1 / 37

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.

taima
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related