1. Global QCD Analysis of Polarized SIDIS Data and Fragmentation Functions Tokyo Tech 1. Motivation 2. pQCD Analysis of Fragment Functions (FFs) 3. Results 4. Effects of FFs on A 1 h Calculation 5. Summary Contents Oct. 3rd, 2006 Y. Imazu, T.-A. Shibata, Y. Miyachi - Evaluation of Fragmentation Functions in the Framework of Global QCD Analysis -

2. 1. Motivation Polarized Inclusive DIS : Polarized Semi-Inclusive DIS : SIDIS Asymmetry How large is the effect? The error of FFs could affect the determination of ⊿ q. We are working on global QCD analysis of ⊿ q including SIDIS asymmetry data. Fragmentation functions (FFs) are important elements in SIDIS asymmetry. “ Kretzer ” : Phys. Rev., D62, (2000) 054001 Fragmentation Functions (FFs) : ← determined by pQCD analysis of hadron productions in e + e － collision “ KKP ” : Nucl. Phys., B582, (2000) 514, However, the errors of FFs have not been evaluated. We adopt Kretzer parameterization as it is widely used in analysises of many experiments. the same date set as Kretzer’s

3. 2. Analysis of Fragmentation Functions Parameterization of FFs at Initial Scale 11 free parameters for π, K each Q 2 evolution of FF is analogous to DGLAP equation. : Charge Symmetry

4. Experimental data used in our fit (the same as Kretzer analysis) SLAC-PEP-TPC ( 0.1 < z < 0.8 ) SLAC-SLC-SLD ( 0.05 < z < 0.8 ) SLAC-PEP-TPC ( 0.1 < z < 0.8 ) SLAC-SLC-SLD ( 0.05 < z < 0.8 ) 10 2514 11 2716 00 00 29.0 GeV 91.2 29.0 GeV 91.2 70 in total 63 in total s

5. 3. Results SLAC-TPC SLAC-SLD SLAC-SLD_c SLAC-SLD_b NLOLO 0.1 1 Z Z Experiment Theory h =

6. Results TPC SLD SLD_c SLD_b NLOLO 0.1 1 Z Z Experiment Theory h = It was found that D g K± cannot be determined with the e + e - data. These parameters were fixed at certain values in the following K analysis.

7. FF results : parameters and plots LO NLO 1.82 1.62 ※ ※： the same as above ※ ※ : the above +1 ※ ※ ※※ ※ ※※ ※ ※※ ※ u → π + g → π + χ 2 /d.o.f.

8. FF results : parameters and plots LO NLO 1.060.98 ※※ ※ ※※ ※ ※※ ※ ※※ ※ ※： the same as above ※ ※ : the above +1 ※ ※ ※ : the above +2 ※※ ※ ※ ※※ ※ ※ ※※ ※ ※ ※※ ※ ※ u → K + χ 2 /d.o.f. D g K+ cannot be determined

9. Calculation of A 1 h of SIDIS using these FFs

10. 4. Effects of FFs on A 1 h Calculation Ex. used in ⊿ q analysis by D. de Florian et al.: Phys. Rev. D71, (2005) 094018 χ 2 ( a ) : a chi-square with the fit parameter a X ( a ) : a physical quantity which depends on a 1. Set a certain λ value, and minimize by varying a 2. As the result, χ 2 and X obtain new values with a new a 3. Iterate the processes of 1 and 2, and obtain χ 2 curve of a quantity X. Lagrange Multiplier Method : 4. Plot χ 2 as the function of X.

11. h = π + The effect on A 1 h (LO) calculation proton target

12. h = K + The effect of FF to A 1 h (LO) deuteron target

13. 4. Summary ・ By performing pQCD (LO, NLO) fit to e + e - experimental data, we obtained the FFs. They are consistent with those of Kretzer. ・ We estimated the error bands of the FFs. ・ Fragmentation functions (FFs) are important elements in pQCD analysis of SIDIS. However, the errors of FFs had not been estimated. Outlook: NLO results are coming soon. ・ The effect of FFs on SIDIS A 1 h calculation (LO) was studied with Lagrange Multiplier Method. The effect is less than 1% in case of. ・ the error in D g π+ is larger than D u π+ ・ D g K+ cannot be determined both in LO and NLO Outlook: fit to all the available data

14. The effect of FF to (LO) K+K+ π+π+ K+K+ π+π+

15. 4. Summary ・ By performing pQCD (LO, NLO) fit to e+ e- experimental results, we obtained the FF results, which are consistent with those of Kretzer. ・ We estimated the errors contained in the FFs. ・ Fragmentation functions (FFs) are needed for pQCD calculation of SIDIS process. However, the errors of FFs had not been estimated. ・ Outlook ; NLO results is coming shortly! ・ The effect of FFs to SIDIS chi-square value (LO) was investigated with chi-square value of FF fit to see the impact to pPDF determination. ・ The effect of FFs to SIDIS A 1 h calculation (LO) was evaluated with chi-square value of FF fit to e+ e- data. (Lagrange Multiplier Method) The effect turned out to be less than 1% ( in case of ).

16. Scale effect comparison of Kaon and Pion KAONPION

18. : : : : Fitting Process Evolution of partial differentiated distributions Error Calculation D D D D

19. Comparison of FF parameters (pion)

20. Comparison of FF parameters (kaon)

21. Chi-square curves of the first moments of FFs (LO) Pion FFs

22. Chi-square curves of the first moments of FFs (LO) kaon FFs

23. (Renormalization and Factorization) pQCD framework pQCD range Analogies

24. Hadronic Part Diagrammatic Description of Factorization

26. Evolution of