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Single spin asymmetries in semi-inclusive DIS

Semi-Inclusive Reactions Workshop 2005 May 18 – 20, Jefferson Lab, Newport News. Vrije Universiteit Amsterdam. Single spin asymmetries in semi-inclusive DIS. Fetze Pijlman. in collaboration with. D. Boer C.J. Bomhof P.J. Mulders. Outline. Factorization, universality and Wilson lines

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Single spin asymmetries in semi-inclusive DIS

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  1. Semi-Inclusive Reactions Workshop 2005 May 18 – 20, Jefferson Lab, Newport News Vrije Universiteit Amsterdam Single spin asymmetries in semi-inclusive DIS Fetze Pijlman in collaboration with • D. Boer • C.J. Bomhof • P.J. Mulders

  2. Outline • Factorization, universality and Wilson lines • Experimental input • Interpretation of the Sivers effect

  3. Factorized approach • Cross-sections are usually • expressed as: • Questions: Which observables allow for a factorized description? • Are the parton distributions universal? • Recent claims on transverse momentum dependent factorization in SIDIS, Drell-Yan (and e+ e- annihilation):

  4. gauge link Separation of longitudinally polarized gluons and Wilson lines • Diagrammatic expansion • Take all possible interactions into account • Separation of longitudinally polarized gluons Ward identities F.P. (2004) Brodsky, Hwang, Schmidt (2002)

  5. T-even/T-odd: T-odd: Wilson lines at tree-level in SIDIS and Drell-Yan matrix elements integrated: unintegrated: gauge links in SIDIS integrated: unintegrated: gauge links in Drell-Yan integrated: unintegrated: • outgoing particle-lines yield gauge link via (+) infinity • incoming particle-lines yield gauge link via (-) infinity Efremov, Radyushkin (1981) Belitsky, Ji, Yuan (2003) Boer, Mulders, Pijlman (2003)

  6. Time reversal Wilson lines in fragmentation functions e+ e- annihilation outgoing quark: link via + infinity • SIDIS • incoming quark: link via - infinity We have no relation between the fragmentation functions of the two processes, but of course there could be one. Boer, Mulders, Pijlman (2003) Metz (2002) Gamberg, Goldstein (2003) Collins, Metz (2004)

  7. Is evolution process-dependent? Universality & factorization? Wilson lines at higher orders • results: results: Bomhof, Mulders, F.P. (2004) F.P. (2004)

  8. Factorization & universality • general result: gauge links in a hadron change if there are other • incoming and outgoing QCD (bound) states • possible appearance of loops: • fragmentation in SIDIS • distributions in pp scattering • no loops: • distribution functions in SIDIS • e+ e- annihilation • probably safe observables • integrated SIDIS and Drell-Yan • “two hadron production” in DIS, PP scattering, e+ e- annihilation • if fragmentation is link independent, then unintegrated SIDIS • parts of the azimuthal asymmetries in Drell-Yan in which T-odd effects do not contribute

  9. How to tackle the problems experimentally? • Measure the Sivers function , and Boer-Mulders function • ( if zero ): no effect from gauge link, factorization & universality • if nonzero: factorization & universality needs to be studied • Compare T-odd distribution functions in different processes (Drell-Yan / SIDIS), is there a sign change or more? • Compare transverse momentum dependent fragmentation functions • T-even and T-odd • Measure in jet-production in electron-proton scattering

  10. Lorentz invariance relations • “Lorentz invariance relations”: • Vector dependence also leads to new functions • Beam-spin-asymmetry for the jet (neglecting quark masses) Goeke et al. (2003) Bacchetta, Mulders, F.P. (2004)

  11. Sivers effect • L-R asymmetry • gluon-magnetic field only nonzero in hadron, vector fields provide the effect • topological effect (1, 5/4,etc) Speculations on the Sivers effect • Aharanov-Bohm effect • L-R asymmetry • magnetic fields only nonzero in solenoid, vector fields provide the effect • topological effect (1, 2, etc) The first QCD analogue of the Aharanov-Bohm effect?

  12. Summary • Transverse momentum dependent distribution and fragmentation functions contain rich information on the structure of the nucleon and theoretical progress is being made • Access to non-perturbative physics with interesting interpretations • Gauge links are essential for understanding SSA’s • (such as SIDIS, Drell-Yan, and also p+p -> + X) • In general gauge loops can appear in processes and will probably be an essential ingredient in considerations on factorization

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