1. 1 Como, September 7, 2005 Aram Kotzinian Cahn and Sivers effects in the target fragmentation region of SIDIS Introduction Hadronization in SIDIS Cahn and Sivers asymmetries in the current fragmentation regions Cahn and Sivers asymmetries in LEPTO Discussion & Conclusions Aram Kotzinian Torino University & INFN On leave in absence from YerPhI, Armenia and JINR, Russia hep-ph/0504081

2. 2 Como, September 7, 2005 Aram Kotzinian SIDIS in LO QCD: CFR Well classified correlations in TMD distr. and fragm. functions Sivers distribution Boer distribution Helicity distribution Collins effect in quark fragmentation N q q h p Mulders distribution

3. 3 Como, September 7, 2005 Aram Kotzinian Cahn effect in CFR Quadratic in M.Anselmino, M.Boglione, U.DAlesio, A.K., F.Murgia and A.Prokudin: PRD 71, 074006 (2005); Linear in and proportional to Azimuthal modulation of lepton-quark hard scattering cross section in unpolarized SIDIS

4. 4 Como, September 7, 2005 Aram Kotzinian Sivers Effect in CFR Azimuthal modulation of quark transverse momentum in a transversely polarized nucleon M.Anselmino, M.Boglione, U.DAlesio, A.K., F.Murgia and A.Prokudin: PRD 71, 074006 (2005); hep-ph/0507181 Parameters were extracted from combined analysis of HERMES and COMPASS data (details in the talk of A. Prokudin)

5. 5 Como, September 7, 2005 Aram Kotzinian Ed. Berger criterion (separation of CFR &TFR) The typical hadronic correlation length in rapidity is Illustrations from P. Mulders:

6. 6 Como, September 7, 2005 Aram Kotzinian SIDIS in LO QCD: TFR N q h 1994: Trentadue & Veneziano; Graudenz; … Fracture functions: conditional probability of finding a parton q with momentum fraction x and a hadron h with the CMS energy fraction z More correlations for TMD dependent FracFuncs

7. 7 Como, September 7, 2005 Aram Kotzinian SIDIS Event Generators and LUND String Fragmentation Soft Strong Interaction qq q Rank from diquark Rank from quark h Parton DF, hard X-section & Hadronization are factorized Implemented in PHYTIA and LEPTO + JETSET (hadronization)

8. 8 Como, September 7, 2005 Aram Kotzinian Quark k T in MC generators PYTHIA and LEPTO - Generate virtual photon – quark scattering in collinear configuration: - Before - After hard scattering - Rotate in l-l plane - Generate intrinsic transverse momentum of quark (Gaussian k T ) - Generate uniform azimuthal distribution of quark (flat by default) - Rotate around virtual photon

9. 9 Como, September 7, 2005 Aram Kotzinian Sivers effect in pp l + l - + X One class of nonperturbative input: only distribution functions, no hadronization effects are present Modify PYTHIA to include Sivers effect: azimuthal correlations of the parton transverse momentum and transverse spin on nucleon in distribution functions STST

10. 10 Como, September 7, 2005 Aram Kotzinian Sivers effect in pp l + l - + X Similar values as in Anselmino et al: hep-ph/0507181

11. 11 Como, September 7, 2005 Aram Kotzinian Implementing Cahn and Sivers effects in LEPTO The common feature of Cahn and Sivers effects Unpolarized initial and final quarks Fragmenting quark-target remnant system is similar to that in default LEPTO but the direction of is now modulated Cahn: Sivers: Generate the final quark azimuth according to above distributions

12. 12 Como, September 7, 2005 Aram Kotzinian Results: Cahn Imbalance of measured in TFR and CFR: neutrals? Charged hadrons azimuth EMC Collaboration (280GeV)

13. 13 Como, September 7, 2005 Aram Kotzinian Results: Sivers Predictions for x F -dependence at JLab 12 GeV Red triangles with error bars – projected statistical accuracy for 1000h data taking (H.Avagyan). z, x Bj and P T dependences

14. 14 Como, September 7, 2005 Aram Kotzinian Results: Sivers JLab 12 GeV

15. 15 Como, September 7, 2005 Aram Kotzinian Bjorken variable dependence of FFs in LEPTO The dependence of FFs on x cannot be attributed to Q 2 evolution

16. 16 Como, September 7, 2005 Aram Kotzinian Dependence on target remnant spin state (unpolarized LEPTO) Example: valence u-quark is removed from proton. Default LEPTO: the remnant (ud) diquark is in 75% (25%) of cases scalar (vector) Even in unpolarized LEPTO there is a dependence on target remnant spin state (ud) 0 : first rank Λ is possible (ud) 1 : first rank Λ is impossible

17. 17 Como, September 7, 2005 Aram Kotzinian Target remnant in Polarized SIDIS JETSET is based on SU(6) quark-diquark model Probabilities of different string spin configurations depend on quark and target polarizations, target type and process type 90% scalar 100% vector

18. 18 Como, September 7, 2005 Aram Kotzinian Polarized SIDIS & HF In contrast with FFs, HFs in addition to z depend on x and target type and on struck quark and target polarization: are the spin dependent cross section and HFs and double spin effect (struck quark & target), as in DFs. Spin dependence of hadronization: A.K. (hep-ph/0410093, EPJ C, 2005)

19. 19 Como, September 7, 2005 Aram Kotzinian Asymmetries The standard LO expression for helicity asymmetry of SIDIS is obtained when and For TMD dependent HFs the new spin-azimuth correlations depending on both transverse momentum of quark in nucleon and final hadron are possible: Unpolarized lepton, long. polarized target Unpolarized target, long. polarized lepton Unpolarized lepton, trans. polarized target

20. 20 Como, September 7, 2005 Aram Kotzinian Conclusions Hadronization functions provide a general description of SIDIS in the whole kinematics of hadrons Both Cahn and Sivers effects are implemented in LEPTO. Possible polarization effects in hadronization were neglected. Existing data in the CFR are well described by modified LEPTO The measured Cahn effect in the TFR is not well described It is important to perform new measurements of Cahn, Sivers and other azimuthal asymmetries in the TFR (JLab, HERMES, Electron Ion Colliders) This will help better understand spin dynamics in hadronization: Do neutral hadrons compensate the Cahn effect in CFR? Are there asymmetries present in TFR that compensate the Sivers effect in CFR? Do there exist any other spin-dependent azimuthal asymmetries in TFR? The access to TFR opens a new field both for theoretical and experimental investigations

21. 21 Como, September 7, 2005 Aram Kotzinian additional slides

22. 22 Como, September 7, 2005 Aram Kotzinian MC tuning Monte Carlo: Lepto in combination with JETSET; PDF: CTEQ-6L Fragmentation parameters tuned to HERMES multiplicities in the acceptance Data: Q 2 >1GeV 2, W 2 >10GeV 2, z>0.2, 2GeV <p< 15GeV (, K, and P) Excellent Agreement even at the cross section level DATA/MC <10%! + - + - P+P+P+P+ P-P-P-P-

23. 23 Como, September 7, 2005 Aram Kotzinian HERMES check x F ? x F > 0.1