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

Tokyo Tech

1. Motivation2. FF and pPDF Analyses3. Effects of the error of FFs on pPDF analysis4. Summary

ContentsMar. 25, 2007

Y. Imazu, Y. Miyachi, T.-A. Shibata

- 縦偏極パートン分布関数解析に対する、破砕関数の影響 -

1. Motivation

XheNe

XeNe

Polarized Inclusive DIS :

Polarized Semi-Inclusive DIS :

SIDIS Asymmetry

How large is the effect?The error of FFs could affect the determination of q.⊿

Fragmentation functions (FFs) are important elements in SIDIS asymmetry.

Fragmentation Functions (FFs) :← determined by pQCD analysis of hadron productions in e+ e － collision

I estimated the errors of FFs based on Ktetzer parameterization

Universality

“ Kretzer ” : Phys. Rev., D62, (2000) 054001“ KKP ” : Nucl. Phys., B582, (2000) 514,

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)

2. pPDF and FF Analyses

0.1 10.01

Expe

rimen

t

Theo

ry

XheNe �

NLOSemi-inclusive DIS

: Error from fit ( χ2⊿ ＝１ )

With the assumption of SU(3) symmetric sea, motivated by D. de Florian et al. (DNS05): Phys. Rev. D71, (2005) 094018

Results of NLO q analysis with SIDIS data with central values of my FFs⊿Parton Helicity Distributions

to obtain well-defined error bands; well converged covariant matrix

⊿u = 0.85±0.05 d = -0.41±0.13 sea = -0.07±0.04 g = 0.04±0.33⊿ ⊿ ⊿

SLAC-TPC

SLAC-SLD

SLAC-SLD_c

SLAC-SLD_b

NLO

0.1 1)(7.94),(8.1072 NLOLOFFs Z

Z

Expe

rimen

t

Theo

ry

Hadron Production in e+ e- collision

EX. h =

EX. Results of the analysis of NLO pion FF with Kretzer parameterization

up → π + gluon → π +

Fragmentation Functions

3. Effects of the errors of FFs on pPDF analysis

( AExp – AThe ) / σA_FF @ NLO (σA_FF : From Pion FF )

・ Comparison of σA_FF with experimental errors (bar) and pPDF induced errors (band)

: Error from pPDF fit

pPDF: Fixed・ The effect of FF on @ NLOSIDIS2

FFs2

K+

1.02 SIDIS

12 FFFFs2

π+ 2.02 SIDIS

π+

K+

4. Summary

・ 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.

・ Rather strong dependence on the choice of FF models

・ 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 NLOStatistical error on Kretzer-type FF

Future Subjects:

D. de Florian et al. (DNS05): Phys. Rev. D71, (2005) 094018

Investigation of new models of FF and its validity

278.0

・ Current chi-squared values of pPDF fit

3. Effects of the errors of FFs on pPDF analysispPDF: Fixed

)()(),( 12 hhh

FFsh DADD

)(2 DFFs

)(1 DA p

12

001.0187.0)5.2,09.0( 221 GeVQxA p

proton target

σA_FF = Few % @ LO

Almost the same effect even @ NLO

h = π+

・ Estimation of σA_FF : A1h error from FFs