1. Determination of g/g from Hermes High-pT hadrons
P.Liebing, RBRC,
For the Hermes Collaboration
RHIC Spin Collaboration Meeting, Tokyo, Sep. 2006

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

3. Hermes and HERA e beam 27.5 GeV, polarization: 50%
Internal H, D gas target, polarization 75-85%
Cherenkov(until 1997):  ID; RICH(from 1998): ,K,p ID
lepton/hadron contamination < 1%
Limited acceptance: 40mrad gap, |x|<170, | y|<140 mrad

4. Data Sets 3 different kinematic regions (Proton and Deuteron targets)
1.) “anti-tagged” h+, h- data main data sample
Positron + Electron veto
Disclaimer: This is NOT quasi-real photoproduction
Asymmetries vs. pT(beam) (pT w/respect to beam axis)
2.) “tagged” h+,h- data  sample for consistency check
Positron detected: Q2>0.1, W2>4 GeV2, 0.05<y<0.95
Asymmetries vs. pT(*) (pT w/respect to virtual photon axis)
3.) Inclusive hh Pairs  sample for consistency check
Positrons and electrons allowed (but not required) in the event
Asymmetries vs. lower cut on (pT(beam))2 (pT w/respect to beam axis)
All charge combinations
Not quite independent from (anti-)tagged samples (~6% correlation)
Deuteron, antitagged, (h++ h-) data for final results

5. Measured Asymmetries
Relative syst. error on polarization measurement  4% (Deuterium)
Target polarization measured every  10s
Target spin flipped every s
Beam polarization measured every  1min

6. Measured Asymmetries Tagged Data: Antitagged Data: Pairs:
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 is due to quarks only!

7. 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 !

8. The Physics of Pythia
Model: Mix processes with different photon characteristics
Small Q2: VMD+anomalous (=„resolved“) photon dominate
Large Q2: LO DIS dominates
Choice of hard process according to hardest scale involved:
If all scales are too small: „soft“ VMD (diffractive or „low-pT“)
The „resolved“ part is modelled to match the world data on  (p)
...
VMD-
direct
anomalous photon
„Soft“ VMD:
Elastic, diffractive and nondiffractive („minimum bias“, „low-pT“) processes
Hard VMD:
QCD 22 processes
QCD-Compton
PGF
LO DIS (virtual photons)
(QED) Splitting of qq
QCD 22 processes

9. 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

10. 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

11. Monte Carlo vs. Data
Vs. pT, MC cross sections at pT(beam,*)>1 ((pT(beam))2 >1.5) are 3-4 times lower than the data in ALL regions
Reason: Increasing weight of NLO corrections to hard QCD processes
NOTE: It is not possible to apply k-factors to g/g extraction using LO MC

12. 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

13. Monte Carlo: Fractions and Asymmetries
Antitagged, charge combined Deuteron data:
Subprocess Asymmetries
(using GRSV std.)
Subprocess Fraction
VMD decreasing with pT
DIS increasing with pT
Hard QCD increasing with pT
Signal Process 1/2 PGF/QCD2->2
DIS increasing with pT (x) - positive
|PGF| increasing with pT - negative
All others flat and small, but:
Important for background asymmetry!

14. g/g Extraction
Deuteron, antitagged, charge combined data for final result
But: Subprocess fractions and -asymmetries are different for different regions, targets and charges
Use other regions/target/charge separated sample for consistency check
Cuts:
1.05 < pT < 2.5 GeV (antitagged, 4 bins)
1 < pT < 2 GeV (tagged, 1 bin)
p2T,1+ p2T,2 > 2 GeV (pairs, 1 bin)

15. g/g Extraction
Extraction: Compare measured asymmetry with MC calculated one:
Signal asymmetry is folded unpolarized cross section, hard subprocess asymmetry and g/g(x)
Each of these quantities has a different x-dependence
Everything else
(hard, soft)
Contribution from hard
gluons in nucleon ~ g/g

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

18. g/g Results: Method 1
Comparison of results from all (almost independent) data sets
Results agree within statistics

19. 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)

20. 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

21. 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

22. g/g Results: Method 1&2 Average g/g from function:
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

23. 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)

24. 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

25. g/g Systematics
The “Model” (MC and calculated asymmetries) uncertainty is estimated by varying
MC parameters within a reasonable range
1/2Q2 standard scale 2Q2
Cutoff parameters
Intrinsic kT and fragmentation pT
Polarized/unpolarized nucleon/photon PDFs
Assumptions used in asymmetry calculation
Low-pT asymmetry

26. 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
Experimental (stat.+syst.) added in quadrature
syst. uncertainty from 4% scaling uncertainty 14% on g/g

27. What did we learn? For an accurate g/g extraction: From our results:
Need NLO MC and/or NLO pQCD with initial/final state radiation effects (resummation??)
From our results:
g/g is (likely) mostly small or even negative(?)
There is a slight hint that it may be positive, and larger at large x

28. Conclusions
Although (systematic) errors are large, this is the most sophisticated direct extraction of g/g so far (besides indirect NLO fits)
Note that effects like pT smearing also influence higher energy (DIS and pp experiments)
We think that the conservative linear adding of systematic model uncertainties is covering for the unknown systematics, i.e.,
the uncertainty due to the Pythia model
the uncertainty due to the NLO corrections

29. BACKUP Slides

30. 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

31. 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

32. 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)

33. 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)

34. 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

35. 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)

36. 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!)

37. 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