A Measurement of the Polarized Parton Distribution
Functions Through Semi-Inclusive Deep-Inelastic
Scattering at HERMES
Joshua G. Rubin
University of Illinois
For the HERMES
Collaboration
SPIN 2004 – Trieste, Italy
• A. Airapetian et al, submitted to Phys. Rev D – hep-ex/0407032
• A. Airapetian et al, Phys. Rev. Lett. 92 (2004) 012005 – hep-ex/0307064
Overview
1.
Introduction – Deep-Inelastic Scattering at HERMES and DIS
Kinematics
2.
Formalism and Extraction Method
–
NLO Inclusive Approaches
–
The LO Semi-Inclusive Approach
–
Purity Method
–
Data Unfolding Procedure
Asymmetries and Dq Results
3.
4.
–
The Light Sea
–
Ds Isoscalar Extraction
Remarks
Joshua Rubin - SPIN2004 - October, 2004
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Deep-Inelastic Scattering and DIS Kinematics
Var.
x
Year
Beam and
Polarization
Target and
Polarization
1996
e+ 52.8 %
H 74.8 %
1997
e+ 53.1 %
H 85.0 %
1999
e- 52.1 %
D 81.7 %
1999
e+ 53.3 %
D 81.0 %
2000
e+ 53.3 %
D 84.5 %
SIDIS Requirements
Description
Light Cone Momentum Fraction of Parton
Q2
Negative Squared Photon Momentum
Q2 > 1 GeV2
W2
Final State Invariant Mass
W2 > 10 GeV2
zh
Energy Fraction carried by Hadron h
0.2 < zh < 0.8
Joshua Rubin - SPIN2004 - October, 2004
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Two ways to measure Dq
#1 NLO Inclusive Analysis (SMC, SLAC, previous HERMES):
• At NLO, moments of g1 are proportional to linear combinations of Dq functions.
• Sensitive to combinations of flavor contributions  Constrains DS well.
• Forced to make assumptions about SU(3) flavor symmetry and dependent on
hyperon b decay data.
Joshua Rubin - SPIN2004 - October, 2004
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Extracting Dq: Semi-inclusive DIS
Experimental Asymmetry:
N 
N
 A|| and A1 are
related by
depolarization and
kinematic factors
N   N 
A||  
N  N 
LO expression:
1
1
g1(x)   eq2 q  ( x)  q  ( x)   eq2 Dq( x)
2 q
2 q


 Use correlation between struck
quark and observed hadrons to
flavor-tag events
 Extract quark contributions with
semi-inclusive analysis
 1h/ 2   3h/ 2
A  h

h
 1/ 2   3 / 2
h
1

2
2
h
2
e
D
q
(
x
,
Q
)
D
(
z
,
Q
)
q
q
q
2
2
h
2
e
q
'
(
x
,
Q
)
D
(
z
,
Q
)
 q'
q'
q'
Joshua Rubin - SPIN2004 - October, 2004
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Extracting Dq: The Purity Method
Let’s
write,
Dq
A  P
with
q
q
h
1
h
q
Pqh ( x, Q 2 , z ) 
e
2
q'
eq2 Dqh ( z, Q 2 )
2
h
q'
2
q' ( x, Q ) D ( z, Q )
.
q'
This purity matrix can be computed by
Monte Carlo simulation:
Monte Carlo
•DIS Generation (LEPTO)
•Fragmentation (JETSET) Tuned to:
•Detector Model (GEANT)
Joshua Rubin - SPIN2004 - October, 2004
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Generated Purities
• Purities correlate observed
hadron with struck quark.
• Systematic error bands estimated using a
JETSET tune that poorly describes
multiplicities in HERMES kinematic domain.
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Extraction Method
Purity Matrix


p
h
 u
N
(
x
)
q
i
Pqh ( xi ) 
 
h
N q ( xi )   

 ps
q'







k 
ps 

k
u
p
Asymmetry Vector
 A1, p ( xi ) 
Contains an



asymmetry for

A( xi )  

 k

each hadron from
 A1, d ( xi ) 


each target

Dq Vector
 Du ( xi ) 


Contains an entry for Q ( x )  



i
each Dq.
 Ds ( x ) 
i 

We now solve,


A1 ( x)  N ( x) P( x)Q( x),
where N is the nuclear
mixing matrix, by
minimizing,





 T 1 
T
  A1  NPQ  A A1  NPQ .
2
-1A is a covariance
matrix relating statistical
uncertainties in the bins
of A.
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Data Production
• Data corrected for acceptance and
radiative effects via a new, more rigorous,
bin to bin unfolding procedure.
• Eliminates model dependence introduced
by fitting techniques.
• Completely uncorrelates systematic
uncertainties.
• Causes error bar inflation, but produces a
correlation matrix.
Data sample included
in this Dq analysis
Target
DIS Events
Hadrons
Hydrogen
1.7 x 106
+ -
Deuterium
6.7 x 106
+ - K+ K-
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Deuteron Asymmetry Ah1,D
• Consistent with, but more
precise than the undifferentiated
SMC hadron asymmetries


inc
1, p
•K- is a particularly good probe of the
sea. The asymmetry shows no sign of
predicted strong negative sea
polarization (Ellis-Jaffe sum rule).
inc
1, d also measured and used in this analysis
A1, p , A1, p , A , A
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5-Flavor Dq Extraction
• Du is positive and Dd is negative. Both
are of the greatest magnitude in the
valence quark range.
• All the sea quark polarizations are
consistent with zero (2/ndf = 7.4/7, 11.2/7,
and 4.3/7 for u, d, and s respectively).
• Almost equally consistent with
GRSV2000 and BB01 LO
Parameterizations.
D s  0 as it is not well constrained in the
fit. All sea quarks are set to zero for
x>0.3.
Joshua Rubin - SPIN2004 - October, 2004
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Comparison with Model Predictions for
the Light Sea Polarization
Model
Prediction
2/ndf
Meson Cloud
Model
8.1/7
Chiral Quark
Soliton Model
17.6/7
Symmetric Light
Sea
7.7/7
 But, u+d is highly asymmetric!
The HERMES data favors a symmetric light sea.
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Isoscalar Method and Ds
An alternative Ds extraction doesn’t require Monte Carlo fragmentation model.
Ds + Ds has no isospin and deuteron is isoscalar.
1) Form purity matrix:
 pu u  d  d
p( x)   k   k 
 PS


k k
Pu u  d  d 
ps


2) Compute purities directly from
parameterized fragmentation functions.
3) Extract as described previously.
• 5 parameter and Isoscalar
methods in agreement
• Both support a symmetric
strange sea polarization
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Concluding Remarks
• For the first time, HERMES has measured independently five of
the six possible quark helicity distributions.
• This semi-inclusive LO QCD approach takes advantage of
HERMES excellent particle identification to flavor-tag events and
make possible Dq extraction with a purity method.
• A new, more rigorous, unfolding technique used:
– Corrects acceptance and QED radiative effects
– Removes any systematic uncertainty correlations from asymmetries
– Causes statistical uncertainty inflation, but is properly taken into account
by correlation matrix
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