1. 1 Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian Correlations between SIDIS azimuthal asymmetries in target and current fragmentation regions Polarized SIDIS Introduction: CFR TFR, STMD fracture functions M.Anselmino, V.Barone and AK, arXiv:1102.4214; PLB 699 (2011) 108 DSIDIS: TFR+CFR AK, DIS2011; arXiv:1107.2292 M.Anselmino, V.Barone and AK, articles in preparation Aram Kotzinian Uni&INFN, Torino & YerPhI, Armenia

2. 2 Introduction DIS: only lepton used as a probe No access to quark k T and transverse polarization at LO SIDIS: lepton and produced hadron used as a probe We need excellent understanding of hadronization and factorization Exploited in CFR: x F > 0 For better understanding one have to exploit also TFR: x F < 0 New nonperturbative objects – Spin and Transverse Momentum Dependent Fracture Functions Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

3. 3 STMD DFs Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

4. 4 SIDIS: CFR Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

5. 5 LO cross section in SIDIS CFR Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian 8 terms out of 18 Structure Functions, 6 azimuthal modulations

6. 6 SIDIS: TFR Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian M.Anselmino, V.Barone and A.K., arXiv:1102.4214; PL B699 (2011) 108 Probabilistic interpretation at LO

7. 7 Quark correlator Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian At LO 16 STMD fracture functions

8. 8 Decomposition of quark correlator Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

9. 9 STMD Fracture Functions for spinless hadron production Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

10. 10 Sum Rules Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian Nonzero fracture functions u,l,t. Useful for modeling.

11. 11 LO cross-section in TFR Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian At LO only 4 terms out of 18 Structure Functions, 2 azimuthal modulations No access to quark transverse polarization

12. 12 Quark spin in hard l-q scattering Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian sTsT CFR TFR

13. 13 DSIDIS: TFR & CFR Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

14. 14 Integrated over one hadron transverse momentum cross-sections Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian M.Anselmino, V.Barone and AK, article next week to ArXive Only 8 k T -dependent “capless” fracture functions. Same prefactors as in TMDs P T -integrated fracture functions

15. 15 DSIDIS cross section integrated over P T2 Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

16. 16 DSIDIS cross section integrated over P T1 Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian Compared with one hadron production in TFR, presence of known integrated fragmentation functions D 1 (z) allows quark flavor separation of “tilded” fracture functions As in SIDIS in TFR only k T -integrated fracture functions contribute

17. 17 Unintegrated DSIDIS cross-section Transversity 2011, Lošinj, August 30, 2011Aram Kotzinian

18. 18 Examples Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian AK @ DIS2011; arXiv:1107.2292

19. 19 A LU asymmetry Transversity 2011, Lošinj, August 30, 2011Aram Kotzinian

20. 20 Hints from LEPTO: h-q azimuthal correlation, a 1 (ζ) Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

21. 21 h-q azimuthal correlation, a 2 (ζ) Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

22. 22 h 1 -h 2 azimuthal correlation, a 1 (ζ) Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

23. 23 A LU Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

24. 24 CONCLUSIONS New members appeared in the polarized TMDs family -- 16 LO STMD fracture functions For SIDIS in the TFR, only 4 k T -integrated fracture functions of unpolarized and longitudinally polarized quarks are probed. SSA contains only a Sivers-type modulation sin(φ h -φ S ) but no Collins-type sin(φ h +φ S ) or sin(3φ h -φ S ). The eventual observation of Collins-type asymmetry will indicate that LO factorized approach fails and long range correlations between the struck quark polarization and P T of produced in TFR hadron might be important. DSIDIS cross section at LO contains 2 azimuthal independent and 20 azimuthally modulated terms. Integrated over one hadron transverse momentum DSIDIS cross-section expressions are rather simple. The measurements of these cross-sections allow to access transverse quark polarization and perform flavor separation. The ideal place to test the fracture functions factorization and measure these new nonperturbative objects are JLab12 and EIC facilities with full coverage of phase space. The role of STMF FracFuns in pp → μ + μ - + h +X, pp → h +X. Factorization? Transversity 2011, Lošinj, August 30, 2011 Aram Kotzinian

25. 25 σ UL DIS2011, JLab, April 14, 2011Aram Kotzinian

26. 26 σ UT DIS2011, JLab, April 14, 2011Aram Kotzinian

27. 27 σ LU, σ LL, σ LT DIS2011, JLab, April 14, 2011Aram Kotzinian

28. 28 Convolutions & tensorial decomposition DIS2011, JLab, April 14, 2011 Aram Kotzinian

29. 29 Structure functions DIS2011, JLab, April 14, 2011 Aram Kotzinian