SWADHIN TANEJA(STONY BROOK UNIVERSITY)

K. BOYLE, A. DESHPANDE, C. GAL,DSSV COLLABORATION

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Uncertainty determination of Polarized gluon distributions

from Global Analysis of World Data

Introduction

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Parton distribution functions, (Pdfs), f(x,μ2). Essential input in high energy calculation. Their precision determines physics.

Global Analysis, Assessing uncertainties is a challenge

Including experimental statistical and systematic errors. Non-gaussian sources of uncertainties from pQCD(e.g.

higher order corrections, power law corrections etc.) Parametrization choice of Pdfs at an input energy scale (μ0

2).

All these sources of uncertainties are studied individually and there combined effect on pdfs evaluated systematically .

Polarized parton distribution functions

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Proton spin structure: Proton spin puzzle (1988 EMC experiment) Global analysis, [PRL101:072001,2008] ΔG not well constrained by fits to fixed target pDIS

Polarized pdf global analysis, Large number of data points (∼ 467 in DSSV) Many experiments (∼ 9) A variety of physical processes (∼ 5− 6 and growing)

with diverse characteristics, precision, and error determination.

Many independent fitting parameters (∼ 20)

DSSV – a global analysis of polarized data

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Data Selection:

semi-inclusive DIS data

so far only used in DNS fit! flavor separation

“classic” inclusive DIS data

routinely used in PDF fits! q + q

first RHIC pp data (never used before)

! g

467 data pts in total (10% from RHIC)

Marco Stratmann, Spin’08

Phys.Rev.D80:034030,2009.

Setup of DSSV

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Parametrization, defined at Q02 = 1 GeV2

for sea quarks and delta g , simple forms j = 0

Strong coupling constant, αs , from MRST, also use MRST for positivity bounds

Positivity constraint for large x imposed via

Setup of DSSV

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Avoid assumptions on parameters unless data cannot discriminate:

Large x , x--> 1, behavior is unconstrained, as there are no data sensitive to > ~0.6

Allows for SU(3) symmetry breaking with a χ2 penalty.

Lagrange multiplier in global analysis

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Minimize a new function,

With “λ” as a Lagrange multiplier and “Δf[a,b]” the moment of “f” in x range [a,b] ,

CTEQ, JHEP 0207:012,2002.

Physical observable

Goodness of fit (best fit)

χ2 distribution vs. ΔΣ (x range 0.001, 1)

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vs

χ2 vs ΔΣ χ2 vs λ

Quark spin contribution (1/2 ΔΣ) at Δχ2 =1 (x range 0.001, 1)

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Polarized quark distribution:

χ2 distribution vs. ΔG (x range 0.001,1)

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vs

χ2 vs ΔG χ2 vs λ χ2 vs. ΔG x [0.2, 1] χ2 vs ΔG x [0.05, 0.2]χ2 vs ΔG x [0.001, 1]

Polarized gluon distribution, Δg (x):

DSSV+ NEW (RUN-9 PHENIX) pp neutral pion asymmetry data

DSSV

Polarized gluon distribution at Δχ2 =1 (x range 0.001, 1)

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Effort to constrain the x distribution of polarized gluon

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Ignores correlation between x regions.

Splitting the x region in two, meaningfully, and constraining these regions simultaneously

χ2 distribution vs. ΔG1 , ΔG2 (ΔG constrained in x range [0.001, 0.05] and [0.05,

1])

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χ2 distribution of pol. gluon from two x ranges:

χ2 vs ΔG1, ΔG2Δχ2 =1 ellipse

Polarized gluon distribution:

Polarized gluon distributions at Δχ2 =1 (x range 0.001, 0.05 and 0.05, 1)

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DSSV+ NEW (RUN-9 PHENIX) + Two X- region (envelope) uncertainty.

DSSV+ NEW (RUN-9 PHENIX)

Effort to constrain the x distribution of polarized gluon

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Ignores correlation between x regions.

Splitting the x region in two , meaningfully, and constraining these regions simultaneously

Splitting the x region in three , meaningfully, and constraining these regions simultaneously

χ2 distribution vs. ΔG1 , ΔG2 and ΔG3

(x range [0.001, 0.05], [0.05, 0.2] and [0.2,1])

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Polarized gluon distribution:

+ Three X- region (envelope) uncertainty.

+ Two X- region (envelope) uncertainty.

DSSV+ NEW (RUN-9 PHENIX)

Effect at small X !!

Polarized gluon distributions at Δχ2 =1 (x range [0.001, 0.05], [0.05, 0.2] and [0.2, 1])

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Scale μ = pT Scale μ = pT , 2pT Scale μ = pT , 2pT , pT /2

Theory energy scale (μ) uncertainty

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Summary

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In summary, we included Run-9 PHENIX pp π0 data in the DSSV global analysis.

We showed, using Lagrange multiplier method, constraining gluon spin contribution ΔG over an x range [0.001:1] under estimates the uncertainty represented in the polarized gluon distribution function Δg(x).

We showed the effect of including the theory energy scale uncertainty on ΔG by varying the scale value by one half and twice the value of pT of the outgoing particle in pp.

Outlook

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Global analysis is more than just fitting data: Include experimental systematic uncertainty properly

(Normalization). Other uncertainties

alpha strong, parameterization, energy scales. role of higher twists.

Include new sets of data e.g. charged pion, direct photon, STAR inclusive jet, di-jet from RHIC...

Only after all uncertainties are included (x range) and accounted for, a clearer picture on ΔG will appear.

Back up

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Effects of Normalization Uncertainty:

Preliminary

Back up

Parameterization uncertainty (not global analysis):

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• The gluon polarization distribution as a function of x from five fits to polarized DIS data.

PRL 103, 012003 (2009)

Back up

Scale uncertainty in cross section and asymmetry:

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0 @ 200 GeV (PRD76, 051106)

GRSV – stdGRSV – zero

μ = 2pT , pT , pT /2

vs.

χ2 distribution vs. ΔG (x range 0.2, 1)

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χ2 vs. ΔG ΔG vs. λx [0.2, 1]

χ2 distribution vs. ΔG (x range 0.05, 0.2)

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vs

χ2 vs ΔG ΔG vs λx [0.05, 0.2]

vs

χ2 distribution vs. ΔG (x range 0.001, 0.05)

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ΔG vs λχ2 vs ΔG x [0.001, 1]