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Stephan Dürr

Publications and source records attributed to Stephan Dürr.

54 records · Page 3Linked to original sources
arXiv2002

Lattice QCD data versus Chiral Perturbation Theory: the case of $M_π$

I present a selection of recent lattice data by major collaborations for the pseudo-Goldstone boson masses in full ($N_f=2$) QCD, where the valence quarks are chosen exactly degenerate with the sea quarks. At least the more chiral points should be consistent with Chiral Perturbation Theory for the latter to be useful in extrapolating to physical masses. Perspectives to reliably determine NLO Gasser-Leutwyler coefficients are discussed.

hep-ph↗
arXiv2002

Modified iterative versus Laplacian Landau gauge in compact U(1) theory

Compact U(1) theory in 4 dimensions is used to compare the modified iterative and the Laplacian fixing to lattice Landau gauge in a controlled setting, since in the Coulomb phase the lattice theory must reproduce the perturbative prediction. It turns out that on either side of the phase transition clear differences show up and in the Coulomb phase the ability to remove double Dirac sheets proves vital on a small lattice.

hep-lat↗
arXiv2001

Topology and pion correlators -- a study in the N_f=2 Schwinger model

I readdress the issue whether the topological charge of the gauge background has an influence on a hadronic observable. To this end pion correlators in the Schwinger model with 2 dynamical flavours are determined on subensembles with a fixed topological charge. It turns out that the answer depends on a specific function of the sea-quark mass and the box volume which is in close analogy to the Leutwyler-Smilga parameter in full QCD.

hep-lat↗
arXiv2001

Simple check of the vacuum structure in full QCD lattice simulations

Given the increasing availability of lattice data for (unquenched) QCD with $N_f=2$, it is worth while to check whether the generated vacuum significantly deviates from the quenched one. I discuss a specific attempt to do this on the basis of topological susceptibility data gained at various sea-quark masses, since for this observable detailed predictions are available. The upshot is that either discretization effects in dynamical simulations are still untolerably large or the vacuum structure in 2-flavour QCD substantially deviates from that in the theory with 3 (or 2+1) light quarks.

hep-lat↗
arXiv2001

Topological susceptibility in full QCD: lattice results versus the prediction from the QCD partition function with granularity

Recent lattice data from CP-PACS, UKQCD, SESAM/TXL and the Pisa group regarding the quark mass dependence of the topological susceptibility in 2-flavour QCD are compared to each other and to theoretical expectations. The latter get specified by referring to the QCD finite-volume partition function with ``granularity'' which accounts for the entropy brought by instantons and anti-instantons. The chiral condensate in $N_f=2$ QCD, if determined by this method, turns out surprisingly large.

hep-lat↗
arXiv2000

QCD in a finite box: Numerical test studies in the three Leutwyler-Smilga regimes

The Leutwyler-Smilga prediction regarding the (ir)relevance of the global topological charge for QCD in a finite box is subject to a test. To this end the lattice version of a suitably chosen analogue (massive 2-flavour Schwinger model) is analyzed in the small ($VΣm \ll 1$), intermediate ($VΣm \simeq 1$) and large ($VΣm \gg 1$) Leutwyler-Smilga regimes. The predictions for the small and large regimes are confirmed and illustrated. New results about the role of the functional determinant in all three regimes and about the sensitivity of physical observables on the topological charge in the intermediate regime are presented.

hep-lat↗
arXiv2000

Study of the Leutwyler-Smilga regimes: Lessons for full QCD simulations

Some key points out of my recent study of the characteristic features of the small ($x \ll 1$), intermediate ($x \simeq 1$) and large ($x \gg 1$) Leutwyler-Smilga regimes for QCD-type theories in a finite volume ($x = V Σm$) are presented, and a few immediate consequences for full QCD simulations are discussed.

hep-lat↗
arXiv2000

The phase transition in the multiflavour Schwinger model

A summary is given of a quantization of the multiflavour Schwinger model on a finite-temperature cylinder with chirality-breaking boundary conditions at its spatial ends, and it is shown that the analytic expression for the chiral condensate implies that the theory exhibits a second order phase transition with $T_c = 0$.

hep-th↗
arXiv2000

IR-Divergence and Anomalous Temperature Dependence of the Condensate in the Quenched Schwinger Model

The Schwinger model is used to study the artifacts of quenching in a controlled way. The model is solved on a finite-temperature cylinder of circumference $β=1/T$ with bag-inspired local boundary conditions at the two ends $x^1=0$ and $x^1=L$ which break the $γ_5$-invariance and thus play the role of a small quark mass. The quenched chiral condensate is found to diverge exponentially as $L\to\infty$, and to diverge (rather than melt as for $N_{\rm f}\geq1$) if the high-temperature limit $β\to0$ is taken at finite box-length $L$. We comment on the generalization of our results to the massive quenched theory, arguing that the condensate is finite as $L\to\infty$ and proportional to $1/m$ up to logarithms.

