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1
Extracting FL Moments from Data
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Gluon sum rule
How do we get gluon information from the data
Data Analysis
Dealing with regions of (xB, Q2) with no data
Error Analysis
Assigning errors when interpolating over regions of no data
Plans and goals for the future
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Gluon Distributions
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Large error bands for current gluon distribution calculations
This analysis aims to significantly reduce the errors at large x
Gluon distribution sensitive to F2
only through logarithmic Q2 evolution
FL directly sensitive to the glue
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Longitudinal Structure Function FL
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Next-to-Leading Order
Gluons contribute to F2 and F
L
Obtain a “gluon sum rule”
Obtain gluon distributions, G(y), by fit to F2 and F
L data (at fixed Q2)
Parametrize G(y) and encode within a global fit to data
coefficients dependent on number of quark flavors
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Operator Product Expansion
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Simple form of Q2 evolution of Moments of structure functions
The gluon sum rule for moments of structure functions is
N-th moment structure function Wilson coefficientsfit coefficients
If Wilson coefficients are known, the moments Mk[n] calculable for any Q2
Obtain G[n](Q2) directly from structure function data
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Data Coverage in Q2 and xB
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Only using L/Tseparated data
Proton data only
JLab data coversresonance region
higher x, lower Q2
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Plot Structure Functions in Q2 Bins
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Include datasets from SLAC, BCDMS,NMC, and JLab
Using different models for different W2
ranges
F2allm + R1990 => W2 > 9 GeV2
Christy-Bosted Fit => 3.85 < W2 < 9 GeV2
Liang Fit => W2 < 3.85 GeV2
Issues to consider
random point-to-point uncertainties
gaps in the data
large missing regions in x – fewconstraint points
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Fill in the Gaps!
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Some empty bins, with no data
Linear interpolation between pointsreflects random errors in data
Use model calculations in empty bins
apply rescale factor based on thestatistical average of adjacent points
reasonable over small x ranges
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Random Error Estimation
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Calculate moment by integrating datafrom x = 0.01 – 1.0
Considering bins of width 0.01 in x
For each data point, generate a randomnumber within the error bar of that point
generate a complete pseudo-dataset
Fill in any gaps in dataset, via interpolationor rescaling the model
Integrate to generate moment for thatpseudo-dataset
Repeat 100 times
obtain distribution of moments from pseudo-datasets
Distribution width is measure of randomerror
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Dealing with Large Missing x Regions
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Higher Q2, gluon contribution is largerat low x!
Few data points
single data point can dictate the model rescaling factor or the linearinterpolation!
2D interpolation over Q2 and x
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Evaluate Moments and Methods
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Difference in moments from two models largest in Q2 bins with missing x ranges
Expect more consistent results with 2D interpolation method
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Plans for the Future
Peter Monaghan “Extracting FL Moments from Data” 22nd January 2010
Fill in blank data regions using 2D interpolation over data ranges
Evaluate contributions to random errors
Calculate n=2 and n=4 moment for FL
Extract gluon moments from data and compare with gluon PDFs
Use FL data in a global fit to constrain the gluon distribution