1. Determination of g/g from Hermes High-pT hadrons
P.Liebing, RBRC,
For the Hermes Collaboration
Spin 2006, Kyoto, Oct. 2006

2. Outline Data sets and asymmetries Monte Carlo studies
Extraction of g/g: Methods
Extraction of g/g: Results

3. Data Set(s) “antitagged”, inclusive charged hadrons
Deuteron target (from 2000)
Antitagged = Positron veto
Disclaimer: This is NOT quasi-real photoproduction!
Asymmetries vs. pT(beam) (pT w/respect to beam axis)
Other data sets from different target (proton), kinematic region (semiinclusive, Q2>0.1 GeV2), selection (hadron pairs) for consistency check of final result
Results consistent within statistics

4. Measured Asymmetries Antitagged Data:
Compare measured asymmetries to asym-metries calculated from MC using
g/g = 0 (central curve)
g/g = -1 (upper curve)
g/g = +1 (lower curve)
The g/g=0 asymmetry shows the contribution of the quarks!

5. Monte Carlo
Pythia 6.2 is used to provide the additional info needed to extract g/g from asymmetries
Relative contributions R of background and signal subprocesses in the relevant pT-range of the data
Background asymmetries and the hard subprocess asymmetry of the signal processes
Subprocess type, flavors and kinematics of partons
MC Asymmetries are calculated event by event and then averaged over the relevant pT-range !

6. Pythia: Reminder
Pythia simulates the total ep (*p) cross section using a mixture of different subprocesses
VMD (exclusive, diffractive, soft nondiffractive, hard nondiffractive)
Anomalous ( ) processes
Direct photon processes (QCDC, PGF)
LO DIS 
QCD
22

7. Monte Carlo vs. Data
Integrating over pT, data and MC cross sections agree within 10-20%
Observed Cross Section vs. pT
Reason for disagreement at pT>1GeV: Increasing weight of NLO corrections
K-factors for hard QCD subprocesses according to B. Jäger et. Al., Eur.Phys. J. C44(2005) 533

8. Monte Carlo: Fractions and Asymmetries
Subprocess Asymmetries
(using GRSV std.)
Subprocess Fraction
VMD decreasing with pT
DIS increasing with pT
Hard QCD increasing with pT
Signal Process PGF&QCD2->2
have  same magnitude
DIS increasing with pT (x) - positive
|PGF| increasing with pT - negative
All others flat and small, but:
Important for background asymmetry!

9. g/g Extraction
Extraction: Compare measured asymmetry with MC calculated one:
2 Methods to account for the different x distributions folded into the signal asymmetry (cross section, hard subprocess asymmetry and g/g)
Everything else
(hard, soft)
Contribution from hard
gluons in nucleon ~ g/g

10. g/g Extraction: Method 1
Method 1: Assume that g/g(x) is flat or only very weakly dependent on x
Then:
And:

11. g/g Extraction: Method 2
Use
And minimize the difference between
and
By fitting a function for g/g(x).
Use scan over parameters of function to find the minimum 2.
Scale (Q2) dependence of g/g(x, Q2) ignored absorbed into scale uncertainty (see later)

12. g/g Results Mean g/g from function:
1.05 < pT < 2.5 GeV
(deuteron,
antitagged,
4 pT bins)
error bars/bands: stat. and total errors (see later)
For Method 2 the errors are correlated (100%) through the fit parameter
Method 1 and 2 agree for the average of the data, determined by lowest pT points

13. g/g Systematics Uncertainties from each of 3 (4) groups
MC parameters
Pol./unpol. PDFs
Low-pT asymmetry
(Method 2 only) Fit function choice (1 or 2 params.)
Summed linearly to “Models” uncertainty
Hopefully this conservative approach would also cover for the unknown uncertainties due to
Using a LO approximation
Using Pythia as a model
Experimental (stat.+syst.) added in quadrature
syst. uncertainty from 4% scaling uncertainty 14% on g/g

14. Final Results&Conclusions
Hermes point (averaged over pT) from Method 1, curves for two fit functions
g/g is (likely) mostly small or even negative(?)
There is a slight hint that it may be positive, and larger at large x
Systematic errors have been investigated in depth
Need more data within really large x range to learn more

15. BACKUP

16. g/g Extraction: x-distributions
Unpolarized cross section vs. x from Pythia for antitagged data:
Hard subprocess asymmetry distribution:
g/g(x)?
Data cover 0.07<x<0.7,
most sensi-tive in 0.2<x<0.3

17. g/g Results: Method 2 Fit results
Final 2 functions used are polynomials with 1(2) free parameters
Fix g/gx for x0 and g/g1 for x1 (Brodsky et al.)
|g/g(x)|<1 for all x
Difference between functions is systematic uncertainty
Light shaded area: range of data
Dark shaded area: center of gravity for fit

