Helicity amplitudes and crossing relations for antiproton proton reactions

Antiproton proton annihilation reactions allow unique access to the moduli and phases of nucleon electromagnetic form factors in the time like region. We present the helicity amplitudes for the unequal mass single photon reaction $p \bar{p}\to l^+ l^-$ in the s channel including the lepton mass. The relative signs of these amplitudes are determined using simple invariance properties. Helicity amplitudes for the annihilation reaction $p \bar{p} \to N \bar{N}$ are also given, where $N$ is any spinor particle with structure. Crossing relations between the $e p \to e p$ scattering and the $p \bar{p}\to l^+ l^-$ annihilation channels are discussed and the crossing matrix for the helicity amplitudes is given. This matrix may be used to verify known expressions for the space like helicity amplitudes due to one photon exchange.Comment: 15 pages, 5 figures, submitted to EPJ

Spin Observables for Polarizing Antiprotons

The PAX project at GSI Darmstadt plans to polarize an antiproton beam by repeated interaction with a hydrogen target in a storage ring. Many of the beam particles are required to remain within the ring after interaction with the target, so small scattering angles are important. Hence we concentrate on low momentum transfer (small t), a region where electromagnetic effects dominate the hadronic effects. A colliding beam of polarized electrons with energy sufficient to provide scattering of antiprotons beyond ring acceptance may polarize an antiproton beam by spin filtering. Expressions for spin observables are provided and are used to estimate the rate of buildup of polarization of an antiproton beam.Comment: 4 pages, 2 figures, to be published in the Proceedings of the 17th International Spin Physics Symposium (SPIN 2006), Kyoto, Japan; October 2-7, 200

Dynamics of polarization buildup by spin filtering

There has been much recent research into polarizing an antiproton beam, instigated by the recent proposal from the PAX (Polarized Antiproton eXperiment) project at GSI Darmstadt. It plans to polarize an antiproton beam by repeated interaction with a polarized internal target in a storage ring. The method of polarization by spin filtering requires many of the beam particles to remain within the ring after scattering off the polarized internal target via electromagnetic and hadronic interactions. We present and solve sets of differential equations which describe the buildup of polarization by spin filtering in many different scenarios of interest to projects planning to produce high intensity polarized beams. These scenarios are: 1) spin filtering of a fully stored beam, 2) spin filtering while the beam is being accumulated, i.e. unpolarized particles are continuously being fed into the beam, 3) the particle input rate is equal to the rate at which particles are being lost due to scattering beyond ring acceptance angle, the beam intensity remaining constant, 4) increasing the initial polarization of a stored beam by spin filtering, 5) the input of particles into the beam is stopped after a certain amount of time, but spin filtering continues. The rate of depolarization of a stored polarized beam on passing through an electron cooler is also shown to be negligible.Comment: 15 pages, references added, introduction elaborated on, some variables defined in more detail. Submitted to Eur. Phys. J.

An absolute polarimeter for high energy protons

A study of the spin asymmetries for polarized elastic proton proton collisions in the electromagnetic hadronic interference (CNI) region of momentum transfer provides a method of self calibration of proton polarization. The method can be extended to non-identical spin half scattering so that, in principle, the polarization of a proton may be obtained through an analysis of its elastic collision with a different polarized particle, helium 3 for instance. Sufficiently large CNI spin asymmetries provide enough information to facilitate the evaluation of nearly all the helicity amplitudes at small t as well as the polarization of both initial spin half fermions. Thus it can serve equally well as a polarimeter for helium 3

Energy Dependence of the Pomeron Spin-Flip

There is no theoretical reason to think that the spin-flip component of the Pomeron is zero. One can measure the spin-flip part using Coulomb-nuclear interference (CNI). Perturbative QCD calculations show that the spin-flip component is sensitive to the smallest quark separation in the proton, while the non-flip part probes the largest separation. According to HERA results on the proton structure function at very low x the energy dependence of the cross-section correlates with the size of the color dipole. Analysing the data from HERA we predict that the ratio of the spin-flip to non-flip amplitude grows with energy as $r(s)\propto (1/x)^{0.1-0.2}$, violating Regge factorisation of the Pomeron.Comment: A few comments and references are added. Based on invited talks at the International Workshop on Diffraction Physics, Rio de Janeiro, February 16-20, 1998, and at DIS'98, Brussels, April 4-8, 199

Polarisation observables in lepton antilepton to proton antiproton reactions including lepton mass

General expressions, including the lepton mass, for the spin averaged differential cross section for the annihilation reaction lepton antilepton to proton antiproton are given, as well as general formulae for the single and double spin asymmetries in the centre of mass frame. In particular we discuss the single spin asymmetry, normal to the scattering plane, which measures the relative phase difference between nucleon electromagnetic form factors $G_E$ and $G_M$. Recent experimental investigations of these form factors in the space and time like region are reviewed. It is thought that measurements of the phase of these form factors will provide fundamental information on the internal nucleon structure. The phases between $G_E$ and $G_M$ are accessible through polarisation observables measured in the antiproton proton to lepton antilepton reaction, or in its time reversed process.Comment: 14 pages, to be submitted to EPJ

Impact of saturation on spin effects in proton-proton scattering

For pomerons described by a sum of two simple-pole terms, a soft and a hard pomeron, the unitarity bounds from saturation in impact-parameter space are examined. We consider the effect of these bounds on observables linked with polarisation, such as the analyzing power in elastic proton-proton scattering, for LHC energies. We obtain the s and t dependence of the Coulomb-nuclear interference at small momentum transfer, and show that the effect of the hard pomeron may be observed at the LHC.Comment: 8 pages, 2 figures, presented by O.V.S. at the Advanced Studies Institute "Symetries and Spin" (SPIN-Praha-2004), Prague, July 5 - July 10, 200