HERMES によるパートン helicity 分布関数の QCD 解析

Tokyo Inst. of Tech.

1. Quantum Chromo-Dynamics (QCD)2. Parton Helicity Distribution and Nucleon Spin Problem3. Polarized Semi-Inclusive Deep Inelastic Scattering4. QCD Analysis and Results5. Summary

Contents

Mar. 28th, 2006

Y. Imazu, T. Kobayashi, T. Hasegawa, Y. Miyachi,T.-A. Shibata, and HERMES Collaboration

High Energy : Low Energy : Asymptotic Freedom 　　　 Color Confinement

1. Quantum Chromo-Dynamics (QCD)QCD : Dynamics of quark-gluon (partons) system

High Energy Interaction associated with Hadron e.g. Deep Inelastic Scattering (DIS)

Perturbative QCD (pQCD)

Parton Distribution Function (PDF) (non-perturbative)

Structure Function

: Factorization

We don’t know exactlyhow hadron is composedof partons.

Running Coupling : Energy of a System :

→ 0As → infinite,

Prediction from pQCD framework

Convolution Integral :

DGLAP Equation

Structure Function

We can extract the initial distributions so that they reproduce well the experimental results over many energy scales.

x

Evolution

Unpolarized PDF

2. Parton Helicity Distribution and Nucleon Spin Problem

: the probability density giving the spin polarization of a parton “p” to the direction of the nucleon spin

: extracted through (longitudinally) polarized DIS

(Longitudinally) Polarized PDF = Parton Helicity Distribution

:

Nucleon Spin Problem

Angular Momentum (Spin) Sum Rule

:

I extracted polarized PDF with polarized SIDIS data and investigated the value in the framework of pQCD.

　 0.12 (12%)

EMC result (1989)

at < Q2 > 　 = 10.7 GeV2

Nucleon Spin ProblempQCD Analysis

ABFR (1998), LSS (1998), AAC (2000)dFS (2000) , GRSV (2001), BB (2002)

Including polarized SIDIS dFNS (2005)

polarized DIS

3. Longitudinally Polarized Semi-Inclusive Deep Inelastic Scattering (Polarized SIDIS)

・・・

Polarized SIDIS

Ambiguity for the Determination :

Polarized DIS

・・・

Elimination of the ambiguity is achieved without the assumptions

→ Assumptions

Polarized SIDIS at HERMES

HERMES experiment : 27.5 GeV polarized electron/positron beam at DESY-HERA ring

Target : H, D

Pion, Kaon, ProtonFor ( 2 < p < 15 ) GeV/c

Hadron Identification

Ring Imaging Cherenkov Counter (RICH)

RICH

Electron

HERMES

Fragmentation Function : “ ” : Phys. Rev., D62:054001

Unpolarized PDF : “ ”

4. pQCD Analysis and Results・ I analyzed polarized PDF to the LO.

From -DecayFrom Hyperon Decay

“ ”

parameters and were fixed with GRSV01 results

: Free Parameters

: Phys. Rev., D63:094005

Parameterization of Polarized PDF at

Experimental constraints to the first moments at

Eliminated by including SIDIS data

Assumption of GRSV01 Analysis

: Eur. Phys. J., C5:461

Experimental data used in my fitting

Polarized DIS

Polarized SIDIS

100 steps in1000 steps inI took

for numerical calculation

fitting process with

Parameters were determined by

Numerical Calculation and minimization

Results

N freedom = N data - N parameters

= 1.31N freedom

Comparison of My Fit Result with g1p Data

Fit Results

HERMES SIDIS Data with Fitted Curve at

= 0.20 (20%)

5. Summary

I made the numerical calculation program for polarized DIS and SIDIS based on pQCD framework.

Fitting was performed to the LO with polarized DIS and SIDIS data. The reduced value was 1.3.

With polarized SIDIS data, polarized PDFs were determined without additional assumptions. became 0.20.

Future Subjects I will estimate the uncertainty in my analysis.

I will improve the program for the NLO analysis.