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Uncertainty determination of Polarized gluon distributions from Global Analysis of World Data

Uncertainty determination of Polarized gluon distributions from Global Analysis of World Data. Swadhin Taneja (Stony Brook University) K. Boyle, A. Deshpande , C. Gal, DSSV Collaboration. Introduction. Parton distribution functions, (Pdfs), f(x, μ 2 ).

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Uncertainty determination of Polarized gluon distributions from Global Analysis of World Data

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  1. Uncertainty determination of Polarized gluon distributions from Global Analysis of World Data SwadhinTaneja (Stony Brook University) K. Boyle, A. Deshpande, C. Gal, DSSV Collaboration S. Taneja- DIS 2011 Workshop

  2. Introduction • 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 (μ02). • All these sources of uncertainties are studied individually and there combined effect on pdfs evaluated systematically . S. Taneja- DIS 2011 Workshop

  3. Polarized parton distribution functions • 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) S. Taneja- DIS 2011 Workshop

  4. “classic” inclusive DIS data routinely used in PDF fits !Dq + Dq semi-inclusive DIS data so far only used in DNS fit !flavor separation first RHIC pp data (never used before) !Dg DSSV – a global analysis of polarized data Phys.Rev.D80:034030,2009. • Data Selection: 467 data pts in total (10% from RHIC) Marco Stratmann, Spin’08 S. Taneja- DIS 2011 Workshop

  5. Setup of DSSV • Parametrization, defined at Q02 = 1 GeV2 for sea quarks and delta g , simple forms kj = 0 • Strong coupling constant, αs , from MRST, also use MRST for positivity bounds • Positivity constraint for large x imposed via S. Taneja- DIS 2011 Workshop

  6. Setup of DSSV • 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. S. Taneja- DIS 2011 Workshop

  7. Lagrange multiplier in global analysis Goodness of fit (best fit) Physical observable • Minimize a new function, • With “λ” as a Lagrange multiplier and “Δf[a,b]” the moment of “f” in x range [a,b] , Lagrange (non-parabolic) Hessian (parabolic) CTEQ, JHEP 0207:012,2002. S. Taneja- DIS 2011 Workshop

  8. χ2 distribution vs. ΔΣ (x range 0.001, 1) • vs χ2 vs λ χ2 vs ΔΣ S. Taneja- DIS 2011 Workshop

  9. Quark spin contribution (1/2 ΔΣ) at Δχ2 =1 (x range 0.001, 1) • Polarized quark distribution: x ΔΣ (x) (polarized quark distribution) x (longitudinal momentum fraction) S. Taneja- DIS 2011 Workshop

  10. χ2 distribution vs. ΔG (x range 0.001,1) • vs χ2 vs ΔG x [0.001, 1] χ2 vs λ χ2 vs ΔG x [0.2, 1] χ2 vs. ΔG x [0.05, 0.2] χ2 vs ΔG S. Taneja- DIS 2011 Workshop

  11. Polarized gluon distribution at Δχ2 =1 (x range 0.001, 1) • Polarized gluon distribution, Δg (x): DSSV+NEW (RUN-9 PHENIX) pp neutral pion asymmetry data DSSV S. Taneja- DIS 2011 Workshop

  12. Effort to constrain the x distribution of polarized gluon • Ignores correlation between x regions. • Splitting the x region in two, meaningfully, and constraining these regions simultaneously S. Taneja- DIS 2011 Workshop

  13. χ2 distribution vs. ΔG1 , ΔG2 (ΔG constrained in x range [0.001, 0.05] and [0.05, 1]) • χ2 distribution of pol. gluon from two x ranges: Δχ2 =1 ellipse χ2 vs ΔG1,ΔG2 S. Taneja- DIS 2011 Workshop

  14. Polarized gluon distributions at Δχ2 =1 (x range 0.001, 0.05 and 0.05, 1) • Polarized gluon distribution: DSSV+ NEW (RUN-9 PHENIX) DSSV+ NEW (RUN-9 PHENIX) + Two X- region (envelope) uncertainty. S. Taneja- DIS 2011 Workshop

  15. Effort to constrain the x distribution of polarized gluon • 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 S. Taneja- DIS 2011 Workshop

  16. χ2 distribution vs. ΔG1 , ΔG2 and ΔG3(x range [0.001, 0.05], [0.05, 0.2] and [0.2,1]) S. Taneja- DIS 2011 Workshop

  17. Polarized gluon distributions at Δχ2 =1 (x range [0.001, 0.05], [0.05, 0.2] and [0.2, 1]) Effect at small X !! • Polarized gluon distribution: DSSV+ NEW (RUN-9 PHENIX) + Two X- region (envelope) uncertainty. + Three X- region (envelope) uncertainty. S. Taneja- DIS 2011 Workshop

  18. Theory energy scale (μ) uncertainty Scaleμ = pT ,2pT Scaleμ = pT , 2pT ,pT /2 Scaleμ = pT S. Taneja- DIS 2011 Workshop

  19. Summary • In summary, we included Run-9 PHENIX pp π0data 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. S. Taneja- DIS 2011 Workshop

  20. Outlook • 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 ΔGwill appear. S. Taneja- DIS 2011 Workshop

  21. Back up 21 • Effects of Normalization Uncertainty: x Δg (x) (polarized gluon distribution) Preliminary x (gluon longitudinal momentum fraction) S. Taneja- DIS 2011 Workshop

  22. Back up • Parameterization uncertainty (not global analysis): PRL 103, 012003 (2009) • The gluon polarization distribution as a function of x from five fits to polarized DIS data. S. Taneja- DIS 2011 Workshop

  23. Back up • Scale uncertainty in cross section and asymmetry: p0 @ 200 GeV (PRD76, 051106) μ = 2pT , pT , pT /2 GRSV – std GRSV – zero S. Taneja- DIS 2011 Workshop

  24. χ2 distribution vs. ΔG (x range 0.2, 1) • vs. χ2 vs. ΔG ΔG vs. λ x [0.2, 1] S. Taneja- DIS 2011 Workshop

  25. χ2 distribution vs. ΔG (x range 0.05, 0.2) • vs x [0.05, 0.2] ΔG vs λ χ2 vs ΔG S. Taneja- DIS 2011 Workshop

  26. χ2 distribution vs. ΔG (x range 0.001, 0.05) • vs x [0.001, 1] χ2 vs ΔG ΔG vs λ S. Taneja- DIS 2011 Workshop

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