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Determination of thegluon polarisation at HERMES

N. Bianchi

on behalf of:

The HERMES Collaboration

&

The main analyzers (P.Liebing, E.Aschenauer, R.Fabbri, V.Mexner, …)

N.Bianchi, Pacific SPIN07, Vancouver BC

How to measure DG: indirect

For fixed target exp. small x-Q2 lever arm:

g (andq)very badly determined : G 0,5 1

N.Bianchi, Pacific SPIN07, Vancouver BC

How to measure DG: direct (general)

Method: Photon-Gluon-Fusion

Charm-production :

PGF dominated and hard scale by the mass of c-Quarks

Open charm: clean process (no charm quarks in the nucleon wave function)

N.Bianchi, Pacific SPIN07, Vancouver BC

How to measure DG: direct (high pt)

- Open charm needs very high energy to access to charm production (CERN, RHIC experiments)
- At HERMES hidden charm (J/y) is produced and identified :
- low statistics
- less clean channel due to VMD contribution and FSI

Best direct way for HERMES to measure DG:

(Pairs of) hadrons with high transverse momenta (Hard scale: pt = 1 – few GeV range)

N.Bianchi, Pacific SPIN07, Vancouver BC

First HERMES measurement

A. Airapetian et al, Phys. Rev. Lett. 84 (2000) 2584

First longitudinal double spin asymmetries for 2 hadrons

Historical plot : first HERMES data and future projections

N.Bianchi, Pacific SPIN07, Vancouver BC

Old HERMES data

Following SLAC pioneristic measurement on un-tagged single hadron asymmetry ..

Proton Deuteron

HERMES preliminary 2001

…. the differences between the curves (BBS) are less than the differences between any of the curves and the data. This makes it impossible to draw any conclusions about DG(x). ….The present data will provide valuable experimental constraints on such models, and perhaps lead to constraints on the gluon polarization in the nucleon in the future. (E155 - Phys.Lett.B458 (1999) 536)

N.Bianchi, Pacific SPIN07, Vancouver BC

New HERMES data

- improved statistics
- both H and (high statistics) D longitudinally polarized target
- new anti-tagged analysis
- improved a lot the MC knowledge and tuning
- systematic studies
- different channels (anti-tagged, tagged, pairs)

N.Bianchi, Pacific SPIN07, Vancouver BC

Asymmetries (anti-tagged)

•Anti-tagged data:

‣Scattered lepton not

in acceptance

‣pt measured with

respect to beam axis

‣for pt>1.05 GeV : 1272k(419k) for deuteron (proton) sample

•Curves from MC

+asymmetry model using:

‣Δg/g(x)=0 : central

‣Δg/g(x)=-1 : upper

‣Δg/g(x)=+1 : lower

Δg/g(x)=0 asymmetry is due to quarks (DIS at large Q2 and x at large “fake” pT)

Gluons become important for above pt ≈ 1 GeV

N.Bianchi, Pacific SPIN07, Vancouver BC

Asymmetries (tagged)

•Tagged data:

‣Scattered lepton detected

in acceptance

‣pt measured with

respect to virtual photon

‣Q2>0.1 GeV2, W2>4 GeV2

‣for pt>1 GeV : 53k (19k) for deuteron (proton) sample

•Curves from MC

+asymmetry model using:

‣Δg/g(x)=0 : central

‣Δg/g(x)=-1 : upper

‣Δg/g(x)=+1 : lower

Δg/g(x)=0 : large and stable asymmetry is due to quarks in DIS events

averaged in the HERMES acceptance

N.Bianchi, Pacific SPIN07, Vancouver BC

Asymmetries (hadron pairs)

•Anti-tagged data for pairs of charged-hadrons:

‣No regards on scattered lepton (10% are detected)

‣pt measured with respect to beam axis

‣pt(h1,h2) > 0.5 GeV

‣for >2 GeV2 :60k (20k) for deuteron (proton) sample

‣plotted vs. lower cut on:

•Curves from MC+asymmetry model using:

‣Δg/g(x)=0 : central

‣Δg/g(x)=-1 : upper

‣Δg/g(x)=+1 : lower

N.Bianchi, Pacific SPIN07, Vancouver BC

Extraction(general)

•Measured asymmetry is an incoherent superposition of different hard and soft subprocess asymmetries:

