Determination of g/g from Hermes High-pT hadrons

RHIC Spin Collaboration Meeting, Tokyo, Sep. 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

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 IDlepton/hadron contamination < 1%

Limited acceptance: 40mrad gap, |x|<170, | y|<140 mrad

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 hh 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

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

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)

Tagged Data: Pairs:

The g/g=0 asymmetry is due to quarks only!

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 • !

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) ...

VMD- direct anomalous photon

„„Soft“ VMD:Soft“ VMD:Elastic, diffractive Elastic, diffractive and nondiffractive and nondiffractive („minimum bias“,(„minimum bias“, „low-pT“) processes) processes

Hard VMD:Hard VMD: QCD 2QCD 22 2 processesprocesses

QCD-ComptonQCD-ComptonPGFLO DIS (virtual LO DIS (virtual photons)photons)

(QED) Splitting of (QED) Splitting of qqqq QCD 2QCD 22 2 processesprocesses

k⊥

p⊥

Q

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))

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

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

Monte Carlo: Fractions and Asymmetries Antitagged, charge combined Deuteron data:

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!

Subprocess Asymmetries(using GRSV std.)

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+ p2

T,2 > 2 GeV (pairs, 1 bin)

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

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 Extraction: Method 1

Method 1: Assume that g/g(x) is flat or only very weakly dependent on x

Then:

And:

g/g Results: Method 1

Comparison of results from all (almost independent) data sets

Results agree within statistics

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: 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 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

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 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

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

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

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

BACKUP Slides

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)

€

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!)

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