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) , hep-ph/
See also talk by E. Leader
Mauro Anselmino
Partonic structure of hadrons (Concepts and Phenomenology), Trento ECT*, May 9-14, 2005

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

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

4. SIDIS kinematics according to Trento conventions (2004)

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

6. assuming collinear fragmentation, φ = Φh
Cahn: the observed azimuthal dependence is related to the intrinsic k┴ of quarks (at least for small PT values)
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. Find best values by fitting data on Φh and PT dependences
assuming:
one finds
with
clear dependence on
(assumed to be constant)
Find best values by fitting data on Φh and PT dependences

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

10. The closed area shows effects of varying by 20%
Data from E665, ELab= 490 GeV. σ is integrated from PTcut to PTmax. At low PTcut the non perturbative k┴ contributions dominate. At large PTcut NLO pQCD contributions take over

11. EMC data

12. Fitting the unpolarized data leads to the best values
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

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

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

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

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

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

24. 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
………………………..