1. - 縦偏極パートン分布関数解析に対する、破砕関数の影響 -
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
The subject of my master thesis is QCD analysis of parton helicity distributions with HERMES SIDIS data

2. 1. Motivation

3. I estimated the errors of FFs based on Ktetzer parameterization
Polarized Inclusive DIS :
Polarized Semi-Inclusive DIS :
SIDIS Asymmetry
Fragmentation functions (FFs) are important elements in SIDIS asymmetry.
Universality
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)
SIDIS is a DIS process with additional detection of the final state hadron. In my master course study, I did the global QCD analysis.
In the analysis, I included pSIDIS data given by HERMES and SMC to separate quark – anti quark distribution effectively.
In the calculation of pSIDIS asymmetry, fragmentation functions take part to express the hadron fragment process.
By virtue of universality, we can use the FFs which are determined by pQCD analysis
with e+ e- collision results to the SIDIS calculation.
Many FFs are now given by many analysis groups. For the purpose of flavor separation with SIDIS data, I applied Kretzer FF to my analysis. But, because FFs are also determined by pQCD analysis, Kretzer FFs contain errors.
What is still not clear is how much the error of FFs have an effect to the calculation of A1h.
As the first step, we evaluated the errors of FFs and studied the effect of FF error on the A_1^h calc..
I estimated the errors of FFs based on Ktetzer parameterization
How large is the effect?
The error of FFs could affect the determination of ⊿q.

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

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

7. Hadron Production in e+ e- collision NLO
SLAC-TPC
SLAC-SLD
SLAC-SLD_c
SLAC-SLD_b
EX. h =
Experiment Theory
フィットがうまく言ってる。Fitted curve both in LO and NLO. Z
0.1 1 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. ・Comparison of σA_FF with experimental errors (bar)
and pPDF induced errors (band)
( AExp – AThe ) / σA_FF
@ NLO
(σA_FF : From Pion FF )
: Error from pPDF fit

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)
Investigation of new models of FF and its validity

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

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 NLO