Polarized PDF (based on DSSV) Global Analysis of World Data Swadhin Taneja (Stony Brook University) K. Boyle and A. Deshpande EIC EW workshop 12/3/2018

Introduction Parton distribution functions (Pdfs). Essential input in high energy calculation Assessing uncertainties is a challenge Non-gaussian sources of uncertainties from pQCD(e.g. higher order corrections, power law corrections etc.) Parametrization choice of pdf at an input energy scale Including experimental statistical and systematic errors All these sources of uncertainties are studied individually and there combined effect on pdfs evaluated systematically . EIC EW workshop 12/3/2018

Fit complications Problem is more complicated than it appears For example, 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) EIC EW workshop 12/3/2018

Specifics of DSSV – a global analysis Data Selection: “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 467 data pts in total (10% from RHIC) Marco Stratmann, Spin’08 EIC EW workshop 12/3/2018

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 EIC EW workshop 12/3/2018

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. EIC EW workshop 12/3/2018

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] , CTEQ, JHEP 0207:012,2002. EIC EW workshop 12/3/2018

Studies & Results EIC EW workshop 12/3/2018

χ2 distribution vs. ΔΣ (x range 0.001, 1) EIC EW workshop 12/3/2018

Polarized quark distribution: Polarized quark x distribution and uncertainties at Δχ2 =1 from constraints on ΔΣ (x range 0.001, 1) Polarized quark distribution: x ΔΣ (x) (polarized quark distribution) x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

χ2 distribution vs. ΔG (x range 0.001, 1) ΔG vs λ EIC EW workshop 12/3/2018

χ2 distribution vs. ΔG (x range 0.2, 1) ΔG vs λ x [0.2, 1] χ2 vs ΔG EIC EW workshop 12/3/2018

χ2 distribution vs. ΔG (x range 0.05, 0.2) ΔG vs λ EIC EW workshop 12/3/2018

χ2 distribution vs. ΔG (x range 0.001, 0.05) ΔG vs λ EIC EW workshop 12/3/2018

Polarized gluon x distribution: Polarized gluon x distribution and uncertainties at Δχ2 =1 from constraints on ΔG (x range 0.001, 1) Polarized gluon x distribution: x Δg (x) (polarized gluon distribution) x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

Kinematic x, Q2 range of used data sets (DIS) World data on DIS: Q2 x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

EIC Simulation Michael Savastio Use PYTHIA to produce cross section weighted x and Q2 bins. Energies used 10x250 GeV. Generate number of deep inelastic events, N, for a integrated luminosity of 6 fb-1 in those bins. Statistical uncertainty in each bin is then given by 1/√N. Convert this to uncertainty in A1p . Generate new A1p by randomizing around the best fit from DSSV. EIC EW workshop 12/3/2018

Kinematic x, Q2 range of used data sets + EIC simulated data Word data DIS + EIC simulated data: Q2 x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

χ2 distribution vs. ΔG (x range 0.001, 1) using EIC simulated data ΔG vs λ EIC EW workshop 12/3/2018

Rough EIC implications for gluon polarization uncertainties Uncertainty reduction in ΔG due to EIC: x Δg (x) (polarized gluon distribution) Reduction in ΔG uncertainty by more than 1/3 x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

Effort to constrain x distribution of polarized gluon Ignores correlation between x regions. Splitting the x region, meaningfully, and constraining these regions simultaneously Note: Here forth only data included by DSSV is used. EIC EW workshop 12/3/2018

χ2 distribution of pol. quark from two x ranges: χ2 distribution vs. λ1 , λ2 (ΔΣ constrained in x range [0.001, 0.05] and [0.05, 1]) χ2 distribution of pol. quark from two x ranges: χ2 vs λ1, λ 2 Δχ2 =1 ellipse EIC EW workshop 12/3/2018

Uncertainty on pol. quark from two x ranges: Pol. quarks dist. and uncertainties at Δχ2 =1 from constraints on ΔΣ’s (x range [0.001, 0.05] and [0.05, 1]) Uncertainty on pol. quark from two x ranges: x ΔΣ (x) (polarized quark distribution) x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

