Error Estimation of Fragmentation Functions Based on Global QCD Analysis

Tokyo Inst. of Tech.

1. Motivation2. Analysis Method3. Results4. 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., D62:054001

HERMES SIDIS Data with Fitted Curve at

How much does the error of FFs have an effect to A 1h ??

← 　 Determined by pQCD analysis with hadron productions in e+ e － collision

2. Analysis MethodParameterization of FFs at Initial Scale

Totally 11 parameters for π 、Ｋ eachIn 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 )

10

25 14 14

11

27 16 16

0 0

0 029.0

s GeV

91.2

29.0

s GeV

91.2

PION

KAONTotally 70

Totally 63

s

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)

)()(),( 12 hhhh DADD

)(2 KD

)(1 KKd DA

h=kaon

12

0002.00528.0)5.2,9.0( 221 GeVQxA Kd

h=pion

12

)(2 D

)(1 DA p

001.0187.0)5.2,9.0( 221 GeVQxA p

Lagrange Multiplier Method :

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 A1h 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