The Effect of Errors of Fragmentation Functions on the Analysis of Parton Helicity Distribution

1. The Effect of Errors of Fragmentation Functions on the Analysis of Parton Helicity Distribution - 縦偏極パートン分布関数解析に対する、破砕関数の影響 - Tokyo Tech Y. Imazu, Y. Miyachi, T.-A. Shibata Mar. 25, 2007 Contents 1. Motivation 2. FF and pPDF Analyses 3. Effects of the error of FFs on pPDF analysis 4. Summary

2. 1. Motivation

3. SIDIS Asymmetry The error of FFs could affect the determination of ⊿q. How large is the effect? Polarized Inclusive DIS : Polarized Semi-Inclusive DIS : Fragmentation functions (FFs) are important elements in SIDIS asymmetry. Universality Fragmentation Functions (FFs) : ← determined by pQCD analysis of hadron productions in e+ e－collision “ Kretzer ” : Phys. Rev., D62, (2000) 054001 “ KKP ” : Nucl. Phys., B582, (2000) 514, I estimated the errors of FFs based on Ktetzer parameterization

4. 2. pPDF and FF Analyses Analysis including SIDIS data from SMC and HERMES - Brute force method for the convolution integrals in x and z. - Analysis with inclusive data converged and are consistent with other pPDF QCD analysis - LO analysis ( reported in Spring 2006 ) - NLO analysis was carried out. Error estimation of FF - Statistical error estimation for Kretzer-FF ( reported in Autumn 2006)

5. Experiment Theory : Error from fit (⊿χ2＝１) 0.01 0.1 1 NLO Semi-inclusive DIS

6. Parton Helicity Distributions Results of NLO ⊿q analysis with SIDIS data with central values of my FFs ⊿u = 0.85±0.05 ⊿d = -0.41±0.13 ⊿sea = -0.07±0.04 ⊿g = 0.04±0.33 With the assumption of SU(3) symmetric sea, motivated by D. de Florian et al. (DNS05): Phys. Rev. D71, (2005) 094018 to obtain well-defined error bands; well converged covariant matrix

7. SLAC-TPC SLAC-SLD Experiment Theory SLAC-SLD_c SLAC-SLD_b 0.1 1 NLO Hadron Production in e+ e- collision EX. h = Z Z

8. Fragmentation Functions EX. Results of the analysis of NLO pion FF with Kretzer parameterization up → π + gluon → π +

9. 3. Effects of the errors of FFs on pPDF analysis

10. : Error from pPDF fit ・Comparison of σA_FF with experimental errors (bar) and pPDF induced errors (band) ( AExp – AThe ) / σA_FF @ NLO (σA_FF : From Pion FF )

11. ・The effect of FF on @ NLO pPDF: Fixed K+ π+ π+ K+

12. 4. Summary ・Semi-Inclusive DIS, which needs information on FF, is an important process to obtain information on flavor decomposition. ・pPDF and FF analyses are in progress in pQCD numerical calc. framework. SIDIS Analysis at NLO Statistical error on Kretzer-type FF ・The effect of the error of FF on pPDF analysis was studied in several ways, based on my current results of pPDF and FF analyses. ・The effect tuned out to be small. Future Subjects: ・Rather strong dependence on the choice of FF models D. de Florian et al. (DNS05): Phys. Rev. D71, (2005) 094018 Investigation of new models of FF and its validity

14. 278.0 ・ Current chi-squared values of pPDF fit

15. 3. Effects of the errors of FFs on pPDF analysis ・Estimation of σA_FF: A1h error from FFs pPDF: Fixed h = π+ proton target σA_FF=Few % @ LO Almost the same effect even @ NLO