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Investigating Intrinsic Motion Effects in SIDIS Strategy

Explore evidence for transverse motion of partons and hadrons within nucleons and fragmentation jets, including spin-k┴ correlations and effects like Collins, Sivers, and Boer-Mulders. Study SIDIS kinematics, unpolarized and polarized SIDIS, fitting data, and Sivers asymmetry. Utilize EMC and HERMES data for predictions and comparisons to advance QCD understanding of proton structure and hard processes.

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Investigating Intrinsic Motion Effects in SIDIS Strategy

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  1. Searching for intrinsic motion effects in SIDIS Strategy (within LO parton model): Based on work in collaboration with E. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin Phys. Rev. D71 (2005) 074006, hep-ph/0501196 See also talk by E. Leader Mauro Anselmino Partonic structure of hadrons (Concepts and Phenomenology), Trento ECT*, May 9-14, 2005

  2. Plenty of theoretical and experimental evidence for transverse motion of partons within nucleons and of hadrons within fragmentation jets • Uncertainty principle • Gluon radiation • qTdistribution of lepton pairs in D-Y processes • pT distribution of hadrons in SIDIS, • Hadron distribution in jets in e+e– processes • Large pTparticle production in • ···· Transverse motion is usually integrated, but there might be important spin-k┴ correlations

  3. Spin-k┴ correlations in distribution and fragmentation functions π Pq k┴ Collins effect = fragmentation of polarized quark depends onPq· (pqx k┴) pq q P k┴ Sivers effect = number of partons in polarized proton depends onP· (p x k┴) p Pq q Boer-Mulders effect = polarization of partons in unpolarized proton depends onPq· (p x k┴) k┴ p PΛ Λ Polarizing fragmentation function = polarization of final hadron (Λ) depends onPΛ· (pqx k┴) k┴ pq Pq· (pqx k┴), P · (p x k┴)~ Collins, Sivers angles

  4. SIDIS kinematics according toTrento conventions (2004)

  5. Unpolarized SIDIS (LO) M. Arneodo et al (EMC): Z. Phys. C 34 (1987) 277

  6. Cahn: the observed azimuthal dependence is related to the intrinsic k┴of quarks (at least for small PTvalues) assuming collinear fragmentation,φ= Φh These modulations of the cross section with azimuthal angle are denoted as “Cahn effect”.

  7. The situation is more complicated as the produced hadron has also intrinsic transverse momentum with respect to the fragmenting parton. neglecting terms

  8. assuming: one finds with clear dependence on (assumed to be constant) Find best values by fitting data onΦhandPTdependences

  9. EMC data,µp and µd, E between 100 and 280 GeV. Dashed line = exact kinematics, red solid line= only terms up toO(k┴/Q)

  10. The closed area shows effects of varying by 20% Data fromE665, ELab= 490 GeV. σ is integrated fromPTcut to PTmax.At low PTcut the non perturbative k┴ contributions dominate. At large PTcut NLO pQCD contributions take over

  11. EMC data

  12. EMC data Fitting the unpolarized data leads to the best values

  13. Polarized SIDIS and Sivers asymmetry possibility of SSA Sivers effect: can be isolated by proper weighting

  14. hydrogen target Ee = 27.57 GeV

  15. PDF: MRST LO 2001 FF: Kretzer our best fits + predictions for PT dependence ------ = exact kinematics = only terms upto O(k┴/Q) closed area corresponds to one-sigma deviation at 90% CL

  16. comparisons of our previous fits (+ predictions) with new data

  17. COMPASS data for charged hadron production Al parameters fixed from HERMES data

  18. HERMES data on In this case both Sivers and Collins effect can contribute; results show a clear need for Collins or H-T contributions

  19. Our predictions for K production at HERMES FF: Kretzer

  20. Conclusions A complete QCD description of the proton structure and hard processes requires the explicit inclusion of transverse motion, which is essential for spin effects Attempted consistent phenomenological approach in SIDIS and in hadro-production Many progresses and many (more) open problems: x, z and Q2 dependence of <k┴2> and <p┴2> QCD evolution of spin-k┴ dependent distribution and fragmentation functions More and more precise experimental data ………………………..

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