Recent%20results%20of%20the%20AAC%20analysis

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Recent results of the AAC analysis

• Masanori Hirai
• TUS, Noda
• (Asymmetry Analysis collaboration)
• Collaborators S. Kumano and N. Saito
• arXiv0808.0413 hep-ph
• 2009 1 10,KEK

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Contents

• Introduction
• AAC08 analysis
• Global analysis of the polarized PDFs
• Data sets
• Assumptions positivity condition, antiquark
  SU(3)f symmetry
• Impact of RHIC p0 data
• Discussion about a functional form of Dg(x)
• Impact of E07-011 data
• Relative errors dDG/DG ?
• Summary

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Introduction

• Origin of the nucleon spin 1/2
• 1/2 1/2 DS DG Lq,g
• Quark spin component from polarize DIS DS
  0.1-0.3
• Unknown orbital angular moments Lq,g
• Quantitative value from sum rule of GPDFs
• Qualitative understanding ?
• DG is an important piece of the spin puzzle !
• Undetermined DG 0.49 ? 1.27 (AAC03)
• Experimental data from RHIC-Spin
• p0 production RUN05, PRD76, 051106 (2007)
• AAC analysis
• AAC00 PRD62, 0304017 (2000) DIS
• AAC04 PRD69, 054021 (2004) DIS, uncertainty
  estimation
• AAC06 PRD74, 014015 (2006)DISp0, uncertainty,
  DG
• AAC08 arXiv0808.0413 hep-ph DISp0,
  uncertainty, E07-011(J-Lab)

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Polarized deeply inelastic scattering

• Cross section
• Hadron tensor (asymmetric part)
• Structure function g1

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Spin asymmetry A1(x,Q2)

• L. W. Whitlow et al.,
• Phys. Lett. B 250 (1990) 193

• Polarized DIS experiments
• Proton E130, E143, EMC, SMC, HERMES,
  E155,CLAS
• Deuteron E143, E155, SMC, HERMES, COMPASS, CLAS
• Neutron E142, E154, HERMES, J-Lab (Hall-A)
• Q2 dependence is obtained by the DGLAP equation

Total data 441 points (Q2gt1GeV2)
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Spin asymmetry of p production

• Cross section
• gg?gg, gg?qq,qg?qg
• qq?qq, qq?qq
• qq?qq, qq?gg, qq?qq
• Consistent with unpolarized data
• Fragmentation functions (FFs)
• Determined by ee- data
• Ambiguity of Dgp (z)
• Sing problem
• gg process dominates at low pT
• ALLp0 ? Dg(x)2, negative or positive ?

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AAC analysis and uncertainty estimation

• Initial distribution of polarized PDF
• Constraint condition
• Positivity condition
• Imposing on positive Dg(x), but not impose on
  node type
• Antiquark SU(3)f symmetry
• Fixed 1st moments Duv0.926, Ddv ?0.341
• Fixed mq1.0 undetermined small-x behavior
• PDF uncertainty by Hessian method

• Unpol PDFGRV98
• Q02 1 GeV2

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Value of Dc2

• Hessian method
• K(N,s) c2 distribution
• D?2 N (N number of parameters)
• 1s error of normal distribution in
  multi-parameter space
• Not 1s error for PDF uncertainties
• Correspondence between uncertainties and
  variations of experimental data
• Dc21 statistically correct
• 1s error for 1 degree of freedom
• Asymmetry A1
• X-sections

Data-theory
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AAC08 analysis

• Added new data
• DIS CLAS(p,d), COMPASS(d, renewal data)
• p0production RHIC Run 5 final data (10 points)
• Data sets
• Set-A DIS data only
• Set-B DIS p0 data
• Set-C DIS fake data of the E07-011 experiment
• Impact on the determination of Dg(x)
• Set-A vs. Set-B effect on the functional form,
  node or positive
• Set-B vs. Set-C an impact on determination of
  the gluon spin
• contribution
  DG

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Fake data of the E07-011 experiment

• Update experiment of the J-Lab
• Expected errors for g1(x)
• Converted to asymmetry errors
• Expected asymmetry error

