Error Estimation of Fragmentation Functions Based on Global QCD Analysis Tokyo Inst. of Tech. 1. Motivation 2. Analysis Method 3. Results 4. Summary Contents.

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Error Estimation of Fragmentation Functions Based on Global QCD Analysis Tokyo Inst. of Tech. 1. Motivation 2. Analysis Method 3. Results 4. Summary Contents 20th Sep., 2006 Y. Imazu, Y. Miyachi, T. Hasegawa, Xiaorui Lu, T.-A. Shibata - 摂動論的 QCD に基づいた破砕関数の誤差評価 -

1. Motivation Fragmentation Function : “ ” : Phys. Rev., D62: HERMES SIDIS Data with Fitted Curve at How much does the error of FFs have an effect to A 1 h ?? ← Determined by pQCD analysis with hadron productions in e + e － collision

2. Analysis Method Parameterization of FFs at Initial Scale Totally 11 parameters for π 、Ｋ each In the calculation of cross section

Experimental data used in my fitting 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 ) GeV GeV 91.2 PION KAON Totally 70 Totally 63 s

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

3. Results

PION FF results : parameters and plots LO NLO up → π +charm → π +gluon → π +

KAON FF results : parameters and plots LO NLO charm → K +up → K +

The effect of FF ambiguity to A1h (LO) h=kaon h=pion Lagrange Multiplier Method :

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

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

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. ・ The effect of FF ambiguity to SIDIS A 1 h calculation (LO) was evaluated with chi-square value of FF fit (Lagrange Multiplier Method) to e+ e- data. The effect turned out to be less than 1%. ・ Fragmentation functions (FFs) are needed for pQCD calculation of SIDIS process. However, the errors of FFs had not been estimated. ・ Outlook ; chi-square of SIDIS data

Comparison of FF parameters (pion)

Comparison of FF parameters (kaon)

(Renormalization and Factorization) pQCD framework pQCD range Analogies

Hadronic Part Diagrammatic Description of Factorization

Evolution of