Coordinate space methods for the evaluation of Feynman diagrams in lattice field theory

We describe an efficient position space technique to calculate lattice Feynman integrals in infinite volume. The method applies to diagrams with massless propagators. For illustration a set of two-loop integrals is worked out explicitly. An important ingredient is an observation of Vohwinkel that the free lattice propagator can be evaluated recursively and is expressible as a linear function of its values near the origin.Comment: 27 pages, postscript file, now compressed & uuencode

Background field technique and renormalization in lattice gauge theory

Lattice gauge theory with a background gauge field is shown to be renormalizable to all orders of perturbation theory. No additional counterterms are required besides those already needed in the absence of the background field. The argument closely follows the treatment given earlier for the case of dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS, background gauge and shift symmetries of the lattice functional integral.Comment: 26 pages, uuencoded compressed postscript fil

Heavy Quark Effective Theory at one-loop order: An explicit example

We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the difference between the full and the effective theory in the continuum limit. In the full theory we find a term non-analytic in 1/m, revealing the asymptotic character of the 1/m-expansion. In general, deviations from the m-to-infinity limit turn out to be small and are well described by the first non-trivial terms when m is a factor 2-3 above the external scale. We also investigate the mass dependence of discretization errors, and find that the behaviour of the correlation functions at finite lattice spacing differs significantly from that in the continuum limit when the quark mass is large.Comment: 21 pages, 9 figures, submitted to Nucl. Phys. B; acknowledgement adde

Universality and the approach to the continuum limit in lattice gauge theory

The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.Comment: 33 pages, 172 kB uu-tar-compressed ps-fil

Renormalization and O(a)-improvement of the static-light axial current

A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schr\"odinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its relation to other schemes is computed to 1-loop order and the 2-loop anomalous dimension is derived. In finite volume renormalization schemes such as the SF-scheme, the renormalization scale dependence of the renormalized quantities is described by the step scaling function which can be computed by MC- simulations. We evaluate its lattice spacing effects in perturbation theory.Comment: 42 pages, 19 eps figures; Improved notation and discussion for the case of finite delta m; corrected and added one referenc

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.

Match-action: the role of motion and audio in creating global change blindness in film

An everyday example of change blindness is our difficulty to detect cuts in an edited moving-image. Edit Blindness (Smith & Henderson, 2008) is created by adhering to the continuity editing conventions of Hollywood, e.g. coinciding a cut with a sudden onset of motion (Match-Action). In this study we isolated the roles motion and audio play in limiting awareness of match-action cuts by removing motion before and/or after cuts in existing Hollywood film clips and presenting the clips with or without the original soundtrack whilst participants tried to detect cuts. Removing post-cut motion significantly decreased cut detection time and the probability of missing the cut. By comparison, removing pre-cut motion had no effect suggesting, contrary to the editing literature, that the onset of motion before a cut may not be as critical for creating edit blindness as the motion after a cut. Analysis of eye movements indicated that viewers reoriented less to new content across intact match-action cuts than shots with motion removed. Audio played a surprisingly large part in creating edit blindness with edit blindness mostly disappearing without audio. These results extend film editor intuitions and are discussed in the context of the Attentional Theory of Cinematic Continuity (Smith, 2012a)

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.Comment: 61 pages, 3 figures, RevTe

Proboscidean Mitogenomics: Chronology and Mode of Elephant Evolution Using Mastodon as Outgroup

We have sequenced the complete mitochondrial genome of the extinct American mastodon (Mammut americanum) from an Alaskan fossil that is between 50,000 and 130,000 y old, extending the age range of genomic analyses by almost a complete glacial cycle. The sequence we obtained is substantially different from previously reported partial mastodon mitochondrial DNA sequences. By comparing those partial sequences to other proboscidean sequences, we conclude that we have obtained the first sequence of mastodon DNA ever reported. Using the sequence of the mastodon, which diverged 24–28 million years ago (mya) from the Elephantidae lineage, as an outgroup, we infer that the ancestors of African elephants diverged from the lineage leading to mammoths and Asian elephants approximately 7.6 mya and that mammoths and Asian elephants diverged approximately 6.7 mya. We also conclude that the nuclear genomes of the African savannah and forest elephants diverged approximately 4.0 mya, supporting the view that these two groups represent different species. Finally, we found the mitochondrial mutation rate of proboscideans to be roughly half of the rate in primates during at least the last 24 million years

Short-Snouted Toothless Ichthyosaur from China Suggests Late Triassic Diversification of Suction Feeding Ichthyosaurs

Ichthyosaurs were an important group of Mesozoic marine reptiles and existed from the Early Triassic to the early Late Cretaceous. Despite a great diversity in body shapes and feeding adaptations, all share greatly enlarged eyes, an elongated rostrum with numerous conical teeth, and a streamlined body.. may be linked to the Late Triassic minimum in atmospheric oxygen