1. December 17, 2004 JLab Hall A Upgrade 1 Semi-Inclusive DIS --opportunities at JLab upgrade Feng Yuan RBRC, Brookhaven National Laboratory

2. December 17, 2004 2JLab Hall A Upgrade Outline Introduction Introduction Low P ? SIDIS (TMD) Low P ? SIDIS (TMD) High P ? SIDIS (Quark-gluon correlations) High P ? SIDIS (Quark-gluon correlations) Integrated SIDIS (Flavor decomposition) Integrated SIDIS (Flavor decomposition) Summary Summary

3. December 17, 2004 3JLab Hall A Upgrade Inclusive and Semi-inclusive DIS Inclusive DIS: Partonic Distribution depending on the longitudinal momentum fraction Semi-inclusive DIS: Probe additional information including the transverse distribution

4. December 17, 2004 4JLab Hall A Upgrade Different P ? Region Integrate out P ? Integrate out P ? -- normal factorization, similar to inclusive DIS Large P ? ( À QCD ) Large P ? ( À QCD ) -- hard gluon radiation, can be calculated from perturbative QCD, factorization similar to inclusive DIS Low P ? ( » QCD ) Low P ? ( » QCD ) -- nonperturbative information: new factorization formula ? ! 12GeV 12GeV

5. December 17, 2004 5JLab Hall A Upgrade Semi-Inclusive DIS at Low P ? Transverse Momentum Dependent (TMD) Parton Distributions Transverse Momentum Dependent (TMD) Parton Distributions Novel Single Spin Asymmetries Novel Single Spin Asymmetries

6. December 17, 2004 6JLab Hall A Upgrade TMD Parton Distributions The gauge invariant definition The gauge invariant definition Belitsky, Ji, Yuan (03)

7. December 17, 2004 7JLab Hall A Upgrade Polarized TMD Quark Distributions Quark Nucleon Unpol. Long. Trans. Unpol.Long.Trans. q(x, k ) q T (x, k ) Δq L (x, k ) Δq T (x, k ) δq(x, k ) δq L (x, k ) δq L (x, k ) δq T (x, k ) δq T (x, k ) δq T '(x, k ) Boer, Mulders, Tangerman (96&98)

8. December 17, 2004 8JLab Hall A Upgrade The Physics We can learn from TMD Internal structure, transverse momentum dis. Internal structure, transverse momentum dis. Quark Orbital Angular Momentum Quark Orbital Angular Momentum e.g, Sivers function ~ the wave function amplitude with orbital angular momentum! Vanishes if quarks only in s-state! e.g, Sivers function ~ the wave function amplitude with orbital angular momentum! Vanishes if quarks only in s-state! Friends: Friends: Pauli Form Factor F 2 (t) Pauli Form Factor F 2 (t) Spin-dependent structure function g 2 (x) Spin-dependent structure function g 2 (x) Generalized Parton Distribution E(x, ξ, t) Generalized Parton Distribution E(x, ξ, t)

9. December 17, 2004 9JLab Hall A Upgrade Connection between TMD and GPD Wigner distributions Wigner distributions After integrating over r, one gets TMD After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs After integrating over k, one gets Fourier transform of GPDs Ji: PRL91,062001(2003)

10. December 17, 2004 10JLab Hall A Upgrade SIDIS Cross Section At leading power of 1/Q The structure functions depend on Q 2, x B, z, P h?

11. December 17, 2004 11JLab Hall A Upgrade Low P ? SIDIS Factorization Ji, Ma, Yuan, hep-ph/0404183,hep-ph/0405085

12. December 17, 2004 12JLab Hall A Upgrade SIDIS: at Large P ? Large P ? SIDIS can be calculated from perturbative QCD Large P ? SIDIS can be calculated from perturbative QCD Polarized scattering will provide information on the quark-gluon correlations in the nucleon Polarized scattering will provide information on the quark-gluon correlations in the nucleon Single Spin Asymmetry at large P ? is not suppressed by 1/Q, but by 1/P ? Single Spin Asymmetry at large P ? is not suppressed by 1/Q, but by 1/P ? With enough luminosities, we could measure these asymmetries at large P ? at JLab 12GeV? With enough luminosities, we could measure these asymmetries at large P ? at JLab 12GeV?

13. December 17, 2004 13JLab Hall A Upgrade SSA at Large P ? Qiu-Sterman mechanism Qiu-Sterman mechanism It is suppressed by 1/P ? It is suppressed by 1/P ? Efremov & Teryaev: 1982 & 1984 Qiu & Sterman: 1991 & 1999 Quark-gluon correlations

14. December 17, 2004 14JLab Hall A Upgrade Transition from Perturbative region to Nonperturbative region? Compare different region of P ? Compare different region of P ? Nonperturbative TMDPerturbative region

15. December 17, 2004 15JLab Hall A Upgrade SIDIS: Integrated over P ? The factorization formulas are much simpler The factorization formulas are much simpler Flavor decomposition for (polarized) PDF Flavor decomposition for (polarized) PDF Frankfurt et al 89; Melnitchouk et al 98, HERMES, EMC… NLO: de Florian et al 96-98; Leader et al 01; Kretzer 04 Altarelli et al 79 (NLO)

16. December 17, 2004 16JLab Hall A Upgrade Flavor Decomposition for PDF (Leading Order) In the valence region (large x), In the valence region (large x), Isospin relation, Isospin relation, D u + =D d -, favored; D u - =D d +, unfavored; D u - << D u +

17. December 17, 2004 17JLab Hall A Upgrade favored unfavored Well described by leading particle ansatz Stefan Kretzer

18. December 17, 2004 18JLab Hall A Upgrade Continue, Similarly, from the polarized scattering, Similarly, from the polarized scattering, d/u at large x!!

19. December 17, 2004 19JLab Hall A Upgrade Summary Semi-inclusive DIS at JLab upgrade provides various opportunities to study nucleon structure Semi-inclusive DIS at JLab upgrade provides various opportunities to study nucleon structure Low P ? probes TMD parton distributions Low P ? probes TMD parton distributions High P ? probes quark-gluon correlations ? High P ? probes quark-gluon correlations ? Integrated P ? probes flavor decomposition of PDFs, especially for large x quark and helicity distributions. Integrated P ? probes flavor decomposition of PDFs, especially for large x quark and helicity distributions.