Measurement of Flavor Separated Quark Polarizations at HERMES: Past, Present, and Future

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Measurement of Flavor Separated Quark
Polarizations at HERMESPast, Present, and Future
Joshua G. Rubin University of Illinois For the
HERMES Collaboration WWND 2006 - San Diego March
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Overview

• Introduction DIS and Dq(x)
• Past The Published HERMES 5-Flavor Dq
  Extraction
• Present Isoscalar extraction of Ds
• Future An Improved 5-Flavor Dq Extraction
• Remarks

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Deep-Inelastic Scattering and DIS Kinematics at
HERMES
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Dq(x) and How to Measure it
Experimental Asymmetry
(A and A1 are related by depolarization and
kinematic factors)
LO expression
How can we get at Dq(x) then?!

• Method 1 NLO Inclusive Analysis (SMC, SLAC,
  previous HERMES)
• g1 is proportional to linear combinations of Dq
  functions (not shown)
• Sensitive to combinations of flavors ?
  Constrains DS well
• Requires assumptions about SU(3) flavor symmetry
  and hyperon b decay data
• Limited Q2 coverage of g1(x,Q2) measurements --
  Unlike F1(x,Q2)

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The Published HERMES 5-Flavor Dq(x) Extraction
A. Airapetian et al. Phys. Rev., D71012003, 2005
Method 2 Use final state hadrons
? Purity is probability that hadron h came from
quark flavor q. ? Use correlation between struck
quark and observed hadrons to flavor-tag
events ? Extract quark contributions with
semi-inclusive analysis
The semi-inclusive version of A1
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Generating Purities with Monte Carlo
Fragmentation model tuned by minimizing c2
comparison of unpolarized data and MC
multiplicities
Monte Carlo

• DIS Generation (LEPTO)
• Fragmentation (JETSET)
• Detector Model (GEANT)

PARJ2 Strange Quark Suppression PARJ41
Lund-String a parameter (tension) PARJ42
Lund-String b parameter PARJ45 a correction
parameter for diquarks
Fragmentation model uncertainties estimated
through JETSET tunes that poorly describe
multiplicities in HERMES kinematic domain
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Extraction Method
We now solve,
where N is the nuclear mixing matrix, by
minimizing,
n-1A is a covariance matrix relating statistical
uncertainties in the bins of A.
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5-Flavor Dq(x) 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 (c2/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.

as it is not well constrained in the fit.
All sea quarks are set to zero for xgt0.3.
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Comparison with Model Predictions for the Light
Sea Polarization
? But, u-d is highly asymmetric!
The HERMES data favors a symmetric light sea.
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The Present Isoscalar extraction of Ds
Extract isoscalar combinations of Dq(x)
Asymmetries measured form isoscalar deuteron data

• Inclusive purities are simple combinations of
  unpolarized PDFs.
• Kaon purities can be computed from the
  unpolarized K multiplicity assuming only charge
  symmetry in fragmentation.

Excellent agreement -- No MC Dependence
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Isoscalar method result
DS(x) consistent with zero
but NLO fits of g1(x) suggest a negative 1st
moment for DS(x)!
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The Future 5-Flavor Dq(x) Extraction Revisited

• Theres still room for improvement
• Statistical uncertainties?
• Not all possible asymmetries were utilized.
  Some may have significant leverage over the sea
  quarks (ks).
• Systematic uncertainties?
• The published Monte Carlo related systematic
  uncertainty was hopefully conservative.
• Confirm rigorously
• Potentially reduce!

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Comparison of Uncertainties of Old and New
Asymmetries
2-4GeV deuterium gives additional pions and kaons
Additional asymmetries available

• Published
• New

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Correlating MC tune and Dq(x) systematic
uncertainty
68 Contour
1. Scan c2 surface around best Monte Carlo tune.
Fit with quadratic Polynomial.
Best MC Tune

• 2. Find 68 contour. Two factors
• Height of 68 of d-dimensional Gaussian
  Distribution.
• The height of c2 minimum to accommodate model
  imperfection. PDG does something like this.

c2
c2minC
c2min
parj b
parj a
3. Compute Dq(x) along contour Use Hessian
method to sample along uncorrelated parameter
directions. CTEQ does something like this.
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The real thing

• Scan the c2 surface around the best Monte Carlo
  tune.
• Correlations are quite clear between parameters
• Generate and diagonalize the matrix of 2nd
  derivatives to find linear combinations that are
  uncorrelated

Jetset/Lund c2 surface in Fragmentation Parameter
Basis

• Blue ellipses represent 68 contour
• Colored lines represent uncorrelated parameter
  directions

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MC Multiplicities

• Black dots are generated at the best Monte Carlo
  tune.
• Colored dots are generated at the 68 contour in
  the uncorrelated parameter directions
• 9 Hessian vectors
• ? 18 parameter sets to include

So, where are the new Dq(x) uncertainties?! Resul
ts not yet released, but should be greatly
reduced (gt50 in some bins).
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Concluding Remarks

• New Isoscalar Extraction of Ds(x)
• Excellent confirmation of Monte Carlo based
  5-flavor extraction
• Suggests exciting new physics for Ds(x) in the
  xlt0.02 range
• New 5-Flavor extraction
• Takes full advantage of the HERMES longitudinal
  target data statistical power by incorporating
  many new asymmetries.
• Addresses (and will reduce considerably!) Monte
  Carlo related systematic uncertainties in a
  rigorous way.