Spin effects in MC generators

1. Spin effects in MC generators • The spin and azimuthal asymmetries in the current and target fragmentation regions • The flavor separation of the quark helicity distributions • Conclusions Aram Kotzinian JINR, Dubna and Torino University & INFN On leave in absence from YerPhI, Armenia Dubna, SPIN-05 AramKotzinian

2. 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

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

4. 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

5. SIDIS Event Generators and LUND String Fragmentation π+ q ρ0 π- Soft Strong Interaction h Rank from diquark Rank from quark K+ Λ qq Parton DF, hard X-section & Hadronizationare factorized Target remnant quark Implemented in PHYTIA and LEPTO + JETSET (hadronization) AramKotzinian

6. Quark transverse momentum in MC generators - 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

7. 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: A.K. hep-ph/0504081 Generate the final quark azimuth according to above distributions AramKotzinian

8. Results: Cahn Imbalance of measured in TFR and CFR: neutrals? AramKotzinian

9. 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

10. Results: Sivers JLab 12 GeV AramKotzinian

11. Purity method for flavor separation h q q N Purities are calculated using LEPTO AramKotzinian

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

13. Target type dependence of “FFs” in LEPTO Example of target remnant type: removed valence u-quark: There is dependence of “FFs” on the target type at 10% level AramKotzinian

14. 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

15. Asymmetry The standard expression for SIDIS asymmetry is obtained when and Spin dependence of hadronization: A.K. (hep-ph/0410093, EPJ C, 2005) For validity of purity method most important is the second relation AramKotzinian

16. Toy model using PEPSI MC Model A: default PEPSI Model B: neglect contribution of events to asymmetries with hadrons origin pointing to diquark (A.K. PLB 552, 2003) AramKotzinian

17. Beam Energy Dependence • Situation is different • for higher energies: • dependencies of “FFs” • extracted from MC • on x, target type • and target remnant • quantum numbers • are weaker AramKotzinian

18. Remarks on TMD hadronization Unpolarized lepton, long. polarized target Unpolarized target, long. polarized lepton Unpolarized lepton, trans. polarized target For TMD dependent HFs the new spin-azimuth correlations depending on both transverse momentum of quark in nucleon and final hadron are possible: AramKotzinian

19. Conclusions (flavor separation) • The new concept of (polarized) hadronization is introduced and studied using LEPTO event generator • The hadronization in LEPTO is more general than simple LO x-z factorized picture with independent fragmentation, for example, it describes well TFR. • One can try to modify PEPSI MC event generator by including polarization in hadronization. • The purity method have to be modified to take into account the polarized HFs. • Within this new approach one can include all hadrons (CFR+TFR) for flavor separation analysis. • More studies on the accuracy of different methods of the polarized parton DF extraction using SIDIS asymmetries are needed. • Alternative measurements are highly desirable • SIDIS at different beam energies: COMPASS, JLab, EIC • W production in polarized p+p collisions • (Anti)neutrino DIS on polarized targets (Neutrino Factory) AramKotzinian

20. Conclusions (azimuthal asymmetries) • Both Cahn and Sivers effects are implemented in LEPTO. Possible effects of polarized hadronization were neglected. • Existing data in 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 both Cahn and Sivers effects in the TFR (JLab, HERMES, Electron Ion Colliders) • This will help better understand hadronization mechanism • Do the neutral hadrons compensate Cahn effect in CFR? • Is there Sivers effect in TFR compensating asymmetry in CFR? • Access to TFR opens a new field both for theoretical and experimental investigations AramKotzinian

21. additional slides AramKotzinian

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

23. Hadronization Functions (HF) Even for meson production in the CFR the hadronization in LEPTO is more complicated than SIDIS description with independent FFs We are dealing with LUND Hadronization Functions: More general framework -- Fracture Functions (Teryaev, T-odd, SSA…) LEPTO provides a model for Fracture Functions: Violation of naïve x-z factorization and isotopic invariance of FF The dependence on target flavor is due to dependence on target remnant flavor quantum numbers.What about spin quantum numbers? AramKotzinian

24. 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

25. 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

26. Polarized SIDIS & HF and -- spin dependentcross section and HFs These Eqs. coincide with those proposed by Gluk&Reya (polarized FFs). In contrast with FFs, HFs in addition to zdepend on x and target type double spin effect, as in DFs. AramKotzinian

27. AramKotzinian

28. HERMES check xF ? xF > 0.1 AramKotzinian

29. LO x-z factorization AramKotzinian