arXiv subjects

S. Shcheredin

Publications and source records attributed to S. Shcheredin.

At least 19 recordsLinked to original sources

arXiv2008

Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to O(a^n) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show, that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations.

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arXiv2006

Meson correlation functions at high temperatures

We present preliminary results for the correlation- and spectral functions of different meson channels on the lattice. The main focus lies on gaining control over cut-off as well as on the finite-volume effects. Extrapolations of screening masses above the deconfining temperature are guided by the result of the free ($T=\infty$) case on the lattice and in the continuum. We study the quenched non-perturbatively improved Wilson-clover fermion as well as the hypercube fermion action which might show less cut-off effects.

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arXiv2006

Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit

The overlap hypercube fermion is a variant of a chirally symmetric lattice fermion, which is endowed with a higher level of locality than the standard overlap fermion. We apply this formulation in quenched QCD simulations with light quarks. In the p-regime we evaluate the masses of light pseudoscalar and vector mesons, as well as the pion decay constant and the renormalisation constant Z_A. In the epsilon-regime we present results for the leading Low Energy Constants of the chiral Lagrangian, Sigma and F_pi. To this end, we perform fits to predictions by chiral Random Matrix Theory and by different versions of quenched Chiral Perturbation Theory, referring to distinct correlation functions. These results, along with an evaluation of the topological susceptibility, are also compared to the outcome based on the standard overlap operator.

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arXiv2005

Overlap Hypercube Fermions in QCD

We present simulation results obtained with overlap hypercube fermions in QCD near the chiral limit. We relate our results to chiral perturbation theory in both, the epsilon-regime and in the p-regime. In particular we measured the pion decay constant by different methods, as well as the chiral condensate, light meson masses, the PCAC quark mass and the renormalisation constant Z_A.

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arXiv2005

Exploring Topology Conserving Gauge Actions for Lattice QCD

We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. By choosing strong bare gauge couplings we arrive at values for the physical lattice spacings of O(0.1 fm). Such gauge actions tend to confine the Monte Carlo history to a single topological sector. This topological stability facilitates the collection of a large set of configurations in a specific sector, which is profitable for numerical studies in the epsilon-regime. The suppression of small plaquette values is also expected to be favourable for simulations with dynamical quarks. We use a local Hybrid Monte Carlo algorithm to simulate such actions, and we present numerical results for the static potential, the physical scale, the topological stability and the kernel condition number of the overlap Dirac operator. In addition we discuss the question of reflection positivity for a class of such gauge actions.

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arXiv2005

Testing Topology Conserving Gauge Actions for Lattice QCD

We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. Such actions originate from the admissibility condition in order to conserve the topological charge. The suppression of small plaquette values is expected to be advantageous for numerical studies in the $ε$-regime and also for simulations with dynamical quarks. Performing simulations at a lattice spacing of about 0.1 fm, we present numerical results for the static potential, the physical scale $r_0$, the stability of the topological charge history, the condition number of the kernel of the overlap operator and the acceptance rate against the step size in the local HMC algorithm.

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arXiv2005

Low Energy Constants from the zero mode contribution to the pseudo-scalar correlator

We apply different types of overlap operators in quenched QCD simulations to compute the zero mode contribution to the pseudo-scalar correlator. In particular we use the conventional Neuberger Dirac operator and the overlap hypercube Dirac operator. Confronting our data with the analytical predictions by Chiral Perturbation Theory we evaluate the pion decay constant and the parameter αof the quenched chiral Lagrangian.

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arXiv2005

Overlap hypercube fermions in QCD with light quarks

We report on simulation results with overlap hypercube fermions (overlap HF) - a type of exactly chiral lattice fermions - and their link to chiral perturbation theory. We first sketch the construction of the overlap HF and discuss its high level of locality. Next we show applications in the p-regime of QCD, where we evaluate m_π, m_ρ, the quark mass according to the PCAC relation, the renormalisation constant Z_A and the pion decay constant F_π as functions of the bare quark mass. F_π is then reconsidered at even smaller quark masses in the epsilon-regime, along with the scalar condensate Σ. In that context we also discuss results for the topological charges and susceptibility.

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arXiv2005

Relating Chiral Perturbation Theory and QCD Simulations with Overlap Hypercube Fermions

We present simulation results for lattice QCD with light pions. For the quark fields we apply chirally symmetric lattice Dirac operators, in particular the overlap hypercube operator, along with the standard overlap operator for comparison. This allows us to simulate at very low pion masses. The results are related to Random Matrix Theory and to Chiral Perturbation Theory in order to extract information about the pion decay constant, the scalar condensate and the topological susceptibility.

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arXiv2005

Simulations of Lattice Fermions with Chiral Symmetry in Quantum Chromodynamics

This thesis is dedicated to explore the feasibility of numerical calculations in the $ε$--regime of QCD for the extraction of physical information. We apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator and the hypercube overlap operator to compute the observables of interest. As a main result we present the comparison of the distributions of the leading individual eigenvalues of the Neuberger operator in QCD and the analytical predictions of chiral random matrix theory. We observe a good agreement as long as each side of the physical volume exceeds about $L\approx 1.12\fm$. It turns out that this bound for $L$ is generic and sets the size of the physical volume where the axial correlator behaves according to chiral perturbation theory. This allows us to compute a value for the pion decay constant $F_π$. As an alternative procedure we only consider the contribution from the zero modes. Here we are able to obtain an estimate for $F_π$ and $α$. As a theoretical development the Lüscher topology conserving gauge action is investigated. This enables us to sample the observables of interest in the $ε$--regime without recomputing the index. We can report that a promising gauge action has been identified.

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arXiv2005

Simulating chiral quarks in the epsilon-regime of QCD

We present simulation results for lattice QCD with chiral fermions in small volumes, where the epsilon-expansion of chiral perturbation theory 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_{pi} and Sigma.

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arXiv2004

Lattice Gauge Actions for Fixed Topology

We test a set of lattice gauge actions for QCD that suppress small plaquette values and in this way also suppress transitions between topological sectors. This is well suited for simulations in the epsilon-regime and it is expected to help in numerical simulations with dynamical quarks.

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arXiv2004

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 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.

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arXiv2004

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 $ε$-regime. The same action may also be useful for simulations with dynamical quarks. The update is performed with a local HMC algorithm.

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arXiv2004

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.

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arXiv2004

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 epsilon-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 epsilon-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.

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arXiv2003

Meson Correlation Functions in the epsilon-Regime

We present a numerical pilot study of the meson correlation functions in the epsilon-regime of chiral perturbation theory. 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.

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arXiv2003

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 8^{4}, 10^{4} and 12^{4} 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 ε-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.

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