Single spin asymmetries in semi-inclusive DIS

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Presentation transcript:

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 Experimental input Interpretation of the Sivers effect

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): Factorization / universality Ji, Ma, Yuan (2004) yes Bomhof, Mulders, Pijlman (2004) unclear due to gauge link Pijlman (2004) looks problematic for some processes Collins, Metz (2004)

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

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 T-even/T-odd: T-odd: Efremov, Radyushkin (1981) Belitsky, Ji, Yuan (2003) Boer, Mulders, Pijlman (2003)

Wilson lines in fragmentation functions SIDIS incoming quark: link via - infinity e+ e- annihilation outgoing quark: link via + infinity Time reversal 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)

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

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

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

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)

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

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