1. HERMES による パートン helicity 分布関数の QCD 解析 Tokyo Inst. of Tech. 1. Quantum Chromo-Dynamics (QCD) 2. Parton Helicity Distribution and Nucleon Spin Problem 3. Polarized Semi-Inclusive Deep Inelastic Scattering 4. QCD Analysis and Results 5. Summary Contents Mar. 28th, 2006 Y. Imazu, T. Kobayashi, T. Hasegawa, Y. Miyachi, T.-A. Shibata, and HERMES Collaboration

2. High Energy : Low Energy : Asymptotic Freedom Color Confinement 1. Quantum Chromo-Dynamics (QCD) QCD : Dynamics of quark-gluon (partons) system High Energy Interaction associated with Hadron e.g. Deep Inelastic Scattering (DIS) Perturbative QCD (pQCD) Parton Distribution Function (PDF) (non-perturbative) Structure Function : Factorization We don’t know exactly how hadron is composed of partons. Running Coupling : Energy of a System : → 0 As → infinite,

3. Prediction from pQCD framework Convolution Integral : DGLAP Equation Structure Function We can extract the initial distributions so that they reproduce well the experimental results over many energy scales. x Evolution

4. Unpolarized PDF 2. Parton Helicity Distribution and Nucleon Spin Problem : the probability density giving the spin polarization of a parton “p” to the direction of the nucleon spin : extracted through (longitudinally) polarized DIS (Longitudinally) Polarized PDF = Parton Helicity Distribution :

5. Nucleon Spin Problem Angular Momentum (Spin) Sum Rule : I extracted polarized PDF with polarized SIDIS data and investigated the value in the framework of pQCD. 0.12 (12%) EMC result (1989) at = 10.7 GeV 2 Nucleon Spin Problem pQCD Analysis ABFR (1998), LSS (1998), AAC (2000) dFS (2000), GRSV (2001), BB (2002) Including polarized SIDIS dFNS (2005) polarized DIS

6. 3. Longitudinally Polarized Semi-Inclusive Deep Inelastic Scattering (Polarized SIDIS) ・・・ Polarized SIDIS Ambiguity for the Determination : Polarized DIS ・・・ Elimination of the ambiguity is achieved without the assumptions → Assumptions

7. Polarized SIDIS at HERMES HERMES experiment : 27.5 GeV polarized electron/positron beam at DESY-HERA ring Target : H, D Pion, Kaon, Proton For ( 2 < p < 15 ) GeV/c Hadron Identification Ring Imaging Cherenkov Counter (RICH) RICH Electron HERMES

8. Fragmentation Function : “ ” : Phys. Rev., D62:054001 Unpolarized PDF : “ ” 4. pQCD Analysis and Results ・ I analyzed polarized PDF to the LO. From -Decay From Hyperon Decay “ ” parameters and were fixed with GRSV01 results : Free Parameters : Phys. Rev., D63:094005 Parameterization of Polarized PDF at Experimental constraints to the first moments at Eliminated by including SIDIS data Assumption of GRSV01 Analysis : Eur. Phys. J., C5:461

9. Experimental data used in my fitting Polarized DIS Polarized SIDIS

10. 100 steps in 1000 steps inI took for numerical calculation fitting process with Parameters were determined by Numerical Calculation and minimization

11. Results N freedom = N data - N parameters = 1.31 N freedom Comparison of My Fit Result with g 1 p Data Fit Results

12. HERMES SIDIS Data with Fitted Curve at

13. = 0.20 (20%)

14. 5. Summary I made the numerical calculation program for polarized DIS and SIDIS based on pQCD framework. Fitting was performed to the LO with polarized DIS and SIDIS data. The reduced value was 1.3. With polarized SIDIS data, polarized PDFs were determined without additional assumptions. became 0.20. Future Subjects I will estimate the uncertainty in my analysis. I will improve the program for the NLO analysis.

15. Kinematical Coverage

16. Evolution of LO = 0.26 GeV 2

17. Evolution of NLO = 0.40 GeV 2

18. Computation Time for Mapping the Entire x, Q 2 space of PDFs x max 1 0 100 steps in 1000 steps inI took for numerical calculation fitting process with Parameters were determined by Numerical Calculation and minimization max = 200 GeV 2 = 0.26 GeV 2

19. Momentum Conservation Sum Rule The Way of Calculation of Deuteron g 1 2

20. Comparison the Polarized PDFs of Fitting Result with GRSV01 Result

21. Differential Cross Section in Single-Inclusive e + e － Annihilation Structure Function F 2 p in Unpolarized DIS

22. Comparison of Numerical Calculation Results with that of GRSV01 for g 1 p

23. A hit pattern on the PMT plane by a pion with 4.4 GeV/c Cherenkov angle θ n: refractive index βc : particle velocity Ring Imaging Cherenkov Counter θ Cherenkov light Particle Material Cherenkov angle

24. : Equation of motion in electromagnetic field Principle of the Measurement of Momentum,

25. PDF : including all the information on the structure of a hadron (nucleon) Knowing the Structure of a Nucleon as a Composition of Quarks and Gluons Extracting PDF from High Energy Interaction LONLO