118986549
Chiral limit of strongly coupled lattice gauge theories
Abstract We construct a new and efficient cluster algorithm for updating strongly coupled U ( N ) lattice gauge theories with staggered fermions in the chiral limit. The algorithm uses the constrained monomer–dimer representation of the theory and should also be of interest to researchers working on other models with similar constraints. Using the new algorithm we address questions related to the chiral limit of strongly coupled U ( N ) gauge theories beyond the mean field approximation. We show that the infinite volume chiral condensate is non-zero in three and four dimensions. However, on a square lattice of size L we find ∑ x 〈 ψ ψ(x) ψ ψ(0)〉∼L 2−η for large L where η =0.420(3)/ N +0.078(4)/ N 2 . These results differ from an earlier conclusion obtained using a different algorithm. Here we argue that the earlier calculations were misleading due to uncontrolled autocorrelation times encountered by the previous algorithm.
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.
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.
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.
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.
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.
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 .
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.
121757543
Measurement of single spin asymmetry for direct photon production in pp collisions at 200 GeV/c
The single spin asymmetry for inclusive direct-photon production has been measured using a polarized proton beam of 200 GeV/c with an unpolarized proton target at −0.15 < xf < 0.15 and 2.5 < pt < 3.1 GeV/c at Fermilab. The data on the cross section for pp → γX at 2.5 < pt < 3.8 GeV/c are also provided. The measurement was done using lead-glass calorimeters and photon detectors which surrounded the fiducial area of the calorimeters. Background rejection has been done using these surrounding photon detectors. The cross section obtained is consistent with the results of previous measurements assuming a nuclear dependence of A1.0. The single spin asymmetry, AN, for the direct-photon production is consistent with zero within experimental uncertainty.
122179155
Comparison of spin asymmetries and cross sections in π0 production by 200 GeV polarized antiprotons and protons
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.