Correlations between SIDIS azimuthal asymmetries in target and current fragmentation regions

1. Correlations between SIDIS azimuthal asymmetries in target and current fragmentation regions • Polarized SIDIS • Introduction: CFR • TFR, STMD fracture functions • M.Anselmino, V.Baroneand 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 Aram Kotzinian

2. Introduction • DIS: only lepton used as a probe • No access to quark kT 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: xF > 0 • For better understanding one have to exploit also TFR: xF < 0 • New nonperturbative objects – Spin and Transverse Momentum Dependent Fracture Functions Aram Kotzinian

3. STMD DFs Aram Kotzinian

4. SIDIS: CFR Aram Kotzinian

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

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

7. Quark correlator At LO 16 STMD fracture functions Aram Kotzinian

8. Decomposition of quark correlator Aram Kotzinian

9. STMD Fracture Functions for spinless hadron production Aram Kotzinian

10. Sum Rules Nonzero fracture functions u,l,t. Useful for modeling. Aram Kotzinian

11. LO cross-section in TFR At LO only 4 terms out of 18 Structure Functions, 2 azimuthal modulations No access toquark transverse polarization Aram Kotzinian

12. Quark spin in hard l-q scattering sT TFR CFR Aram Kotzinian

13. DSIDIS: TFR & CFR Aram Kotzinian

14. Integrated over one hadron transverse momentum cross-sections M.Anselmino, V.Barone and AK, article next week to ArXive Only 8 kT-dependent “capless” fracture functions. Same prefactors as in TMDs PT-integrated fracture functions Aram Kotzinian

15. DSIDIS cross section integrated over PT2 Aram Kotzinian

16. DSIDIS cross section integrated over PT1 As in SIDIS in TFR only kT-integrated fracture functions contribute Compared with one hadron production in TFR, presence of known integrated fragmentation functions D1(z) allows quark flavor separation of “tilded” fracture functions Aram Kotzinian

17. Unintegrated DSIDIS cross-section Aram Kotzinian

18. Examples AK @ DIS2011; arXiv:1107.2292 Aram Kotzinian

19. ALU asymmetry Aram Kotzinian

20. Hints from LEPTO: h-q azimuthal correlation, a1(ζ) Aram Kotzinian

21. h-q azimuthal correlation, a2(ζ) Aram Kotzinian

22. h1-h2azimuthal correlation, a1(ζ) Aram Kotzinian

23. ALU Aram Kotzinian

24. CONCLUSIONS • New members appeared in the polarized TMDs family -- 16 LOSTMDfracture functions • For SIDIS in the TFR, only 4 kT-integrated fracture functions of unpolarized and longitudinally polarized quarks are probed. • SSA contains only a Sivers-type modulation sin(φh-φS) but no Collins-type sin(φh+φS) or sin(3φh-φS). The eventual observation of Collins-type asymmetry will indicate that LO factorized approach fails and long range correlations between the struck quark polarization and PT 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? Aram Kotzinian

25. σUL AramKotzinian

26. σUT AramKotzinian

27. σLU, σLL,σLT AramKotzinian

28. Convolutions & tensorial decomposition AramKotzinian

29. Structure functions AramKotzinian