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.
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.
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.
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.
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.
121937710
On the relevance of the Dirac equation to the scattering of medium-energy nucleons from nuclei☆
Abstract The differences between relativistic and nonrelativistic descriptions of medium-energy nucleon—nucleus scattering are discussed. Special attention is paid to a recently developed Dirac optical model in which we point out an ambiguity resulting from the use of an incomplete representation for relativistic nucleon—nucleon scattering amplitude. This ambiguity is reflected in contributions from negative-energy states and in the implementation of the impulse approximation. We also review how a nonrelativistic optical potential can be modified to include relativistic projectile kinematics.
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.
120295653
Quick polarization analyzer (QPAN)
Abstract A high count rate polarimeter for the measurement and monitoring of the polarization of an intermediate energy neutron beam has been developed. The device, QPAN, consists of a double arm telescope with adjustable copper absorbers. The asymmetry of the protons scattered from the liquid hydrogen (LH 2 ) target is calculated from the count differential between two arms, positioned above and below the beam.
26597722
Spin structure of the proton from polarized inclusive deep-inelastic muon-proton scattering
We have measured the spin-dependent structure function g(1)(p) in inclusive deep-inelastic scattering of polarized muons off polarized protons, in the kinematic range 0.003<x<0.7 and I GeV2<Q(2)<60 GeV2. A next-to-leading order QCD analysis is used to evolve the measured g(1)(p)(x,Q(2)) to a fixed Q(0)(2). The first moment of g(1)(p) at Q(0)(2)=10 GeV2 is Gamma=0.136+/-0.013 (stat) +/-0.009 (syst) +/-0.005 (evol). This result is below the prediction of the Ellis-Jaffe sum rule by more than two standard deviations. The singlet axial charge a(0) is found to be 0.28+/-0.16. Ln the Adler-Bardeen factorization scheme, Delta g similar or equal to 2 is required to bring Delta Sigma in agreement with the quark-parton model. A combined analysis of all available proton, deuteron, and He-3 data confirms the Bjorken sum rule.
195865040
Scintillating pad detectors
We have been investigating the performance of scintillating pad detectors, individual small tiles of scintillator that are read out with wavelength-shifting fibers and visible light photon counters, for application in high luminosity colliding beam experiments such as the DO Upgrade. Such structures could provide "pixel" type readout over large fiducial volumes for tracking, preshower detection and triggering.