Chapter
2.3 The discrete transformations
2.4 Fields and wave functions
2.4.1 The discrete transformations of the fields
2.4.2 Isospin multiplets for antiparticles
3 The spin density matrix
3.1 The non-relativistic density matrix
3.1.2 Some general properties of pmm>
3.1.3 Combined systems of several particle types
3.1.4 The independent parameters specifying p
3.1.5 The multipole parameters
3.1.6 Multipole parameters for combined systems of particles
3.1.7 Even and odd polarization
3.1.8 The effect of rotations on the density matrix
3.1.9 Diagonalization of p. The quantization axis
3.1.10 Other choices of basis matrices
3.1.11 Invariant characterization of the state of polarization of an ensemble
3.1.12 Spin-1 particles and photons
3.1.13 Positivity of the density matrix
3.2 The relativistic case
3.2.1 Definition of the helicity density matrix
3.2.2 Definition of helicity multipole parameters
3.2.3 The effect of Lorentz transformations on the helicity density matrix
3.2.4 Transformation law for multipole parameters
3.3 Choices of reference frame for a reaction
3.3.1 Density matrix for the initial particles
3.3.2 Density matrix of final state particles
3.4 Covariant spin vectors
4.1 Helicity amplitudes for elastic and pseudoelastic reactions
4.2 Symmetry properties of helicity amplitudes
4.2.3 Identical particles
4.3 Some analytic properties of the helicity amplitudes
4.4 Crossing for helicity amplitudes
4.5 Transition amplitudes in field theory
4.6 Structure of matrix elements
4.6.1 Matrix elements of a vector current
4.6.2 Vector and axial-vector coupling
5 The observables of a reaction
5.2 The final state helicity density matrix
5.2.3 Angular momentum constraints near 6 = 0, n
5.3 The CM observables and the dynamical reaction parameters
5.3.1 Properties of the CM reaction parameters
5.4 Experimental determination of the CM reaction parameters
5.4.1 Unpolarized initial state
5.4.2 Polarized beam, unpolarized target
5.4.3 Polarized target, unpolarized beam
5.4.4 Polarized beam and target
5.5 The laboratory reaction parameters
5.6 Applications: Cartesian formalism for initial particles with spin 1/2
5.6.1 The reaction spin 1/2 + spin 1/2 -> spin 1/2 + spin 1/2
5.6.2 The reactions spin 0 + spin 1/2 —• spin 0 + spin 1/2 and spin 1/2 + spin 1/2 -> spin 0 + spin 0
5.6.3 The reactions spin 1/2 + spin 1/2 —• arbitrary-spin particles
5.6.4 Connection between photon and spin-1/2 induced reactions
5.7 Non-linear relations amongst the observables
5.8 Multiparticle and inclusive reactions
5.8.1 CM reaction parameters and final state density matrix
5.1 The generalized optical theorem
5.1.1 Nucleon-nucleon scattering
5.1.2 Particles of arbitrary spin
5.1.3 Application to deuteron-nucleon and deuteron-deuteron scattering
6 The production of polarized hadrons
6.1 Polarized proton sources
6.2 Polarized proton targets
6.3 The acceleration of polarized particles
6.3.1 Dynamics of the relativistic mean spin vector
6.3.2 Difficulties in the acceleration of polarized particles
6.3.4 Stern-Gerlach polarization of protons and antiprotons
6.4 Polarized secondary and tertiary beams
7 The production of polarized e±
7.1 The natural polarization of electrons circulating in a perfect storage ring
7.1.1 Imperfect storage rings
7.2 Polarization at LEP and HERA
7.2.1 Polarization at LEP
7.2.2 Polarization at HERA
8 Analysis of polarized states: polarimetry
8.1.1 Reaction mechanism understood
8.1.2 Reaction mechanism not known
8.2.1 Two-particle decay of spin-/ resonance
8.2.2 Three-particle decay of a spin-J resonance
9 Electroweak interactions
9.1 Summary of the Standard Model
9.2 Precision tests of the Standard Model
9.2.1 The reaction e~e+ —> fermion-antifermion pair
9.2.2 The reaction e~e+ —> quark-antiquark pair
10 Quantum chromodynamics: spin in the world of massless par tons
10.1 A brief introduction to QCD
10.2 Local gauge invariance in QCD
10.3 Feynman rules for massless particles
10.3.1 The calculus of massless spinors
10.4 The helicity theorem for massless fermions
