1. Event Shape Variables in DIS Update
A. Everett, A. Savin
University of Wisconsin
S. Hanlon, I. Skillicorn, A. Doyle
University of Glasgow
June 18, 2003

2. Approach to Non-Perturbative Calculations
pQCD prediction → measured distribution
Correction factors for non-perturbative (soft) QCD effects
Separates out non-perturbative corrections for any infrared safe event shape variable, F:
Power Correction
independent of any fragmentation assumptions
“non-perturbative parameter” – (Dokshitzer, Webber, Phys. Lett. B 352(1995)451)
Used to determine the hadronization corrections
Two realms: pQCD and npQCD. pQCD is calculable: uses alpha-s. npQCD is not. Recent theoretical work [2], involving power corrections to event shape variables, provides a new approach to determine the hadronisation corrections compared to monte carlo event generators. The new work involves a phenomenological model based around an effective strong coupling which comes in at low Q. This model conveniently reduces the hadronisation corrections to be of a form containing alpha-s and a new phenomenological variable alpha-0.
Define power correction…..
Why do we care? –> because we can’t calculate features of npQCD hadronization
Future plans involve the fitting of parton level next to leading order curves with power corrections to the mean distributions. This will then yield a value for not only alpha-s but also the new phenomenological variable alpha-0 and allow tests on its universality.
Relate hadronization effects to power corrections. Q dependence of the means of the event shape parameters is presented, from which both the power corrections and the strong coupling constant are determined without any assumption on fragmentation models.

3. Event Shape Variables
Previous event shape variables not well correlated with
Study:
New Variables in DIS*
Kout
Azimuthal Correlation (following slides)
*hep-ph/ and hep-ph/
Previous Variables from previous event shape analysis (differential distributions)
Q: Why are these variables better?
A1: They are new and haven't been studied before.
A2: If we believe the theorists, they are more sensitive and they can be used for a good study of QCD. Part of the reason they are more sensitive is because they start at the first order in alpha-s -- whereas the other variables are not.
Q: How will we use this with the previous measurements? How will we reconcile this with the values that are bad?
A: This is an independent analysis. Just as dijet studies are independent of event shape studies are independent of.... It can stand alone for extraction of alpha-s and alpha-0. Later, it may also be used as a complementary measurement with the previous measurements.

4. Kinematic Bins Mean of Event Shape Variables has a Q dependence.
Analysis done in bins of x and Q2.

5. Event Selection Selection Cuts Breit Frame Cuts Zufo Cuts
Q2DA  80 GeV2
yJB > 0.04
yel < 0.95
Vertex with |z| < 40 cm
|x| > 14 cm or |y| > 14 cm
38 < E-pZ < 65 GeV
44 < E-pZ for forward electron
Good positron
Sinistra Probability > 0.9
Ee’> 10 GeV
Breit Frame Cuts
Multiplicitycurrent ≥ 2
Ecurrent/Q > 0.25
For KOut, Acorr:
At least 2 Jets in Breit Frame:
E1,T > 6 GeV
E2,T > 5 GeV
PT,i,Lab  2 GeV
Zufo Cuts
Pt>0.15 GeV
|η|<2.2
good acceptance region

6. C Parameter
Compare previous event shape variables between two analyses
Some small disagreement for uncorrected monte carlo at the detector level, perfect agreement at the “truth” level
Uncorrected Ariadne at detector level
Everett •
Hanlon ┌
Collimated: values tend towards minimum
Isotropic: values tend towards maximum

7. Detector level Ariadne
Invariant Jet Mass
Everett •
Hanlon ┌
Analyses Comparison
Detector level Ariadne
Collimated: values tend towards minimum
Isotropic: values tend towards maximum

8. Energy Flow and Dijets: TT
TT axis
TM axis
TZ axis
Tm axis
axis
Everett •
Hanlon ┌
Detector Level Ariadne
Highlight: Inclusive dijet events are important because we know that everything out of the plane is either because of higher order (in alpha-s) pQCD effects (trijets etc) OR from soft effects (hadronization etc.). If we choose only 2-jet events, then we know everything out of the plane is because of soft effects!
Using a sample of well understood configurations (dijets) rather than the whole sample. 1) The corrections to well understood sample (configurations and calculations) should be better understood than the corrections to the whole sample. 2) Dijets provide the first sensitivity to alpha-s, thus we are cutting out all of the stuff that is not sensitive to alpha-s.
Highlight: We need to have an event plane. We can use dijets to define the plane OR we can use thrust to define the plane. Thrust is not what I am measuring, I am only using it to define the plane. Using jets is not as good because...
Collimated: values tend towards maximum
Isotropic: values tend towards minimum