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Results

• Minimal c2
• 1st moments

Set-A (436 point) Set-A (436 point) Set-B (446 point) Set-B (446 point) Set-C (441 point) Set-C (441 point)
Positive Node Positive Node Positive Node
DIS 381.66 375.87 384.65 381.27 381.66 375.87
p0 ? ? 12.43 11.32 ? ?
Total c2 381.66 375.87 397.08 392.60 381.66 375.87
c2/d.o.f 0.90 0.88 0.91 0.90 0.89 0.87
Set-A Set-A Set-B Set-B Set-C Set-C
Positive Node Positive Node Positive Node
DS 0.24 ? 0.07 0.22 ? 0.08 0.26 ? 0.06 0.25 ? 0.07 0.24 ? 0.05 0.22 ? 0.05
DG 0.63 ? 0.81 0.94 ? 1.66 0.40 ? 0.28 -0.12 ? 1.78 0.63 ? 0.45 0.94 ? 1.09
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Impact of RHIC p0 data

• Insensitive to Duv(x) and Ddv (x)
• Same center values and uncertainties between
  Set-A and B
• gg process dominates
• Dg(x) becomes small
• Gluon uncertainty is reduced by RHIC data
• RHIC data is sensitive to Dg(x)
• Node type (DISp0)
• Less c2 12.43(DGgt0) , 11.32 (DGlt0)
• Changing sign at x0.1
• Large uncertainty in small-x region
• No data to constraint the behavior

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Impact of E07-011 data

• Converged determination of the valence quark
  distributions
• No changed these uncertainties
• Assuming SUf(3) symmetry
• Fixed 1st moments for uv and dv
• Significant reducing the uncertainty of Dg(x)
• Error correlation with antiquark distribution via
  Q2 evolution
• Constraint via NLO gluon term
• Low Q2 data
• Higher twist term ?

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Impact of RHIC p0 and E07-011 data

• Positive type
• DIS large distribution
• p0 small distribution
• Node type
• DIS small negative below x0.02
• p0 large negative at small-x
• Large uncertainty in small-x
• Positive distribution at high-x
• Relative error dDG/DG (xgt0.1)
• Same impact as RHIC Run5 data

Positive Node
Set-B (DISp0) 0.71 0.77
Set-C (E07-011) 0.73 0.54
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Summary

• Polarized PDF from polarized DIS data
• Well determined valence quark distributions
• Undetermined anti-quark and gluon distributions
• Rather large uncertainties of these
  distributions
• Reduction gluon uncertainty due to error
  correlation with antiquark distribution
• NLO gluon term lt statistical errors
• Positive distribution of Dg(x) at medium and
  large-x region
• E07-011 experiment (precise measurement )
• Constraint on Dg(x) via NLO gluon term
• NLO gluon term gt statistical errors
• Same impact as RHIC run5 p0 data
• Dg(x) from p0 production data
• Node type, changing sign around x0.1
• RHIC data covering narrow x-region
• Undetermined small-x behavior
• No data in the small-x region
• AAC08 numerical library http//spin.riken.bnl.gov
  /aac/

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1st moments of Dg(x)

• Full range x01
• 0.1lt X lt1
• CLAS data (x0.175 0.55)
• p0 data (?s200 GeV, pT 1.29 7.79 GeV)

Set-A Set-A Set-B Set-B Set-C Set-C
Positive Node Positive Node Positive Node
DG 0.63 ? 0.81 0.94 ? 1.66 0.40 ? 0.28 -0.12 ? 1.78 0.63 ? 0.45 0.94 ? 1.09
Set-A Set-A Set-B Set-B Set-C Set-C
Positive Node Positive Node Positive Node
DG 0.53 ? 0.72 0.87 ? 0.89 0.36 ? 0.26 0.40 ? 0.31 0.53 ? 0.38 0.87 ? 0.47
dDG/DG 1.36 1.02 0.71 0.77 0.73 0.54
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Comparison of FF for p0 production

• Model dependence of the FF global analysis ?
• Kretzers FFs within LO uncertainty
• KKPs FFs without the uncertainty at large-pT
• Cut of z for 2nd moments of FFs (zgt0.05)
• Heavy quark mass threshold
• Uncertainty from NLO FFs becomes 1/3

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Constraint on large-x behavior of Dg(x)

• Positive Dg(x)/g(x) at large-x
• HERMES A1d
• 0.03 lt xBj lt 0.07, 1.2 lt Q2 lt 1.7
• COMPASS-d 4.5 lt Q2 lt 8.6
• NLO gluon term
• Positive contribution
• Relative increasing for g1D
• euv2 4/9(P) ? 2.5/9(D)
• Positive Dg(x) at large-x

• Other DOF for HERMES-d ?
• Higher Twist effects
• LSS, PRD73(2006)034023
• Antiquark SUf(3) aymmetry
• D. de Florian, et al., PRD71(2005)094018