10.5 Spin structure from a fermion line
10.6 Example: high energy e~ + \T —• e~ + \x~
10.8 Polarization vectors
10.9 Shorthand notation for spinor products
10.10 QED: high energy Compton scattering
10.11 QCD: gluon Compton scattering
10.12 QCD: Multigluon amplitudes
10.12.1 The colour structure
10.12.2 Helicity structure of the rc-gluon amplitude
10.12.3 The amplitude for G + G -> G + G
10.12.4 Colour sums for gluon reactions
10.12.5 Colour sum for GG -> GG
10.12.6 Some properties of n-gluon amplitudes
11 The spin of the nucleon: polarized deep inelastic scattering
11.2 Deep inelastic scattering
11.3 General formalism and structure functions
11.4 The simple parton model
11.5 Field-theoretic generalization of the parton model
11.5.1 Longitudinal polarization: the quark contribution to gi(x)
11.5.2 Transverse polarization: gi{x)
11.6 Moments of the structure functions, sum rules and the spin crisis
11.6.1 A spin crisis in the parton model
11.7 QCD corrections and evolution
11.7.1 Beyond leading order; scheme dependence
11.8 Phenomenology: the polarized-parton distributions
11.8.1 Behaviour as x —• 0 and x —• 1
11.9 The general partonic structure of the nucleon
11.9.1 Evolution for ATq(x,Q2)
11.10 The future: neutrino beams?
12 Two-spin and parity-violating single-spin asymmetries at large scale
12.1 Inclusive and semi-inclusive reactions: general approach
12.2 Longitudinal two-spin asymmetries
12.2.2 Prompt photon production
12.2.3 The Drell-Yan reaction pp -> l+l~X
12.2.4 Drell-Yan production of J/W and X2
12.2.5 Semi-inclusive lepton-hadron scattering
12.3 Parity-violating longitudinal single-spin asymmetries
12.3.1 Small-pr single-spin W± and Z° production
12.3.2 Larger-pT single-spin W- production
12.3.3 Larger-pr single-spin massive Drell-Yan production
12.4 Transverse two-spin asymmetries
13 One-particle inclusive transverse single-spin asymmetries
13.1 Theoretical approaches
13.2 Standard QCD-parton model with soft-physics asymmetries
13.3 Collins mechanism for single-spin asymmetry
13.4 Beyond the standard QCD parton model
13.5 Phenomenological models
13.5.2 The Thomas precession model
13.5.3 Concluding remarks
14 Elastic scattering at high energies
14.1 Small momentum transfer: general
14.2 Electromagnetic interference revisited
14.3 Elastic scattering at large momentum transfer
14.3.1 The asymptotic behaviour
14.3.2 Complications of exclusive reactions
Appendix 1 The irreducible representation matrices for the rotation group and the rotation functions dJ x (6)
Appendix 2 Homogeneous Lorentz transformations and their representations
A2.1 The finite-dimensional representations
A2.3 Connection between spinor and vector representations
Appendix 3 Spin properties of fields and wave equations
A3.1 Relativistic quantum fields
A3.2 Irreducible relativistic quantum fields
A3.3 Parity and field equations
Appendix 4 Transversity amplitudes
A4.1 Definition of transversity amplitudes
A4.2 Symmetry of transversity amplitudes
A4.3 Some analytic properties of transversity amplitudes
Appendix 5 Common notations for helicity amplitudes
Appendix 6 The coefficients Alm/(lm)
Appendix 7 The coefficients ^ ' J m ;
Appendix 8 Symmetry properties of the Cartesian reaction parameters
A8.1 The CM reaction parameters
A8.2 The Argonne Lab 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 465
A10.1 0 + 1/2-> 0 + 1 / 2
A10.2 4(1/2) + £(1/2) -> 0 + 0
A10.3 A + B -» A + 5 all with spin 1/2
A10.4 Photoproduction of pseudoscalar mesons
A10.5 Vector meson production in 0~(l/2)+ -» l~(l/2)+
A10.6 Baryon resonance production in 0~(l/2)+ -> 0~(3/2)+
Appendix 11 The Feynman rules for QCD
A12 Dirac spinors and matrix elements
A 12.1 General properties
A 12.2 Helicity spinors and Lorentz transformations
A12.3 The Dirac-Pauli representation
A 12.4 The Weyl representation
A12.6 The Fierz rearrangement theorem
Spin in Particle Physics
( Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology )
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