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 €

* → qq

€

*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))