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Determination of  g/g from Hermes High-p T hadrons

Determination of  g/g from Hermes High-p T hadrons. P.Liebing, RBRC, For the Hermes Collaboration. RHIC Spin Collaboration Meeting, Tokyo, Sep. 2006. Outline. Data sets and asymmetries Monte Carlo studies Extraction of  g/g: Methods Extraction of  g/g: Results. Hermes and HERA.

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Determination of  g/g from Hermes High-p T hadrons

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  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 60-90 s • Beam polarization measured every  1min

  6. Measured Asymmetries • Antitagged Data: • Pairs: • Tagged 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 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. VMD- direct anomalous photon 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) • ... „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 variablesintegrated over pT

  10. Polarized and unpol. cross sections and k factors (B. Jäger et. al., Eur.Phys. J. C44(2005) 533) Monte Carlo vs. Data Comparison of observed cross sections in antitagged region (vs. pT(beam)) 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. 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 • 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 Fit results • Light shaded area: range of data • Dark shaded area: center of gravity for fit

  21. g/g Results: Method 2 • 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 MC and data asymmetries for pT>1.05 GeV

  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: • 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. 1.05 1.0 2.0 Lower cuts on pT g/g Extraction: Cuts • 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)

  31. Systematics: PDFs • Standard PDFs used: • 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: 0.14-0.18 (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

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