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.
5306804
On the continuum limit of fermionic topological charge in lattice gauge theory
It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the four-torus, given in terms of a spectral flow of the Hermitian Wilson–Dirac operator or, equivalently, as the index of the overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter m0 is in the physical region 0
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.
121731560
A lattice calculation of the R-Torsion for U(1) Chern-Simons theory
We describe a new geometrical discretisation method which exactly preserved topological properties of U(1) Chern-Simons theories. A numerical calculation using these new methods correctly evaluates the Reidemeister Torsion for low order Lens spaces.
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.
5507561
Rooting issue for a lattice fermion formulation similar to staggered fermions but without taste mixing.
Toinvestigatetheviabilityofthe4th roottrickforthestaggered ferm ion determ inantin asim pler setting,weconsidera two taste(avor)lattice ferm ion form ulation with no tastem ixing butwith exact taste-nonsinglet chiralsym m etries analogous to the taste-nonsinglet U(1)A sym m etry of staggered ferm ions.M .Creutz’sobjectionsto therooting trick apply justasm uch in thissetting. To counter them we show thatthe form ulation has robustwould-be zero-m odes in topologically nontrivialgauge backgrounds,and that these m anifestthem selves in a viable way in the rooted ferm ion determ inantand also in the disconnected piece ofthe pseudoscalarm eson propagatoras required to solvetheU(1)problem .Also,ourrooted theory isheuristically seen to bein theright universality classforQCD ifthesam eistrueforan unrooted m ixed ferm ion action theory.
178487761
The ganga user interface for physics analysis and distributed resources
125547122
MEASUREMENT OF 2ND AND 3RD ORDER POLARIZATION OBSERVABLES IN P D ELASTIC SCATTERING
34092114
Spin asymmetry in muon-proton deep inelastic scattering on a transversely-polarized target
Abstract We measured the spin asymmetry in the scattering of 100 GeV longitudinally-polarized muons on transversely polarized protons. The asymmetry was found to be compatible with zero in the kinematic range 0.006 x Q 2 2 . From this result we derive the upper limits for the virtual photon-proton asymmetry A 2 , and for the spin structure function g 2 . For x 2 is significantly smaller than its positivity limit √R .
15397334
Improving the low-lying spectrum of the overlap kernel
Abstract The action of the overlap-Dirac operator on a vector is typically implemented indirectly through a multi-shift conjugate gradient solver. The compute-time this takes to evaluate depends upon the condition number κ of the matrix that is used as the overlap kernel. We examine the low-lying spectra of various candidate kernels in an effort to optimise κ, thereby speeding up the overlap evaluation.
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.