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.
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.
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.
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.
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.
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.
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.
125547122
MEASUREMENT OF 2ND AND 3RD ORDER POLARIZATION OBSERVABLES IN P D ELASTIC SCATTERING
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.
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.