Status of Spin Physics - Experimental Summary

The current status of spin physics experiments, based on talks presented at the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing, 2001, is summarized in this article. Highlights of recent experimental results at SLAC, JLab, and DESY, as well as future plans at these facilities and at RHIC-spin are discussed.Comment: 18 pages, 7 figures, Invited talk presented at the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing, October, 200

Form factors in quantum electrodynamics

The electromagnetic form factors of an electron in pure quantum electrodynamics are analyzed with the techniques of dispersion relations. The viewpoint is adopted here that no subtractions are required in the construction of dispersion relations for the electromagnetic vertex. This leads to coupled integral equations for the form factors in terms of other physical amplitudes; electron-positron scattering, for example. The relation between this and the usual perturbation approach to quantum electrodynamics, and the validity and consequences of the "no-subtraction" philosophy, are discussed

Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

CORE and the Haldane Conjecture

The Contractor Renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper\cite{QGAF} I showed that the Contractor Renormalization group (CORE) method could be used to map a theory of free quarks, and quarks interacting with gluons, into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple Contractor Renormalization group (CORE) computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.Comment: 36 pages, 4 figures, 5 tables, latex; extensive additions to conten

Threshold corrections to rapidity distributions of Z and W^\pm bosons beyond N^2 LO at hadron colliders

Threshold enhanced perturbative QCD corrections to rapidity distributions of $Z$ and $W^\pm$ bosons at hadron colliders are presented using the Sudakov resummed cross sections at N${}^3$LO level. We have used renormalisation group invariance and the mass factorisation theorem that these hard scattering cross sections satisfy to construct the QCD amplitudes. We show that these higher order threshold QCD corrections stabilise the theoretical predictions for vector boson production at the LHC under variations of both renormalisation and factorisation scales.Comment: 17 pages, 8 eps figures. This paper is dedicated to the memory of W.L.G.A.M. van Neerve

Wide-angle pair production and quantum electrodynamics at small distances

Wide-angle photoproduction of high-energy electron-positron pairs in hydrogen is proposed and analyzed as a test of quantum electrodynamics at distances ≤10^-13 cm. The effect of proton structure can be removed in terms of the two form factors measured in the elastic electron-proton scattering process. Cross sections are presented for two classes of pair production experiments: (1) those detecting one of the final particles, and (2) coincidence experiments. In addition to kinematic, anomalous moment, and nucleon form-factor corrections to the Bethe-Heitler formula, dynamical corrections to the proton current and radiative corrections are calculated. The final theoretical formula is believed to be accurate to 2%. A simple cutoff model suggests that a 5% accuracy in an experiment of type (1) tests the electron propagator at distances ∼0.7×10^-13 cm, while a 10% accuracy in a coincidence arrangement of type (2) probes the electron propagator at ∼0.3×10^-13 cm

Dirac-Coulomb scattering with plane wave energy eigenspinors on de Sitter expanding universe

The lowest order contribution of the amplitude of Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given energy and helicity. We find that the total energy is conserved in the scattering process.Comment: 9 pages, no figure

Theory of S-Wave Pion Scattering and Photoproduction at Low Energies

A fixed-source analysis of the s-wave pion-nucleon interaction is constructed along the lines of the Chew-Low-Wick formalism. A bilinear s-wave interaction of the form λ0ϕ·ϕ+λτ·(ϕ×π) is added to the usual p-wave coupling (4π)1/2(f/μ)σ·∇τ·ϕ. Scattering equations are developed and solved in the one-meson approximation. Values for the renormalized coupling parameters λ0 and λ are determined which give reasonable agreement with the s-wave phase shifts up to ∼100-Mev pion kinetic energy. This s-wave interaction with the parameters fixed by the scattering analysis is then applied to the discussion of the π+ and π0 photo-production cross sections. A Kroll-Ruderman theorem is proved for the above nonlocal interaction and it is shown that the contributions to s-wave neutral and charged photoproduction are consistent with experiment. Other experimental implications, in particular as to the possible role of π-π forces, are discussed

Rare decay pi0 -> e+e-: theory confronts KTeV data

Within the dispersive approach to the amplitude of the rare decay pi0 -> e+e- the nontrivial dynamics is contained only in the subtraction constant. We express this constant, in the leading order in (m_e/\Lambda)^2 perturbative series, in terms of the inverse moment of the pion transition form factor given in symmetric kinematics. By using the CELLO and CLEO data on the pion transition form factor given in asymmetric kinematics the lower bound on the decay branching ratio is found. The restrictions following from QCD allow us to make a quantitative prediction for the branching B(pi0 -> e+e-) =(6.2\pm 0.1)*10^{-8} which is 3\sigma below the recent KTeV measurement. We confirm our prediction by using the quark models and phenomenological approaches based on the vector meson dominance. The decays \eta -> l^+l^- are also discussed.Comment: 7 pages, 1 figur

A Renormalization Group Method for Quasi One-dimensional Quantum Hamiltonians

A density-matrix renormalization group (DMRG) method for highly anisotropic two-dimensional systems is presented. The method consists in applying the usual DMRG in two steps. In the first step, a pure one dimensional calculation along the longitudinal direction is made in order to generate a low energy Hamiltonian. In the second step, the anisotropic 2D lattice is obtained by coupling in the transverse direction the 1D Hamiltonians. The method is applied to the anisotropic quantum spin half Heisenberg model on a square lattice.Comment: 4 pages, 4 figure