1. 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

2. 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

3. 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

4. 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

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
EIC EW workshop
12/3/2018

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.
EIC EW workshop
12/3/2018

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

8. Studies & Results
EIC EW workshop
12/3/2018

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

10. 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

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

12. 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

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

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

15. 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

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

17. 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

18. 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

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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

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

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

28. 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

29. 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

30. 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

31. Back up
EIC EW workshop
12/3/2018

32. 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

33. 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

34. 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

35. EIC EW workshop
12/3/2018

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

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

38. 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

39. 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

40. 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

41. 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