9. Energy Flow and Dijets: T
TT axis
TM axis
TZ axis
Tm axis
axis
Detector Level Ariadne
Everett •
Hanlon ┌
Highlight: Inclusive dijet events are important because we know that everything out of the plane is either because of higher order (in alpha-s) pQCD effects (trijets etc) OR from soft effects (hadronization etc.). If we choose only 2-jet events, then we know everything out of the plane is because of soft effects!
Using a sample of well understood configurations (dijets) rather than the whole sample. 1) The corrections to well understood sample (configurations and calculations) should be better understood than the corrections to the whole sample. 2) Dijets provide the first sensitivity to alpha-s, thus we are cutting out all of the stuff that is not sensitive to alpha-s.
Highlight: We need to have an event plane. We can use dijets to define the plane OR we can use thrust to define the plane. Thrust is not what I am measuring, I am only using it to define the plane. Using jets is not as good because...
Collimated: values tend towards maximum
Isotropic: values tend towards minimum

10. Detector Level Ariadne
Broadening: BT
Broadening of particles in transverse momentum wrt. thrust axis
Everett •
Hanlon ┌
Detector Level Ariadne
BT  0
BT  0.5
Thrust Axis
Thrust describes the longitudinal projection, broadening describes the transverse projection. If you think of the event as being described by a cone, Thrust describes the altitude and Broadening the radius of the base.
Collimated: values tend towards minimum
Isotropic: values tend towards maximum

11. Detector Level Ariadne
Broadening: B
Broadening of particles in transverse momentum wrt. photon axis
Detector Level Ariadne
Everett •
Hanlon ┌
B  0
B  0.5
Photon Axis
Thrust describes the longitudinal projection, broadening describes the transverse projection. If you think of the event as being described by a cone, Thrust describes the altitude and Broadening the radius of the base.
Collimated: values tend towards minimum
Isotropic: values tend towards maximum

12. Out-of-plane Momentum
Examine New Variable:
Energy flow out of event plane defined by proton direction and thrust major axis
Sensitive to perturbative & non-perturbative contributions
Events with more than two scattered particles will have some amount of momentum out of the event plane.
With 2 jets, everything out of the plane is “extra.” It comes from either extra jets (higher order in alpha-s), or from non-perturbative QCD effects.

13. Theoretical Prediction for Kout
Prediction by Banfi, Marchesini, Smye, Zanderighi (hep-ph/ )
Plot ln(Kout/Q) since powers of ln(Kout/Q) used in resummation.
PT distribution independent of η cut for larger K/Q
xB = 0.1
Q = 30 GeV
y- = 0.1 < ykt < 2.5

14. Kout/Q Comparison Good agreement between Data and Ariadne
’98 – ’00 Data (Everett) •
Ariadne ┌
Kout/Q
< x < 0.010
320 < Q2 < 640 GeV2

15. Azimuthal Correlation
Examine New Variable:
Momentum weighted function of the azimuthal angle around the photon-proton axis in the Breit frame between pairs (h,h’) of hadrons. h
h’
pth’
pth
This is based on the Energy-Energy Correlation in electron-positron annihilation. EEC used the polar angle between outgoing particles, in DIS we will use the azimuthal angle.
Using the same event plane as for K_out and the photon-proton axis, we can define an azimuthal angle for the outgoing particles.
Illustrated are 2 of many outgoing particles. The observable is the transverse momentum weighted sum over all pairs of outgoing particles separated by a given angle.

16. ACorr Comparison Good initial agreement between Data and Ariadne
’98 – ’00 Data (Everett) •
Ariadne ┌
Add Data vs
MC Plots Here
/2  
< x < 0.6
80 < Q2 < GeV2

17. Summary Good agreement between Glasgow and Wisconsin Analyses
Complementary analyses
Agreement of differential distributions
Early look at new variables
Acceptable level of agreement
Plan :
Systematic studies
Different monte carlo models
Extract S,