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Remarks on angular momentum

Trieste, November 2006. Remarks on angular momentum. Piet Mulders. pjg.mulders@few.vu.nl. Comments. Parton model is not frame dependent (IMF)! Angular momentum is space integral (but space ambiguous!) In QM wave packets are allowed (Gallilean invariance, c  infinity).

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Remarks on angular momentum

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  1. Trieste, November 2006 Remarks on angular momentum Piet Mulders pjg.mulders@few.vu.nl

  2. Comments • Parton model is not frame dependent (IMF)! • Angular momentum is space integral (but space ambiguous!) • In QM wave packets are allowed (Gallilean invariance, c infinity). • In relativistic QM (Lorentz/Poincare invariance) there is a problem. • Can one not avoid problem with spin vector (parameterisation of density matrix) by using explicit spin basis, e.g. helicity states? • These are projections of the fermion fields. Make sure you use a ‘good basis’. • Expansion of nucleon state in terms of partons ‘dangerous’. Do it in front form  Lightcone wave functions, etc. • Transverse spin sumrule can be written down, but use ‘operator expressions’.

  3. (Angular) momentum operators in QCD

  4. Kinematic operators Instant form quantization Front form quantization

  5. D P P’ Local – forward and off-forward Local operators (coordinate space densities): Form factors Static properties: Examples: (axial) charge mass spin magnetic moment angular momentum

  6. Selectivity at high energies: q = p Nonlocal - forward Nonlocal forward operators (correlators): Specifically useful: ‘squares’ Momentum space densities of f-ons: Sum rules  form factors

  7. Selectivity q = p Nonlocal – off-forward Nonlocal off-forward operators (correlators AND densities): Sum rules  form factors GPD’s b Forward limit  correlators

  8. Caveat • We study forward matrix elements, including transverse momentum dependence (TMD), i.e. f(p||,pT) with enhanced nonlocal sensitivity! • This is not a measurement of orbital angular momentum (OAM). Direct measurement of OAM requires off-forward matrix elements, i.e. GPD’s. • One may at best make statements like: linear pT dependence  nonzero OAM no linear pT dependence  no OAM

  9. Aspects of high energy processes • Ability to access matrix elements of specific operators (‘incoherence’) in inclusive processes and • This is not a measurement of orbital angular momentum (OAM). Direct measurement of OAM requires off-forward matrix elements, i.e. GPD’s. • One may at best make statements like: linear pT dependence  nonzero OAM no linear pT dependence  no OAM

  10. Densities and (spacelike) formfactors

  11. Forward limits of (spacelike) form factors

  12. back Caveat • We study forward matrix elements, including transverse momentum dependence (TMD), i.e. f(p||,pT) with enhanced nonlocal sensitivity! • This is not a measurement of orbital angular momentum (OAM). Direct measurement of OAM requires off-forward matrix elements, i.e. GPD’s. • One may at best make statements like: linear pT dependence  nonzero OAM no linear pT dependence  no OAM

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