Cahn and Sivers effects in the target fragmentation region of SIDIS

1. 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, Armeniaand JINR, Russia hep-ph/0504081 AramKotzinian

2. SIDIS in LO QCD: CFR h q q N p Well classifiedcorrelations in TMD distr. andfragm. functions Sivers distribution Mulders distribution Boer distribution Helicity distribution Collins effect in quark fragmentation AramKotzinian

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

4. Sivers Effect in CFR Azimuthal modulation of quark transverse momentum in a transversely polarized nucleon M.Anselmino, M.Boglione, U.D’Alesio, A.K., F.Murgia and A.Prokudin: PRD 71, 074006 (2005); hep-ph/0507181 Parameters were extracted from combined analysis of HERMESandCOMPASS data (details in the talk of A. Prokudin) AramKotzinian

5. Ed. Berger criterion (separation of CFR &TFR) The typical hadronic correlation length in rapidity is Illustrations from P. Mulders: AramKotzinian

6. SIDIS in LO QCD: TFR q N 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 AramKotzinian

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

8. Quark kT in MC generators PYTHIA and LEPTO - Generate virtual photon – quark scattering in collinear configuration: - Before - After hard scattering - Generate intrinsic transverse momentum of quark (Gaussian kT) - Rotate in l-l’ plane - Generate uniform azimuthal distribution of quark (flat by default) - Rotate around virtual photon AramKotzinian

9. Sivers effect in pp l+l- + X ST 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 AramKotzinian

10. Sivers effect in pp l+l- + X Similarvalues as inAnselmino et al: hep-ph/0507181 AramKotzinian

11. 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 AramKotzinian

12. Results: Cahn Charged hadrons azimuth EMC Collaboration (280GeV) Imbalance of measured in TFR and CFR: neutrals? AramKotzinian

13. Results: Sivers Predictions for xF-dependence at JLab 12 GeV Red triangles with error bars – projected statistical accuracy for 1000h data taking (H.Avagyan). z, xBj and PT dependences AramKotzinian

14. Results: Sivers JLab 12 GeV AramKotzinian

15. Bjorken variable dependence of “FFs” in LEPTO The dependence of “FFs” on x cannot be attributed to Q2 evolution AramKotzinian

16. 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 AramKotzinian

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

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

19. Asymmetries The standard LO expression for helicity asymmetry ofSIDIS 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 AramKotzinian

20. 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 AramKotzinian

21. additional slides AramKotzinian

22. Monte Carlo: Lepto in combination with JETSET; PDF: CTEQ-6L Fragmentation parameters tuned to HERMES multiplicities in the acceptance Data: Q2>1GeV2, W2>10GeV2, z>0.2, 2GeV <p< 15GeV (p, K, and P) Excellent Agreement even at the cross section level DATA/MC <10%! p+ p- K+ K- P- P+ MC tuning AramKotzinian

23. HERMES check xF ? xF > 0.1 AramKotzinian