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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

3

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