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New Observables from Color Gauge Invariance

16th international spin physics symposium 10-16 October 2004, Trieste in Italy. Vrije Universiteit Amsterdam. New Observables from Color Gauge Invariance. Fetze Pijlman. in collaboration with. D. Boer C.J. Bomhof P.J. Mulders. Nucl.Phys. B667 (2003) 201. Phys.Lett.B596 (2004) 277.

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New Observables from Color Gauge Invariance

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  1. 16th international spin physics symposium 10-16 October 2004, Trieste in Italy Vrije Universiteit Amsterdam New Observables from Color Gauge Invariance Fetze Pijlman in collaboration with • D. Boer • C.J. Bomhof • P.J. Mulders Nucl.Phys. B667 (2003) 201 Phys.Lett.B596 (2004) 277 hep-ph/0409332

  2. Contents • transverse momentum dependent distribution and fragmentation functions (T-even / T-odd) • single spin asymmetries in semi-inclusive DIS • factorization and gauge links • conclusions

  3. integrated cross-section unintegrated cross-section integrated: unintegrated: Distribution and fragmentation functions distribution functions (leading twist) • semi-inclusive DIS: • cross-section factorized • parton model Mulders, Tangerman, Nucl.Phys. B461 (1996) 197

  4. gauge links in SIDIS integrated: unintegrated: T-even/T-odd: T-odd: T-even & T-odd matrix elements • matrix elements • integrated: • unintegrated: gauge links in Drell-Yan integrated: unintegrated: it is difficult to relate fragmentation functions with different link structures Efremov et al., Theor.Math.Phys. 44 (1981) 774 Brodsky et al., Phys.Lett.B530 (2002) 99 Belitsky et al., Nucl.Phys.B656 (2003) 165 Collins, Phys.Lett.B 536 (2002) 43 Boer et al., Nucl.Phys. B667 (2003) 201 Metz, Phys.Lett.B549 (2002) 139, Collins et al., hep-ph/0408249

  5. Single spin asymmetries • the gauge link itself introduces new functions at twist 3: jet production in DIS: (assuming massless quarks) semi-inclusive DIS: Trento 2004 conventions transversity Sivers Bacchetta, Mulders, F.P., Phys.Lett.B 595 (2004) 309 Korotkov, Nowak, Oganessyan, Eur.Phys.J. C18 (2001) 639 Metz, Schlegel, hep-ph/0403182 Yuan, Phys.Lett.B589 (2004) 28

  6. gauge link Factorization • factorization is often assumed, but its proof is essential to • understand the nucleon in terms of distribution functions • essential step: proof that all IR divergences can be absorbed in • parton distribution functions in a universal manner • what role do the gauge links play? Ward identities Ji, Ma, Yuan, hep-ph/0404183 and Phys.Lett.B597 (2004) 299 Collins, Metz, hep-ph/0406302

  7. Gauge links in SIDIS semi-inclusive DIS at leading order in M/Q + + + + ... = • results: 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 Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277

  8. gauge links are • essential for understanding SSA’s in for instance • Drell-Yan at high , prompt photon production and P+P -> + X • very relevant in the study of factorization Gauge links in Drell-Yan • results: not a peculiarity of QCD also appears in QED F. P., hep-ph/0409332 Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277

  9. Gauge links and factorization 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 • Drell-Yan • P+P -> + X • P+P -> 2 jets • no loops: • distribution functions in SIDIS • e+ e- annihilation Is factorization and universality destroyed? Not at all, there is now a handle to find observables which allow to be factorized! F. P., hep-ph/0409332 Bomhof, Mulders, F.P., Phys.Lett.B596 (2004) 277

  10. insensitive 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 and azimuthal asymmetries in Drell-Yan in which T-odd effects do not contribute Towards factorization in Drell-Yan • an observable has a chance of being factorized if • gauge links do not matter in general • (T-odd distribution functions do not exist) • the observable is insensitive to the difference of various gauge links it has taken a long time before claims on factorization in DY appeared, this might aid the final proof in the future.

  11. Conclusions • transverse momentum dependent distribution and fragmentation functions contain rich information on the structure of the nucleon and theoretical progress is being made (model calculations could be very useful) • 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 • we have listed a set of observables for which a proof of factorization should be nearby.

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