χ2 distribution of pol. gluon from two x ranges: χ2 distribution vs. λ1 , λ2 (ΔG constrained in x range [0.001, 0.05] and [0.05, 1]) χ2 distribution of pol. gluon from two x ranges: χ2 vs λ1, λ 2 Δχ2 =1 ellipse EIC EW workshop 12/3/2018

Uncertainty on pol. gluon due to two x ranges: Pol. gluon dist. uncertainties at Δχ2 =1 from constraints on ΔG’s (x range [0.001, 0.05] and [0.05, 1]) Uncertainty on pol. gluon due to two x ranges: Proper representation of the uncertainty on polarized gluon distribution requires varying ΔG in different x-regions simultaneously. x Δg (x) (polarized gluon distribution) x (longitudinal momentum fraction) EIC EW workshop 12/3/2018

Normalization Uncertainty From DSSV (PRD80:034030,2009), current 2 definition: Including normalization uncertainties is : EIC EW workshop 12/3/2018

Systematic Uncertainty Effects of Normalization Uncertainty: x Δg (x) (polarized gluon distribution) Preliminary x (gluon longitudinal momentum fraction) EIC EW workshop 12/3/2018

Theory energy scale uncertainty Effects of theory scale uncertainty: x Δg (x) (polarized gluon distribution) μ = pT Black μ = pT/2 Red μ = pT Blue x (gluon longitudinal momentum fraction) EIC EW workshop 12/3/2018

Outlook Global analysis: 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, di-jet from RHIC, new COMPASS SIDIS data. Only after all uncertainties are included (x range?) and accounted for a clearer picture on ΔG will appear. EIC EW workshop 12/3/2018

Outlook EIC projections: In the future analyses, detector smeared data from EIC-detector working group should be used. For that we will work with EIC collaborators (meaning task forces at BNL and similar group at JLab). Include SIDIS EIC simulated data. EIC EW workshop 12/3/2018

Back up EIC EW workshop 12/3/2018

DIS @ small x translates into x interesting questions at small x charm contribution to g1 any deviations from DGLAP behavior? precision study of Bjorken sum rule positive Dg (rare example of a well understood fundamental quantity in QCD) EIC EW workshop 12/3/2018 32

Start With Normalization (DIS) Experiment Pb/Pb (%) Pt/Pt (%) f/f (%) EMC 7.6 5.0 SMC(p) 2.4 3.0 SMC(d) 2.7 2.2 COMPASS(d) 6.0 E142(n) 3.1 7.1 8.0 E143(p) 2.5 2.0 E143(d) 4.0 1.5 E154(n) 5.3 5.5 E155(p) 7.0 E155(d) 2.9 HERMES(3He) HERMES(p) 3.4 <10-1 HERMES(d) 1.9 3.5 HALL-A(n) 3.8 CLAS(p) 0.9 (PbPt])/PbPt) --- CLAS(d) 3.9 (PbPt])/PbPt) EIC EW workshop 12/3/2018

Start With Normalization (pp) Each years polarization is correlated with other years from Hjet normalization Experiment PBPY]/PbPY (%) Year to Year Uncorrelated Correlated Run5 200 7.4 5.8 Run6 200 6.7 4.9 Run9 200 6.8 5.7 Run6 62.4 12.7 5.5 Run9 500 17 7.2 EIC EW workshop 12/3/2018

EIC EW workshop 12/3/2018

Lagrange Multiplier Minimize a function while maintaining a constraint. For example , maximize/minimize this: (Function) (Constraint) EIC EW workshop 12/3/2018

Lagrange Multiplier New Function EIC EW workshop 12/3/2018

Polarized quarks x distribution and uncertainties at Δχ2 =1 from constraints on ΔΣ’s (x range [0.001, 0.2] and [0.2, 1]) EIC EW workshop 12/3/2018

Polarized quarks x distribution and uncertainties at Δχ2 =9 from constraints on ΔΣ’s (x range [0.001, 0.2] and [0.2, 1]) EIC EW workshop 12/3/2018

χ2 distribution vs. λ1 , λ2 at Δ χ2 =9 level (ΔΣ constrained in x range [0.001, 0.05] and [0.05, 1]) EIC EW workshop 12/3/2018

Polarized quarks x distribution and uncertainties at Δχ2 =9 from constraints on ΔΣ’s (x range [0.001, 0.05] and [0.05, 1]) EIC EW workshop 12/3/2018