Signal: Gluon of the nucleon in the initial state

Background: all other sub-processes ➟ MC

Lepto : LO and NLO DIS but no photoproduction

Pythia : DIS but also non perturbative model for photoproduction

N.Bianchi, Pacific SPIN07, Vancouver BC

MC Models

- •MC model
- ‣PYTHIA 6.2 ,tuned and adapted for HERMES data
- fragmentation process, intrisic kt, exclusive ρ0 cross section (VMD)
- •Provides
- ‣kinematics of the hard subprocess
- ‣relative contributions fi of the background and signal subprocesses in the relevant pt range
- ‣background asymmetries and the hard subprocess asymmetries
- -weight calculated for every MC event
- -PDFs (unpol/pol):
- Hard process CTEQ5L/GRSV2000 (nucleon)
- Hard resolved photon processes SaS2/GRS (photon)
- -Asymmetry assumptions for soft processes:
- A=0 for exclusive/diffractive processes
- A~A1(low x) from world data for soft nondiffractive (“low-pT”)
- •Vary PDFs/assumptions for syst. error

N.Bianchi, Pacific SPIN07, Vancouver BC

Subprocesses

N.Bianchi, Pacific SPIN07, Vancouver BC

Subprocesses

Antitagged, Charge combined, Deuteron data

VMD(elast.+diffr., soft low-pT):

decreasing with pT

DIS:

increasing (dominating) with pT

QCDC/QCD2->2(q):

increasing with pT

Signal processes are PGF and

QCD2>2(g) (resolved photon)

N.Bianchi, Pacific SPIN07, Vancouver BC

Asymmetries of Subprocesses

Antitagged, Charge combined, Deuteron data

DIS increasing with pT(x):

positive

QCDC/QCD2->2,VMD:

flat and smallbut important for background asymmetry!

|PGF| increasing with pT:

negative

QCD2->2(g):

opposite to PGF, small

N.Bianchi, Pacific SPIN07, Vancouver BC

Dg/g extraction:methods I and II

- Method I:
- Factorize
- Assumes
- No sign change in â(x)
- “flat” g/g(x)
- No information on <x> of measurement
- Gives average g/g over covered x range (0.07<x<0.7)

- Method II:
- Fit: find a g/g(x) such that
- Assumes functional form for g/g(x)
- Only small range in pT
- Gives g/g(x) and average x of measurement

N.Bianchi, Pacific SPIN07, Vancouver BC

DG from method I

Assuming Dg(x)/g(x) const over x :

h+,h- antitagged:

4 points between

1.05<pT<2.5 GeV

h+,h- tagged:

1 point for

pT>1 GeV

Pairs:

1 point for

GeV2

Only statistical errors are shown

- Results for different data samples (diff. mixtures) agree within statistics
- Consistency between the two hadron charges and the two targets
- Dominating sample: Deuteron antitagged -> Used for Method II and syst. error analysis (charge combined)

N.Bianchi, Pacific SPIN07, Vancouver BC

DG from method II

(Anti-tagged only)

- Several test functions
- Final 2 functions used are polynomials with 1(2) free parameters
- Fix:

- g/gx for x0

- g/g1 for x1

- |g/g(x)|<1 for all x
- Difference between functions is a systematic uncertainty

- Light shaded area: range of all data
- Dark shaded area: fit center of gravity (span of the 4 pt bins)

N.Bianchi, Pacific SPIN07, Vancouver BC

DG from method II

- 2/ndf5 mainly due to highest pT point
- Model systematic is not included in fit
- 1-2 parameter function is too smooth
- function 1 used as default and function 2 for systematics

N.Bianchi, Pacific SPIN07, Vancouver BC

Model systematic

- PYTHIA 6.2 has been tuned:
- fair agreement in tagged region
- (see plot vs kinematic variables)
- less agreement in anti-tagged region
- some failures in pt dependence
- checks with LO pQCD (collinear)

- Uncertainties from each group
- PYTHIA params.
- PDFs
- low-pT asym.

summed linearly to “Models” uncertainty

- Experimental (stat.+syst.) added in quadrature
- syst. uncertainty (beam&target) from 4% scaling uncertainty to 14% on g/g

N.Bianchi, Pacific SPIN07, Vancouver BC

Results vsworld data

•Black and blue curves:

pQCD fits to g1

•Black data points:

CERN exp results

•Red data point:

Prel. HERMES Method I

•Red curves

Prel. HERMES Method II: fit Δg(x)/g(x) with 2 functions such that

N.Bianchi, Pacific SPIN07, Vancouver BC

Conclusions

g/g has been extracted by HERMES using two different methods

Method I

+0.125

g/g(x,2) = 0.078 ± 0.034(stat) ± 0.011 (sys-exp) (sys-model)

-0.082

Method II

-0.127

g/g(x,2) = 0.071 ± 0.034(stat) ± 0.010 (sys-exp) (sys-model)

-0.105

Syst. model uncertainties still dominating (PDFs, PYTHIA model)

- DG/G is likely small
- DG/G is unlikely to solve the puzzle of the nucleon missing spin

N.Bianchi, Pacific SPIN07, Vancouver BC

Back up slides

N.Bianchi, Pacific SPIN07, Vancouver BC

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