An Algorithm for Obtaining Reliable Priors for Constrained-Curve Fits

We introduce the ``Sequential Empirical Bayes Method'', an adaptive constrained-curve fitting procedure for extracting reliable priors. These are then used in standard augmented-chi-square fits on separate data. This better stabilizes fits to lattice QCD overlap-fermion data at very low quark mass where a priori values are not otherwise known. We illustrate the efficacy of the method with data from overlap fermions, on a quenched $16^3\times 28$ lattice with spatial size La=3.2 fm and pion mass as low as $\sim$ 180 MeV.Comment: Lattice2003(machine), 3 pages, 3 figure

Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action

We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety

Finite Quantum Gravity Amplitudes -- no strings attached

We study the gravity-mediated scattering of scalar fields based on a parameterisation of the Lorentzian quantum effective action. We demonstrate that the interplay of infinite towers of spin zero and spin two poles at imaginary squared momentum leads to scattering amplitudes that are compatible with unitarity bounds, causal, and scale-free at trans-Planckian energy. Our construction avoids introducing non-localities or the massive higher-spin particles that are characteristic in string theory.Comment: v2: various small improvements/clarifications, version accepted for publicatio

Quenched Chiral Log and Light Quark Mass from Overlap Fermions

We study the quenched chiral behavior of the pion with mass as low as $\approx 180$ MeV. The calculation is done on a quenched lattice of size $16^3\times 28$ and $a = 0.2$ fm with 80 configurations using overlap fermions and an improved gauge action. Using an improved constrained curve fitting technique, we find that the ground state pseudoscalar mass versus bare quark mass behavior is well controlled with small statistical errors; this permits a reliable fit of the quenched chiral log effects, a determination of the chiral log parameter ($\delta = 0.26(3)$), and an estimate of the renormalized mass of the light quark ($m^{\bar{MS}}(\mu=2 {\rm GeV}) = 3.7(3) {\rm MeV}$).Comment: Lattice2002(spectrum), 3 pages, 3 figure

Improved Measure of Local Chirality

It is popular to probe the structure of the QCD vacuum indirectly by studying individual fermion eigenmodes, because this provides a natural way to filter out UV fluctuations. The double-peaking in the distribution of the local chiral orientation parameter (X) has been offered as evidence, by some, in support of a particular model of the vacuum. Here we caution that the X-distribution peaking varies significantly with various versions of the definition of X. Furthermore, each distribution varies little from that resulting from a random reshuffling of the left-handed (and independently the right-handed) fields, which destroys any QCD-induced left-right correlation; that is, the double-peaking is mostly a phase-space effect. We propose a new universal definition of the X parameter whose distribution is uniform for randomly reshuffled fields. Any deviations from uniformity for actual data can then be directly attributable to QCD-induced dynamics. We find that the familiar double peak disappears.Comment: Lattice 2004(topology), Fermilab, June 21-26, 2004; 3 pages, 4 figure

Outlook and appraisal [June 1988]

The growth of the Scottish economy is now moving into line with the rest of the UK. Industrial production is buoyant. The growth of demand is becoming more broadly based between domestic and external sectors. Yet, construction output still remains relatively depressed, and in a significant number of other industries the ratio of Scottish to UK output remains below that of 1980. As yet there is little indication of the favourable changes in unemployment and vacancies during 1987 being reflected in the most recent employment data. But short-term prospects are more favourable than for several years, while growth forecasts for the medium term compare favourably with those for the UK as a whole

The Scottish economy [June 1988]

With the delay in the publication of this quarter's Commentary it should be borne in mind that responses to both the Scottish Chamber's Business Survey (SCBS) and CBI surveys now refer to developments of two months ago. Accordingly, responses do not take account of, or could reasonably be assumed to have anticipated, the recent increases in nominal interest rates and the depreciation of sterling

The world economy [June 1988]

Growth in the world economy appears to be continuing at a brisk rate. Recent forecasts suggest that output should expand by about 3% this year compared with 3.IX in 1987. The outlook therefore appears to be more favourable than when we last reported; a reflection of the limited impact to date of the October stock market crash. Some progress has been made in adjusting the key trade imbalances but progress remains slow