1. THE DEEP INELASTIC SCATTERING ON THE POLARIZED NUCLEONS AT EIC E.S.Timoshin, S.I.Timoshin

2. We have two pictures about the nucleon spin: Jaffe-Manohar, 1990 It is simple parton picture for longitudinal polarization X.Ji, 1996 It is relate to the partons in transverse polarized nucleon Quark helicity Gluon helicity Orbital momentum of quarks and gluons Total angular momentum of quarks Total angular momentum of gluons

3. What do we know? We know fairly well the quark contribution ~ 30% However, the information on polarization of the flavor and sea are still sketchy. Contribution from small ? We know with large uncertains about the gluon contribution ~ 20% (with RHIC data) There not have direct information on the quark and gluon orbital angular momentum. Lattice QCD → and are large, but ~ 0

4. Major advance since 2007: We have new phenomenology to study nucleon structure: Generalized Parton Distributions (GPDs) (3D “imaging”) that provide access to orbital angular momentum in DVCS and Exclusive production. These studies will require high luminosity and polarized beams. Electron–Ion Collider (EIC) High luminosity Low regime High polarization 70% electron and nucleon beams Ion beams from deuteron to the heaviest nuclei Center mass energies 20-100 GeV (upgradable 150 GeV)

5. What can to explore at EIC: Sea/gluon (inclusive DIS, SIDIS at low ), flavor separation. GPD (DVCS, Exclusive meson production) => angular momentum The first constraint on quark orbital contribution to proton spin by combining the sea from EIC and valence from JLab 12 GPD

6. The inclusive DIS with charged current Here are 2 independent polarized structure functions (SF) flavor separation In contrast with SIDIS here not have the fragmentation functions that give essential uncertains.

7. The polarization asymmetries through SF are

8. Where

9. The polarized SF in leading order QCD (improved parton model) where and for lepton (antilepton).

10. The first moment polarized SF where is the quark (antiquark) contribution to the nucleon spin

11. The proton where We use also the measurable quantity – the axial charge that in parton model:

12. The quark contributions to the nucleon spin: The quark flavors

13. The valence quarks The sea quarks

14. We are obtained the quark contributions for the neutron and the deutron. The deutron where is the probability D-state in the wave function of the deuteron.

15. Fig. 1. The asymmetries and

16. Fig. 2. The asymmetries and

17. Fig. 3. The asymmetries and

18. Fig. 4. The asymmetries and

19. Fig.5. QED correction to asymmetry in leading log approximation (LLA) A. De Rujula et al. Nucl. Phys. 1979. V. B154 P.394. J. Blŭmlein. Prog. Part. Nucl. Phys. 2013. V.69. P.28.

20. Fig.6. QED correction to asymmetry in LLA NLO QCD correction to the asymmetries CC DIS are small and LO accuracy is very good approximation ( E.C.Aschenauer et al. Phys. Rev. D 88(2013) 114025).

21. CONCLUSION Data from CC DIS experiments provide complementary information on the spin structure nucleon as they probe combinations of quark flavours different from those accessible in purely electromagnetic DIS. CC DIS can only be studied in high-energy lepton-nucleon collisions (EIC). The quark contributions to the nucleon spin are obtained through the first moments of the polarized SF that can be to extract from the measurable asymmetries CC DIS.