Determination of g/g from Hermes High-pT 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) “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  QCD 22

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

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!

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:

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)

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

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 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

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

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 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

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

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)

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!)

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

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

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

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