hep-lat↗
arXiv2000

Topologically Unquenched QCD: Prospects from an explorative study in 2-flavour QED(2)

The concept of simulating a variant of QCD with sea quarks which interact with the gluon configuration only via global gluonic quantities like $\int F\tilde F dx$ and $\int FF dx$ is tested for the case of the massive 2-flavour Schwinger model. It is found to amount to an importance sampling method which generates -at essentially the costs of a quenched run- an ensemble in between a full and a quenched one, thus providing a competitive alternative to the quenched approximation.

hep-lat↗
arXiv2000

Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory

We calculate the correlator between two external vector-currents having the quantum-numbers of a charged kaon. We give the renormalized expression to two loops in standard chiral perturbation theory in the isospin limit, which, as a physical result, is finite and scale-independent. Applications include a low energy theorem, valid at two loop order, of a flavor breaking combination of vector current correlators as well as a determination of the phenomenologically relevant finite $O(p^6)$-counterterm combination $Q_V$ by means of inverse moment finite energy sum rules. This determination is less sensitive to isospin-breaking effects than previous attempts.

hep-ph↗
arXiv1999

Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory

We present our calculation of the correlator $ $ between two external vector-currents with the quantum-numbers of a charged kaon. The renormalized expression to $O(p^6)$ in $SU(3) \times SU(3)$ standard chiral perturbation theory is finite and scale-independent. The result is used to determine, via an IMFESR, the phenomenologically relevant finite $O(p^6)$-counterterm combination $Q_V$ in a way which is not sensitive to isospin breaking.

hep-ph↗
arXiv1999

Theoretical Aspects of Topologically Unquenched QCD

I give an outline of my proposal to take the QCD functional determinant in lattice simulations partially into account: The determinant is split into two factors, the factor referring to a standard background in each topological sector is kept exactly, the factor describing the effect of the smooth deviation of the actual configuration from the reference background is replaced by one. The issue of how to choose the reference configurations is discussed and it is argued that ``topologically unquenched QCD'' is an interesting starting point to study full QCD in lattice simulations as it gets the main qualitative features right from the beginning.

hep-lat↗
arXiv1999

Prospects of `Topologically Unquenched QCD' from a study of the analogous importance sampling method in the massive Schwinger model

I give a quick summary of my proposal for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. It amounts to include only the topological part of the functional determinant into the measure, thereby absorbing a correction factor into the observable. I discuss the prospects of this concept from a study in the massive $N_f$-flavour Schwinger model, where the correction factor is indeed found to be of order $O(1)$.

hep-lat↗
arXiv1999

Proposal for Topologically Unquenched QCD

A proposal is presented for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. Strengths and shortcomings of the method are discussed and it is argued that the approximation - though being crude - shares some qualitative aspects of full QCD which relate to the issue of chiral symmetry breaking.

hep-lat↗
arXiv1998

Aspects of Quasi-Phasestructure of the Schwinger Model on a Cylinder with Broken Chiral Symmetry

We consider the N_f-flavour Schwinger Model on a thermal cylinder of circumference $β=1/T$ and of finite spatial length $L$. On the boundaries $x^1=0$ and $x^1=L$ the fields are subject to an element of a one-dimensional class of bag-inspired boundary conditions which depend on a real parameter $θ$ and break the axial flavour symmetry. For the cases $N_f=1$ and $N_f=2$ all integrals can be performed analytically. While general theorems do not allow for a nonzero critical temperature, the model is found to exhibit a quasi-phase-structure: For finite $L$ the condensate - seen as a function of $\log(T)$ - stays almost constant up to a certain temperature (which depends on $L$), where it shows a sharp crossover to a value which is exponentially close to zero. In the limit $L \to \infty$ the known behaviour for the one-flavour Schwinger model is reproduced. In case of two flavours direct pictorial evidence is given that the theory undergoes a phase-transition at $T_c=0$. The latter is confirmed - as predicted by Smilga and Verbaarschot - to be of second order but for the critical exponent $δ$ the numerical value is found to be 2 which is at variance with their bosonization-rule based prediction $δ=3$.

hep-th↗
arXiv1997

Finite Temperature Schwinger Model with Chirality Breaking Boundary Conditions

The $N_f$-flavour Schwinger Model on a finite space $0\leq x^1\leq L$ and subject to bag-type boundary-conditions at $x^1=0$ und $x^1=L$ is solved at finite temperature $T=1/β$. The boundary conditions depend on a real parameter $θ$ and break the axial flavour symmetry. We argue that this approach is more appropriate to study the broken phases than introducing small quark masses, since all calculations can be performed analytically. In the imaginary time formalism we determine the thermal correlators for the fermion-fields and the determinant of the Dirac-operator in arbitrary background gauge-fields. We show that the boundary conditions induce a CP-odd $θ$-term in the effective action. The chiral condensate, and in particular its T- and L- dependence, is calculated for $N_f$ fermions. It is seen to depend on the order in which the two lengths $β=1/T$ and $L$ are sent to infinity.

hep-th↗