SWADHIN TANEJA (STONY BROOK UNIVERSITY) K. BOYLE, A. DESHPANDE, C. GAL, DSSV COLLABORATION 2/4/2016 S. Taneja- DIS 2011 Workshop 1 Uncertainty determination of Polarized gluon distributions from Global Analysis of World Data

Introduction 2/4/2016 S. Taneja- DIS 2011 Workshop 2 Parton distribution functions, (Pdfs), f(x, μ 2 ).  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 ( μ 0 2 ).  All these sources of uncertainties are studied individually and there combined effect on pdfs evaluated systematically.

Polarized parton distribution functions 2/4/2016 S. Taneja- DIS 2011 Workshop 3 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 2/4/2016 S. Taneja- DIS 2011 Workshop 4 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! g 467 data pts in total (10% from RHIC) Marco Stratmann, Spin’08 Phys.Rev.D80:034030,2009.

Setup of DSSV 2/4/2016 S. Taneja- DIS 2011 Workshop 5 Parametrization, defined at Q 0 2 = 1 GeV 2 for sea quarks and delta g, simple forms  j = 0 Strong coupling constant, α s, from MRST, also use MRST for positivity bounds Positivity constraint for large x imposed via

Setup of DSSV 2/4/2016 S. Taneja- DIS 2011 Workshop 6 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 χ 2 penalty.

Lagrange multiplier in global analysis 2/4/2016 S. Taneja- DIS 2011 Workshop 7 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) Hessian (parabolic) Lagrange (non-parabolic)

χ 2 distribution vs. ΔΣ (x range 0.001, 1) 2/4/2016 S. Taneja- DIS 2011 Workshop 8 vs χ 2 vs ΔΣχ 2 vs λ

Quark spin contribution (1/2 Δ Σ ) at Δχ 2 =1 (x range 0.001, 1) 2/4/2016 S. Taneja- DIS 2011 Workshop 9 Polarized quark distribution: x (longitudinal momentum fraction)

χ 2 distribution vs. ΔG (x range 0.001,1) 2/4/2016 S. Taneja- DIS 2011 Workshop 10 vs χ 2 vs ΔG χ 2 vs λ χ 2 vs. ΔG x [0.2, 1] χ 2 vs ΔG x [0.05, 0.2] χ 2 vs ΔG x [0.001, 1]

Polarized gluon distribution, Δ g (x) : DSSV+ NEW (RUN-9 PHENIX) pp neutral pion asymmetry data DSSV Polarized gluon distribution at Δχ 2 =1 (x range 0.001, 1) 2/4/2016 S. Taneja- DIS 2011 Workshop 11

Effort to constrain the x distribution of polarized gluon 2/4/2016 S. Taneja- DIS 2011 Workshop 12 Ignores correlation between x regions. Splitting the x region in two, meaningfully, and constraining these regions simultaneously

χ 2 distribution vs. ΔG 1, ΔG 2 (ΔG constrained in x range [0.001, 0.05] and [0.05, 1]) 2/4/2016 S. Taneja- DIS 2011 Workshop 13 χ2 distribution of pol. gluon from two x ranges: χ 2 vs ΔG 1, ΔG 2 Δχ 2 =1 ellipse

Polarized gluon distribution: Polarized gluon distributions at Δχ 2 =1 (x range 0.001, 0.05 and 0.05, 1) 2/4/2016 S. Taneja- DIS 2011 Workshop 14 DSSV+ NEW (RUN-9 PHENIX) + Two X- region (envelope) uncertainty. DSSV+ NEW (RUN-9 PHENIX)

Effort to constrain the x distribution of polarized gluon 2/4/2016 S. Taneja- DIS 2011 Workshop 15 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

χ 2 distribution vs. ΔG 1, ΔG 2 and ΔG 3 (x range [0.001, 0.05], [0.05, 0.2] and [0.2,1]) 2/4/2016 S. Taneja- DIS 2011 Workshop 16

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 Δχ 2 =1 (x range [0.001, 0.05], [0.05, 0.2] and [0.2, 1]) 2/4/2016 S. Taneja- DIS 2011 Workshop 17

Scale μ = p T Scale μ = p T, 2p T Scale μ = p T, 2p T, p T /2 Theory energy scale ( μ ) uncertainty 2/4/2016 S. Taneja- DIS 2011 Workshop 18

Summary 2/4/2016 S. Taneja- DIS 2011 Workshop 19 In summary, we included Run-9 PHENIX pp π 0 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 p T of the outgoing particle in pp.

Outlook 2/4/2016 S. Taneja- DIS 2011 Workshop 20 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 2/4/2016 S. Taneja- DIS 2011 Workshop 21 Effects of Normalization Uncertainty: x (gluon longitudinal momentum fraction) Preliminary

Back up Parameterization uncertainty (not global analysis): 2/4/2016 S. Taneja- DIS 2011 Workshop 22 The gluon polarization distribution as a function of x from five fits to polarized DIS data. PRL 103, (2009)

Back up Scale uncertainty in cross section and asymmetry: 2/4/2016 S. Taneja- DIS 2011 Workshop 23  200 GeV ( PRD76, ) GRSV – std GRSV – zero μ = 2p T, p T, p T /2

vs. χ 2 distribution vs. ΔG (x range 0.2, 1) 2/4/2016 S. Taneja- DIS 2011 Workshop 24 χ 2 vs. ΔG ΔG vs. λ x [0.2, 1]

χ 2 distribution vs. ΔG (x range 0.05, 0.2) 2/4/2016 S. Taneja- DIS 2011 Workshop 25 vs χ 2 vs ΔG ΔG vs λ x [0.05, 0.2]

vs χ 2 distribution vs. ΔG (x range 0.001, 0.05) 2/4/2016 S. Taneja- DIS 2011 Workshop 26 ΔG vs λ χ 2 vs ΔG x [0.001, 1]