18. MC and data asymmetries for
g/g Results: Method 2
MC and data asymmetries for
pT>1.05 GeV
2/ndf5.5: highest pT point
Systematics not included in fit
1 or 2 parameter function cannot change rapidly enough to accommodate highest pT-bin

19. g/g(x) Results: Method 2
x-dependence of g/g can only be determined unambiguously from Method 2 using the Mean Value Theorem for Integrals:
Approximation for Method 1:
 <x> (Method 2)

20. g/g(x) Results: Method 2
g/g at average x (Method 1 and 2) and vs. x (Method 2) for corresponding 4 pT points:
error bars/bands: stat. and total errors (see later)
Method 1 and 2 agree for the average of the data

21. g/g Extraction: Cuts Lower cuts on pT
Cuts are defined to balance statistics with sensitivity (S/B ratio)
Also possible systematics under consideration
Important: Correlation between measured pT and hard pT (x, scale)
Lower cuts on pT
1.05
1.0
2.0

22. Systematics: PDFs Standard PDFs used: Variation: Error:
CTEQ5L(SaS2) for Pythia (unpol., Nucleon(Photon))
GRSV std./GRV98 for q/q going into asymmetries
Variation:
GRV98(GRS) for Pythia (unpol, Nucleon(Photon))
GS-B/GRV94, BB2006/CTEQ5L for q/q(nucleon) going into asymmetries
Error:
For Pythia (unpol) the difference is taken as a 1 error
For q/qI(nucleon) the maximum difference is taken as a 1 error

23. Systematics: Asymmetries
Besides PDFs, there are 2 more sources of uncertainties
Asymmetry of “low-pT” VMD process
Std: Alow-pT=Ainclusive (from fit to g1/F1)
Variation: Alow-pT=0 (!asymmetric error!)
Unknown polarized photon PDFs needed for hard resolved processes
Std: Arithmetic mean of maximal and minimal scenarios of Glück et. al., Phys. Lett. B503 (2001) 285
Variation: maximal and minimal scenarios (symmetric, 1 error)

24. Systematics: pT smearing
Initial state (intrinsic kT of partons in nucleon and photon) and final state (fragmentation) radiation generate additional pT with respect to the collinear “hadron pT” ,
Huge effects on measured cross sections, and the correlation between measured pT and hard subprocess pT , and x
Also large effects on subprocess fractions
See Elke’s study in the paper draft
Std.: kT (0.4 GeV) and pTFragm. (0.4 GeV) from 2 minimization
Variation: 1 error from 2 minimization (0.04/0.02 GeV)

25. Systematics: Scale Dependence
Scale in Pythia was varied by factors 1/2 and 2
Same variation for asymmetry calculation
Error: Maximum difference to std. is taken as 1 uncertainty

26. Systematics: Cutoffs
A number of cutoffs in Pythia (to avoid double counting) can influence subprocess fractions
Most important one: PARP(90) sets the dividing line between
PGF/QCDC and hard resolved QCD
Hard and soft (low-pT) VMD
Std: Default Pythia (0.16)
Variation: (from comparing Pythia LO cross section with theory LO cross section)

27. Systematics: Method 2
An additional uncertainty is assigned for Method 2 due to the choice of functional shape
Std: Function 1 (1 free parameter)
Variation: Function 2 (2 free parameters)
Error = difference (!asymmetric!)

28. pT (of the hard subprocess) and x distributions
MC vs. (N)LO pQCD?
Why can we not (yet) use NLO pQCD calculations to extract g/g?
Example: simple PGF process (LO)
Magenta curves are what LO pQCD would give
Dashed curves are for intrinsic kT is included (0.4 GeV)
Solid curves are intrinsic and fragmentation pT (0.4 GeV) included
pT (of the hard subprocess) and x distributions
Cross sections

29. MC vs. LO QCD
Comparison of LO cross section for hard subprocesses from pQCD (M. Stratmann) and MC (no JETSET, Kretzer FF instead)
Magenta lines: Results from varying scale
Scale definition different for MC and calculation

30. Monte Carlo vs. Data
Pythia code has been modified/Parameters adjusted to match our exclusive  (Q2>0.1) and semiinclusive data (Q2>1)
Comparison of observed
cross sections in
tagged region
Data + MC agree well within 10-20% for variables integrated over pT

31. Monte Carlo vs. Data
Comparison of observed cross sections in antitagged region (vs. pT(beam))
Polarized and unpol. cross sections and k factors (B. Jäger et. al., Eur.Phys. J. C44(2005) 533)
Data + MC agree vs. pT when taking NLO corrections into account