15521983
Structure of logarithmically divergent one-loop lattice Feynman integrals
For logarithmically divergent one-loop lattice Feynman integrals I(p, a), subject to mild general conditions, we prove the following expected and crucial structural result: I(p, a) = f(p)log(aM) g(p) + h(p, M) up to terms which vanish for lattice spacing a→0. Here p denotes collectively the external momenta and M is a mass scale which may be chosen arbitrarily. The f(p) and h(p,,M) are shown to be universal and coincide with analogous quantities in the corresponding continuum integral when the latter is regularized either by momentum cutoff or dimensional regularization. The nonuniversal term g(p) is shown to be a homogeneous polynomial in p of the same degree as f(p). This structure is essential for consistency between renormalized lattice and continuum formulations of QCD at one loop.
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.
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.
13590622
A muon identification and combined reconstruction procedure for the ATLAS detector at the LHC at CERN
Muon identification (MUID) and high-momentum measurement accuracy is crucial to fully exploit the physics potential that will be accessible with the ATLAS experiment at the LHC. The muon energy of physics interest ranges in a large interval from few GeV, where the b-physics studies dominate the physics program, up to the highest values that could indicate the presence of new physics. The muon detection system of the ATLAS detector is characterized by two high-precision tracking systems, namely the inner detector (ID) and the muon spectrometer, (MS) plus a thick calorimeter that ensures a safe hadron absorption filtering with high-purity muons with energy above 3 GeV. In order to combine the muon tracks reconstructed in the ID and the MS, a MUID object-oriented software package has been developed. The purpose of the MUID procedure is to associate tracks found in the MS with the corresponding ID track and calorimeter information in order to identify muons at their production vertex with optimum parameter resolution. The performance of these two combined systems has been evaluated with Monte Carlo studies using single muons of fixed-transverse momentum and with full physics events.
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.
122680242
Measurement of 2‐nd and 3‐rd order spin observables in elastic scattering of 1.6 GeV tensor and vector polarized deuteron beam from a polarized hydrogen target
Seven previously unmeasured spin asymmetries and ten previously unmeasured spin transfer observable have been determined in the momentum transfer range, 0.12<−t<0.85 (GeV/c)2. We used a 1600 MeV polarized deuteron beam incident on a polarized hydrogen target in these measurements. This is equivalent to using an 800 MeV proton beam on a deuteron target. These observables are poorly predicted by the relativistic impulse approximation, which has been used successfully to reproduce spin observables for protons on spin‐zero nuclei.
124601405
MUON IDENTIFICATION AND COMBINED RECONSTRUCTION FOR THE ATLAS DETECTOR AT CERN-LHC
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.