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Single spin asymmetries in hard scattering processes

Partonic structure of hadrons 9 / 14 May 2005, Trento. Vrije Universiteit Amsterdam. Single spin asymmetries in hard scattering processes. Fetze Pijlman. in collaboration with. D. Boer C.J. Bomhof P.J. Mulders. Contents. Factorization and universality

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Single spin asymmetries in hard scattering processes

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  1. Partonic structure of hadrons 9 / 14 May 2005, Trento Vrije Universiteit Amsterdam Single spin asymmetries in hard scattering processes Fetze Pijlman in collaboration with • D. Boer • C.J. Bomhof • P.J. Mulders

  2. Contents • Factorization and universality • Wilson lines in transverse momentum dependent parton distribution functions • 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:

  4. Diagrammatic approach • A field-theory-based approach to hard scattering processes in which hadrons are observed in initial and final state • Extension of the parton model • Valid in perturbation theory • The diagrammatic approach does not • make any assumption on factorization • or universality

  5. Resummation of a class of interactions leads to a gauge link in parton distributions fragmentation functions also contain a gauge link (via minus infinity) semi-inclusive DIS at leading order in M/Q + + + + ... = Diagrammatic approach in semi-inclusive DIS Efremov Radyushkin, Theor.Math.Phys. 44 (1981) 774, Belitsky Ji, Yuan, Nucl.Phys.B656 (2003) 165, Boer, Mulders, F.P., Nucl.Phys. B667 (2003) 201

  6. Leading order cross-section of SIDIS • The other interactions are believed to be suppressed; they need to be worked out and verified. • At this order the cross-section appears to be factorized:

  7. The gauge link in Drell-Yan • Resumming the same class of interactions leads also • to gauge links in the distribution functions • The result can also be written in a factorized form, but it contains different functions. What about universality??

  8. Universality relations • Transverse momentum dependent distribution functions • T-even/T-odd: • Matrix element T-odd: • Transverse momentum dependent fragmentation functions • in semi-inclusive DIS via (-) infinity • in electron-positron annihilation via (+) infinity • there is no relation between the two (unless some higher symmetry) • problem for extracting transversity via Collins effect Boer, Mulders, F.P., Nucl.Phys. B667 (2003) 201 Metz, Phys.Lett.B549 (2002) 139

  9. Higher order in SIDIS Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277

  10. What is happening here? Higher order in Drell-Yan Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277

  11. Evolution of parton distributions Drell-Yan Real: Virtual: • Semi-inclusive DIS • Real: • Virtual: not a peculiarity of QCD also appears in QED Is the evolution of (transverse momentum dependent) distribution functions is process-dependent?

  12. Factorization • For general tree-level diagrams the gauge link can be calculated with a straight-forward algorithm. The gauge link turns out to be diagram-dependent • At first order the gauge link is not modified by virtual corrections • Gauge links in distribution functions get modified under gluon radiation if there are two incoming hadrons (such as pp scattering) • Gauge links in fragmentation functions get modified if there is an incoming hadron (like semi-inclusive DIS, but not in electron-positron annihilation) F.P., hep-ph/0409332 & hep-ph/0411307

  13. 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, 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

  14. in jet-production • Gauge link in the correlator introduces an extra vector, violating • the Lorentz invariance relations • This extra vector leads at twist 3 to new functions for transversely polarized hadrons and unpolarized hadrons, • Beam-spin asymmetry for the jet Metz, Schlegel, Eur.Phys.J.A. 22:489 (2004) Goeke, Metz, Schlegel, hep-ph0504130 Goeke, Metz, Pobylitsa, Polyakov, Phys.Lett.B567:27,2003 Bacchetta, Mulders, F.P., Phys.Lett.B595:309 (2004)

  15. Sivers effect • L-R asymmetry • gluon-magnetic field only nonzero in hadron, vector fields provide the effect • topological effect (1, 5/4,etc) Interpretation of 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?

  16. 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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