Excited-state contribution to the axial-vector and pseudo-scalar correlators with two extra pions

We study multi-particle state contributions to the QCD two-point functions of the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently small quark masses one expects three-meson states with two additional pions at rest to have the lowest total energy after the ground state. We calculate this three-meson state contribution using chiral perturbation theory. We find it to be strongly suppressed and too small to be seen in present-day lattice simulations.Comment: 17 pages, 5 figure

Einfluss der Standortbedingungen auf die Eiben-Schälbelastung im Albisgebiet

The increasing spread of red deer (Cervus elaphus) in the Swiss Plateau is putting Taxus baccata under pressure in some areas. The bark stripping damage to Taxus baccata caused by red deers can lead to the death of the Taxus baccata if the intensity is too high. So far, there are not many reasons of bark stripping, which spatial conditions favour a bark stripping occurrence and at which daily activity bark stripping damage occurs. For this reason, I conducted a field study in the Albis area in the canton of zurich, where I recorded various parameters in the area of cover, wildlife presence and vegetation in a selection of 43 control plots, in order to identify patterns in connection with the intensity of bark stripping. It was found that in control plots affected by bark stripping, the proportion of pole wood was higher and more deer browsing could be detected. Likewise, the proportion of coniferous wood in the tree layer was higher in polluted control plots. The weakly developed ground vegetation and the few red deer records in polluted control plots did not indicate a red deer range at these sites. It was shown that bark stripping damage occurs when red deer move along their game trails through the forest. Both the herbaceous layer and young growth/thickness were very sparse in most of the control plots. This could be an indication that bark stripping occurs due to a lack of food sources and that the red deer compensate their needed nutrients from the bark of the Taxus baccata. The high proportion of coniferous wood in the tree layer of polluted control plots, which was dominated by Taxus baccata, could indicate that a high density of Taxus baccata in a small area attracts the red deer more strongly by smell. However, further analyses with more data sets are necessary to draw more precise conclusions and to derive possible silvicultural measures for the protection of Taxus baccata in the Albis area.Die zunehmende Verbreitung des Rothirschs (Cervus elaphus) im Schweizer Mittelland bringt die Eibe (Taxus baccata) gebietsweise unter Druck. Die Rothirsche schälen die Rinde der Eiben ab und verursachen so Schäden am Baum, die bei zu hoher Intensität zum Absterben der Eiben führen kann. Über die Gründe des Schälens sowie welche räumlichen Gegebenheiten ein Schälvorkommen begünstigen und bei welcher Tagesaktivität die Rothirsche Schälungen verursachen, gibt es bislang nur wenige Anhaltspunkte. Aus diesem Grund führte ich eine Feldstudie im Albisgebiet durch, wo ich in einer Auswahl von 43 Kontrollflächen verschiedene Parameter im Bereich der Deckung, der Wildtierpräsenz sowie der Vegetation aufnahm, um daraus Muster im Zusammenhang mit der Schälbelastung zu erkennen. Es zeigte sich, dass in von Schälung belasteten Kontrollflächen der Anteil an Stangenholz höher ist und mehr Wildwechsel nachgewiesen werden konnte. Ebenso war der Nadelholzanteil in der Baumschicht in belasteten Kontrollflächen höher. Die schwach ausgebildete Bodenvegetation und die wenigen Rothirschnachweise in belasteten Kontrollflächen deuteten nicht auf ein Einstandsgebiet des Rothirschs an diesen Standorten hin. Vielmehr ergab sich das Muster, dass die Rothirsche während ihres Streifens entlang der Wildwechsel durch den Wald die Eiben schälen. Sowohl die Krautschicht wie auch Jungwuchs/Dickung war in den meisten Kontrollflächen nur sehr spärlich vorhanden. Dies könnte ein Hinweis sein, dass Schälungen aufgrund mangelnder Nahrungsquellen auftreten und die Rothirsche ihre benötigten Nährstoffe aus der Rinde der Eiben kompensieren. Der hohe Nadelholzanteil in der Baumschicht bei belasteten Kontrollflächen, in der vor allem die Eibe dominierte, könnte darauf hinweisen, dass eine hohe Eibendichte auf engem Raum den Rothirsch geruchlich stärker anzieht. Es sind jedoch weitere Analysen mit mehr Datensätzen notwendig, um genauere Rückschlüsse ziehen zu können und mögliche waldbauliche Massnahmen zum Schutz der Eiben im Albisgebiet abzuleiten

Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory

We point out a caveat in the proof for automatic O(a) improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic O(a) improvement can fail unless the quark mass satisfies m_q >> a^2 Lambda_QCD^3. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic O(a) improvement. In order to illustrate explicitly automatic O(a) improvement we compute the pion mass in the corresponding chiral effective theory. We consider different definitions for maximal twist and show explicitly the absence or presence of the leading O(a) effect, depending on the size of the quark mass.Comment: 27 pages, no figure

Pion scattering in Wilson ChPT

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) a\Lambda_QCD^2 and (ii) a^2\Lambda_QCD^3. Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the O(a^2) terms the I=0 and I=2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a^2\ln M_{\pi}^2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.Comment: 20 pages, 4 figures. V3: Comments on finite size effects and the axial vector current added, one more reference. To be published in PR

Global anomalies in Chiral Lattice Gauge Theory

As first realized by Witten an SU(2) gauge theory coupled to a single Weyl fermion suffers from a global anomaly. This problem is addressed here in the context of the recent developments on chiral gauge theories on the lattice. We find Witten's anomaly manifests in the impossibility of defining globally a fermion measure that reproduces the proper continuum limit. Moreover, following Witten's original argument, we check numerically the crossing of the lowest eigenvalues of Neuberger's operator along a path connecting two gauge fields that differ by a topologically non-trivial gauge transformation.Comment: LATTICE99(Chiral Gauge Theories) - 6 pages, 2 figure

Vector and Axial Currents in Wilson Chiral Perturbation Theory

We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at O(a). As an application of our results we compute the pion decay constant to one loop in the two flavor theory. Our result differs from previously published ones.Comment: 34 pages, no figure

Global Anomalies in chiral gauge theories on the lattice

We discuss the issue of global anomalies in chiral gauge theories on the lattice. In Luscher's approach, these obstructions make it impossible to define consistently a fermionic measure for the path integral. We show that an SU(2) theory has such a global anomaly if the Weyl fermion is in the fundamental representation. The anomaly in higher representations is also discussed. We finally show that this obstruction is the lattice analogue of the SU(2) anomaly first discovered by Witten.Comment: 22 pages. Some explanations added in section 4.2, typos corrected. Final version to appear in Nucl. Phys.