14198915
Partition function of a quadratic functional and semiclassical approximation for Witten's three manifold invariant
An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in topological quantum field theory, for which no other method has previously been available. In particular it enables the partition functions appearing in the semiclassical approximation for the Witten-invariant to be evaluated in the most general case. The resulting k-dependence is precisely that conjectured by D. Freed and R. Gompf.
85538824
Dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential
A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential is derived which sheds light on the determinant's dependence on these quantities. This is done via a partial zeta regularisation, formally applying a general formula for the zeta-determinant of a differential operator in one variable with operator-valued coefficients. The resulting expression generalises the known one for the free fermion determinant, obtained via Matsubara frequency summation, to the case of general background gauge field; moreover there is no undetermined overall factor. Rigorous versions of this result are obtained in a continuous time--lattice space setting. The determinant expression reduces to a remarkably simple form in the low temperature limit. A program for how to use this to obtain insight into the QCD phase transition at zero temperature and nonzero density is outlined.
8852930
Index of a family of lattice Dirac operators and its relation to the non-Abelian anomaly on the lattice.
In the continuum, a topological obstruction to the vanishing of the non-Abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac operators in 2n dimensions. In this paper an analogous result is derived for chiral fermions on the lattice in the overlap formulation. This involves deriving an index theorem for a family of lattice Dirac operators satisfying the Ginsparg-Wilson relation. The index density is proportional to Lüscher's topological field in 2n+2 dimensions.
14208386
Families index theory for Overlap lattice Dirac operator. I
Abstract The index bundle of the Overlap lattice Dirac operator over the orbit space of lattice gauge fields is introduced and studied. Obstructions to the vanishing of gauge anomalies in the Overlap formulation of lattice chiral gauge theory have a natural description in this context. Our main result is a formula for the topological charge (integrated Chern character) of the index bundle over even-dimensional spheres in the orbit space. It reduces under suitable conditions to the topological charge of the usual (continuum) index bundle in the classical continuum limit (this is announced and sketched here; the details will be given in a forthcoming paper). Thus we see that topology of the index bundle of the Dirac operator over the gauge field orbit space can be captured in a finite-dimensional lattice setting.
16500714
Phase and scaling properties of determinants arising in topological field theories
Abstract In topological field theory determinants of maps with negative as well as positive eigenvalues arise. We give a generalisation of the zeta-regularization technique to derive expressions for the phase and scaling-dependence of these determinants. For theories on odd-dimensional manifolds a simple formula for the scaling dependence is obtained in terms of the dimensions of cohomology spaces. This enables a non-perturbative feature of Chern-Simons gauge theory to be reproduced by semiclassical methods.
13939487
Eradication of singularities in the next-to-leading order RG evolution for the \Delta S = 1 effective Hamiltonian with 3 quark flavours
We consider the renormalization group evolution for the operators in the $\Delta S=1$ effective Hamiltonian with 3 active quark flavors, which is needed in the numerical analysis of data sets for $\epsilon'/\epsilon$ calculated in lattice QCD. Singularities are present in the original solution of Buras et al. at next-to-leading order. We show how these can be eradicated through a method of analytic continuation to obtain the correct finite solution in this case. Furthermore, we trace the origin of the singularities to a breakdown of the approach of Buras et al. in the 3 flavour case, and show how it can be rectified so that singularitites are absent from the beginning.
121758406
A large acceptance cylindrical drift chamber detector
Abstract This paper describes a large acceptance cylindrical drift chamber detector designed and built for the study of the np → pp π − reaction at neutron beam energies in the range 500–800 MeV. Details of construction, electronics, testing, and detection efficiencies and resolutions are presented.
121239422
Accurate intensity measurements for proton beams with a 201 MHz structure
A counting system which measures the absolute beam intensity accurately (< 1%) at intermediate energies with a beam microstructure of 201.25 MHz or lower is described in this paper. The number of beam micropulses containing one or more beam particles are counted and time-sequenced coincidences between micropulses correct this number to obtain the actual number of beam particles using formulas based on Poisson statistics. The counting system, both the experimental setup and the correction method, was examined fully with two different beam microstructures. 10 MHz and 201.25 MHz, the two main beam microstructures at LAMPF. Maximum beam intensities, below which the system is accurate within a few tenths of a percent, were determined to be ∼ 0/4 pA and ∼ 0.1 pA average beam currents for the 5 ns and 100 ns beam microstructures, respectively.
124531134
Measurement of analyzing power and spin correlations in np elastic scattering at 0.744 and 0.794 GeV using a deuteron polarized beam
Abstract The np and the pp analyzing powers A oono d and spin correlations A oonn d and A oosk d were measured simultaneously using the SATURNE II polarized deuteron beam at 0.744 and 0.794 GeV/nucleon. The results for the pp observables coincide with the free pp elastic scattering data. We thus can assume that also the np analyzing power A oono d and spin correlations A oonn d and A oosk d are equal to those for scattering of free polarized neutrons. The np data cover the angular region 95°⩽ θ CM ⩽122°. Our results for A oono d (np) confirm the phase-shift analysis predictions but spin correlations A oonn d (np) and A oosk d (np) have never been measured in this energy region and will considerably affect the PSA solution. Present results allow conclusions about the angular dependence near the minimum of A oono (np) and A oonn (np) in the vicinity of 0.8 GeV.
122626036
Recent results from E-810
Abstract I discuss data from E-810 including K 0 and Λ production, the rise in production of negative particles at small m ⊥ , and the rapidity distributions. The data are compared to various models; in particular they do not agree with a model indicating large nuclear transparency.
122023821
Measurement of the double-spin asymmetry ALL for inclusive multi-γ pair production with 200 GeV/c polarized proton beam and polarized proton target
The invariant double-differential cross section, E1E2d6 delta/dp(1)3dp(2)3, and the double-spin asymmetry, A(LL), for inclusive multi-gamma pair production in which gamma-rays came from neutral mesons were measured with a 200 GeV/c longitudinally-polarized proton beam and a longitudinally-polarized proton target. Most of the multi-gamma pairs comes from two-jet type events which are sensitive to partonic interaction. The A(LL) values were found to be consistent with zero. The invariant double-differential cross section for inclusive pi0pi0 production was also measured. These measured cross sections are consistent with LUND Monte Carlo simulations. Using the LUND Monte Carlo simulation package with the Carlitz-Kaur model of spin dependent distribution functions of valence quarks, the A(LL) values have been compared with theoretical predictions of gluon polarization, DELTAG/G. The results put restrictions on the size of DELTAG/G in the region of 0.05 less-than-or-similar-to x less-than-or-similar-to 0.35.