Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notational conventions
- Errata
- 1 Spin and helicity
- 2 The effect of Lorentz and discrete transformations on helicity states, fields and wave functions
- 3 The spin density matrix
- 4 Transition amplitudes
- 5 The observables of a reaction
- 6 The production of polarized hadrons
- 7 The production of polarized e±
- 8 Analysis of polarized states: polarimetry
- 9 Electroweak interactions
- 10 Quantum chromodynamics: spin in the world of massless partons
- 11 The spin of the nucleon: polarized deep inelastic scattering
- 12 Two-spin and parity-violating single-spin asymmetries at large scale
- 13 One-particle inclusive transverse single-spin asymmetries
- 14 Elastic scattering at high energies
- Appendix 1 The irreducible representation matrices for the rotation group and the rotation functions djλμ(θ)
- Appendix 2 Homogeneous Lorentz transformations and their representations
- Appendix 3 Spin properties of fields and wave equations
- Appendix 4 Transversity amplitudes
- Appendix 5 Common notations for helicity amplitudes
- Appendix 6 The coefficients involved in the parity-invariance relations amongst the dynamical reaction parameters
- Appendix 7 The coefficients involved in the additional invariance constraints on the dynamical reaction parameters for a spin-s particle
- Appendix 8 Symmetry properties of the Cartesian reaction parameters
- Appendix 9 ‘Shorthand’ notation and nomenclature for the Argonne Lab reaction parameters
- Appendix 10 The linearly independent reaction parameters for various reactions and their relation to the helicity amplitudes
- Appendix 11 The Feynman rules for QCD
- Appendix 12 Dirac spinors and matrix elements
- References
- Index
8 - Analysis of polarized states: polarimetry
Published online by Cambridge University Press: 13 January 2010
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notational conventions
- Errata
- 1 Spin and helicity
- 2 The effect of Lorentz and discrete transformations on helicity states, fields and wave functions
- 3 The spin density matrix
- 4 Transition amplitudes
- 5 The observables of a reaction
- 6 The production of polarized hadrons
- 7 The production of polarized e±
- 8 Analysis of polarized states: polarimetry
- 9 Electroweak interactions
- 10 Quantum chromodynamics: spin in the world of massless partons
- 11 The spin of the nucleon: polarized deep inelastic scattering
- 12 Two-spin and parity-violating single-spin asymmetries at large scale
- 13 One-particle inclusive transverse single-spin asymmetries
- 14 Elastic scattering at high energies
- Appendix 1 The irreducible representation matrices for the rotation group and the rotation functions djλμ(θ)
- Appendix 2 Homogeneous Lorentz transformations and their representations
- Appendix 3 Spin properties of fields and wave equations
- Appendix 4 Transversity amplitudes
- Appendix 5 Common notations for helicity amplitudes
- Appendix 6 The coefficients involved in the parity-invariance relations amongst the dynamical reaction parameters
- Appendix 7 The coefficients involved in the additional invariance constraints on the dynamical reaction parameters for a spin-s particle
- Appendix 8 Symmetry properties of the Cartesian reaction parameters
- Appendix 9 ‘Shorthand’ notation and nomenclature for the Argonne Lab reaction parameters
- Appendix 10 The linearly independent reaction parameters for various reactions and their relation to the helicity amplitudes
- Appendix 11 The Feynman rules for QCD
- Appendix 12 Dirac spinors and matrix elements
- References
- Index
Summary
In the previous chapters we have dealt with the production of the polarized states that serve as initial states in reactions. Here we turn to the measurement of the state of polarization of an ensemble of particles, i.e. to polarimetry.
In the analysis of the state of polarization we may be dealing with stable or unstable particles. If the particles are stable it may be possible to rely on well-understood reactions, such as those of QED, to achieve the polarization analysis, via, e.g. Coulomb interference or scattering off a laser beam. Or, if this is impracticable, it is sometimes possible to use a double-scattering technique even if the reaction mechanism is unknown. The only assumption needed for this is time-reversal invariance. If the particles are unstable their decay angular distribution gives information on their state of polarization prior to decay. This is not surprising if the decay is electromagnetic, so that the decay amplitudes are precisely known. What is remarkable, however, is that even when the decay mechanism is not known certain decays are ‘magic’ and still provide information on the polarization state of the decaying particle. Examples are p → ππ, ω → γπ, D* → γD,Ψ → pπ, α2 → pπ etc.
For electron beams, where we can rely on QED, it has been possible to construct very accurate and rapidly acting polarimeters.
One of the most interesting challenges at the moment is to construct efficient high energy proton polarimeters for use at RHIC, UNK and possibly at Fermilab.
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- Spin in Particle Physics , pp. 185 - 233Publisher: Cambridge University PressPrint publication year: 2001