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Global QCD Analysis of Polarized SIDIS Data and Fragmentation Functions

This study presents a global QCD analysis focusing on polarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) data and the evaluation of fragmentation functions (FFs). We determine the FFs using perturbative QCD analysis from e+e- collisions and assess the impact of FF errors on the determination of quark distributions. The results, consistent with prior works, highlight the importance of accurately determined FFs in SIDIS asymmetry calculations. We explore how FFs affect the calculation of the A1h asymmetry and discuss ongoing developments in analyzing NLO results.

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Global QCD Analysis of Polarized SIDIS Data and Fragmentation Functions

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  1. Global QCD Analysis of Polarized SIDIS Data and Fragmentation Functions • Evaluation of Fragmentation Functions • in the Framework of Global QCD Analysis - Tokyo Tech Y. Imazu, T.-A. Shibata,Y. Miyachi Oct. 3rd, 2006 Contents 1. Motivation 2. pQCD Analysis of Fragment Functions (FFs) 3. Results 4. Effects of FFs on A1h Calculation 5. Summary

  2. SIDIS Asymmetry Fragmentation Functions (FFs) : ← determined by pQCD analysis of hadron productions in e+ e－collision “ KKP ” : Nucl. Phys., B582, (2000) 514, “ Kretzer ” : Phys. Rev., D62, (2000) 054001 However, the errors of FFs have not been evaluated. The error of FFs could affect the determination of ⊿q. How large is the effect? 1. Motivation Polarized Inclusive DIS : Polarized Semi-Inclusive DIS : We are working on global QCD analysis of ⊿q including SIDIS asymmetry data. Fragmentation functions (FFs) are important elements in SIDIS asymmetry. 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 Q2 evolution of FF is analogous to DGLAP equation. Parameterization of FFs at Initial Scale : Charge Symmetry 11 free parameters for π, K each

  4. s Experimental data used in our fit (the same as Kretzer analysis) GeV SLAC-PEP-TPC ( 0.1 < z < 0.8 ) 11 0 0 29.0 SLAC-SLC-SLD ( 0.05 < z < 0.8 ) 27 16 16 91.2 70 in total GeV SLAC-PEP-TPC ( 0.1 < z < 0.8 ) 10 0 0 29.0 SLAC-SLC-SLD ( 0.05 < z < 0.8 ) 25 14 14 91.2 63 in total

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

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

  7. FF results : parameters and plots LO NLO ※ ※ ※ ※ ※ ※ ※ ※ χ2/d.o.f. 1.82 χ2/d.o.f. 1.62 ※： the same as above ※ ※: the above +1 g → π+ u → π+

  8. FF results : parameters and plots LO NLO ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ ※ χ2/d.o.f. 1.06 0.98 χ2/d.o.f. ※： the same as above ※ ※: the above +1 ※ ※ ※: the above +2 u → K+ DgK+ cannot be determined

  9. Calculation of A1h of SIDIS using these FFs

  10. 4. Effects of FFs on A1h Calculation Lagrange Multiplier Method : Ex. used in ⊿q analysis by D. de Florian et al.: Phys. Rev. D71, (2005) 094018 χ2( 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, χ2 and X obtain new values with a new a 3. Iterate the processes of 1 and 2, and obtain χ2 curve of a quantity X . 4. Plot χ2 as the function of X .

  11. The effect on A1h (LO) calculation proton target h = π+

  12. 4. Summary ・Fragmentation functions (FFs) are important elements in pQCD analysis of SIDIS. However, the errors of FFs had not been estimated. ・ By performing pQCD (LO, NLO) fit to e+ e- experimental data, we obtained the FFs. They are consistent with those of Kretzer. ・ DgK+ cannot be determined both in LO and NLO ・ We estimated the error bands of the FFs. ・ the error in Dgπ+ is larger than Duπ+ Outlook: fit to all the available data ・ The effect of FFs on SIDIS A1h calculation (LO) was studied with Lagrange Multiplier Method. The effect is less than 1% in case of . Outlook: NLO results are coming soon.

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

  14. ・ The effect of FFs to SIDIS A1h 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 ). 4. Summary ・Fragmentation functions (FFs) are needed for pQCD calculation of SIDIS process. However, the errors of FFs had not been estimated. ・ 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. ・ 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. ・Outlook ; NLO results is coming shortly!

  15. Scale effect comparison of Kaon and Pion KAON PION

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