilon regime: A Numerical study with overlap fermions

We present simulation results employing overlap fermions for the axial correlation functions in the -regime of chiral perturbation theory. In this regime, finite size effects and topology play a dominant role. Their description by quenched chiral perturbation theory is compared to our numerical results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm are necessary to interpret the numerical data obtained in distinct topological sectors in terms of the -expansion. Such lattices are, however, still substantially smaller than the ones needed in standard chiral perturbation theory. However, we also observe severe difficulties at very low values of the quark mass, in particular in the topologically trivial sector.

Going chiral: Overlap versus twisted mass fermions

We compare the behavior of overlap fermions, which are chirally invariant, and of Wilson twisted mass fermions at full twist in the approach to the chiral limit. Our quenched simulations reveal that with both formulations of lattice fermions pion masses of (250 MeV) can be reached in practical applications. Our comparison is done at a fixed value of the lattice spacing a 0.123 fm. A number of quantities are measured such as hadron masses, pseudoscalar decay constants and quark masses obtained from Ward identities. We also determine the axial vector renormalization constants in the case of overlap fermions.We compare the behavior of overlap fermions, which are chirally invariant, and of Wilson twisted mass fermions at full twist in the approach to the chiral limit. Our quenched simulations reveal that with both formulations of lattice fermions pion masses of O(250 MeV) can be reached in practical applications. Our comparison is done at a fixed value of the lattice spacing a=0.123 fm. A number of quantities are measured such as hadron masses, pseudoscalar decay constants and quark masses obtained from Ward identities. We also determine the axial vector renormalization constants in the case of overlap fermions.

Testing a topology conserving gauge action in QCD

We study lattice QCD with a gauge action, which suppresses small plaquette values. Thus the MC history is confined to a single topological sector over a significant time, while other observables are decorrelated. This enables the cumulation of statistics with a specific topological charge, which is needed for simulations of QCD in the e-regime. The same action may also be useful for simulations with dynamical quarks. The update is performed with a local HMC algorithm.

Simulations in the ϵ-regime of chiral perturbation theory

Abstract We discuss the potential of Ginsparg-Wilson fermion simulations in the ϵ-regime of chiral perturbation theory, regarding the determination of the leading low energy constants of the effective chiral Lagrangian. It turns out to be very hard to measure observables in the topologically trivial sector. There a huge statistics would be required, due to the frequent occurrence of very small eigenvalues. Moreover, contact with chiral perturbation theory is only established if the physical volume of the system is sufficiently large.

Comparison between overlap and twisted mass fermions towards the chiral limit

We compare overlap fermions, which are chirally invariant, and Wilson twisted mass fermions in the approach to the chiral limit. Our quenched simulations reveal that with both formulations of lattice fermions pion masses of O(250 MeV) can be reached in practical simulations. Our comparison is done at a fixed lattice spacing a ⋍ 0.123 fm. Several quantities are measured, such as hadron masses and pseudoscalar decay constants.

Meson correlation functions in the ϵ-regime☆

Abstract We present a numerical pilot study of the meson correlation functions in the ϵ-regime of chiral perturbation theory (χPT). Based on simulations with overlap fermions we measured the axial and pseudo-scalar correlation functions, and we discuss the implications for the leading low energy constants in the chiral Lagrangian.

Random matrix theory and the spectra of overlap fermions

The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at topological charge ν = 0, ± 1 and ±2, and found agreement with those predictions — at least for the first non-zero eigenvalue — if the volume exceeds about (1.2 fm)4.

Simulating chiral quarks in the ε-regime of QCD

We present simulation results for lattice QCD with chiral fermions in small volumes, where the e-expansion of chiral perturbation theory ( χ PT) applies. Our data for the low lying Dirac eigenvalues, as well as mesonic correlation functions, are in agreement with analytical predictions. This allows us to extract values for the leading Low Energy Constants F π and Σ.

EVIDENCE FOR DYONIC STRUCTURE OF SU(2) LATTICE GAUGE FIELDS BELOW TC

We report the observation of calorons with nontrivial holonomy and fractional topological charge objects in cooled lattice samples derived from SU(2) equilibrium ensembles at