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Determination of g/g from Hermes High-p T hadrons. P.Liebing, RBRC, For the Hermes Collaboration. Spin 2006, Kyoto, Oct. 2006. Outline. Data sets and asymmetries Monte Carlo studies Extraction of g/g: Methods Extraction of g/g: Results. Data Set(s). - PowerPoint PPT Presentation
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Determination of g/g from Hermes High-pT hadrons
Spin 2006, Kyoto, Oct. 2006
P.Liebing, RBRC,
For the Hermes Collaboration
Outline
Data sets and asymmetries Monte Carlo studies Extraction of g/g: Methods Extraction of g/g: Results
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
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!
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 • !
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 €
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*q → q
QCD22
Integrating over pT, data and MC cross sections agree within 10-20%
Monte Carlo vs. Data
K-factors for hard QCD subprocesses according to B. Jäger et. Al., Eur.Phys. J. C44(2005) 533
Observed Cross Section vs. pT • Reason for disagreement at pT>1GeV: Increasing weight of NLO corrections
Monte Carlo: Fractions and Asymmetries
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!
Subprocess Asymmetries(using GRSV std.)
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
g/g Extraction: Method 1
Method 1: Assume that g/g(x) is flat or only very weakly dependent on x
Then:
And:
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)
g/g Extraction: Method 2
g/g Results Mean 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
1.05 < pT < 2.5 GeV
(deuteron,
antitagged,
4 pT bins)
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
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
BACKUP
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
g/g Results: Method 2 Final 2 functions used are
polynomials with 1(2) free parameters
Fix g/gx for x0 and g/g1 for x1 (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
Fit results
g/g Results: Method 2 2/ndf5.5: 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
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)
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
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)
Lower cuts on pT
1.051.0 2.0
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
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)
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)
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pTh = zˆ p T
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
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)
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!)
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
MC vs. (N)LO pQCD?
Cross sectionspT (of the hard subprocess)
and x distributions
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
Comparison of observed cross sections in tagged region
Data + MC agree well within 10-20% for variables integrated over pT
Monte Carlo vs. Data Pythia code has been modified/Parameters adjusted to match our
exclusive (Q2>0.1) and semiinclusive data (Q2>1)
Monte Carlo vs. Data
Data + MC agree vs. pT when taking NLO corrections into account
Polarized and unpol. cross Polarized and unpol. cross sections and k factors sections and k factors ((B.
Jäger et. al., Eur.Phys. J. C44(2005) 533))
Comparison of observed cross sections in antitagged region (vs. pT(beam))