1. Event Shapes in NC DIS at ZEUS
Alexander A. Savin
University of Wisconsin
On Behalf of the ZEUS Collaboration
DIS 2006, Tsukuba, Japan

2. HERA Kinematic Variables
Breit Frame Definition:
q + 2xBP = 0
Q2, xBj, y
27.5 GeV
920 GeV
W: invariant mass of the system recoiling against the scattered lepton
y: measures inelasticity of interaction. y=1 – E’_e/E_e in proton rest frame
Related to scattering angle **************
y=0: totally elastic
x=0 when y=1. y=0 when x=1.
ZEUS (82.2 pb-1)
80 < Q2 < GeV2
< x < 0.6
DESY , hep-ex/

3. Similar for the means and differential distributions
Power Corrections
Use power corrections to correct for non-perturbative effects in infrared and collinear safe event shape variable.
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.
Universal non-perturbative constant
Similar for the means and differential distributions

4. Analysis Method
Test validity of the power correction method by extracting
from a fit to the data.
For means: NLO + PC as a function of Q
(DISASTER++/DISENT)
For differentials: NLO + NLL + PC in bins of (x,Q2)
(DISASTER++/DISPATCH/DISRESUM)
Hessian method was used

5. Event-shape variables
Axis Dependent:
TT, BT, T, B
Thrust
Broadening
Axis Independent:
C, M2
C Parameter
Jet Mass
Sums are over all momenta in the current hemisphere of the Breit frame

6. Mean Event Shapes Comparison with the ARIADNE
Parton level should be taken as indicative only
Explain (and label) power correction and that one is negative
Add first bullet: NLO + PC to agree with data
Label and explain the double value thing

7. Mean Event Shapes Negative power correction Results of the NLO+PC fit
Simultaneous fit for s and 0
Each shape fit separately
NLO calculation using DISASTER++
Negative power correction
Explain (and label) power correction and that one is negative
Add first bullet: NLO + PC to agree with data
Label and explain the double value thing

8. Mean Event Shapes Extracted parameters: Theoretical errors dominate.
Consistent with the previous measurement
Extracted 0 are consistent (except Tg ) with each other, slightly lower than H1
Extracted s values are consistent with each other, except BT and Tg
High sensitivity of T to PDF
Theoretical errors dominate.
World Average

9. Shape Distributions Only high Q region is used
ARIADNE describes data well
Only high Q region
is used

10. Shape Distributions NLO+NLL+PC NLO+NLL
The differential distributions are fitted over a limited range.
Bins for which theoretical calculations are not expected to be valid are omitted from fit.
NLO+NLL+PC
NLO+NLL

11. Shape Distributions
The differential distributions are fitted over a limited range.
Bins for which theoretical calculations are not expected to be valid are omitted from fit.

12. Extracted Parameters Extracted parameters
Extracted s values are consistent with each other and H1
Major theoretical uncertainties
Fit range ;
Theoretical parameters: renormalization scale, logarithmic rescale factor, power factor in modification term etc

13. Test of Q-independency
Consistent with being independent of the Q range

14. Event Shapes With Jets 2 jets
y2 – resolution cut parameter (2+1) to (1+1) ;
KOUT – out-of-plane momentum
2 jets
Momentum out of plane

15. y2 parameter ARIADNE describes data well at high Q ;
NLO describes data without hadronization correction
LO: Leading order O(alpha_s) correction computed with DISENT
Res: resummation of all leading next-to-leading logarithms of k/Q
NP: leading 1/q non-perturbative corrections

16. Out-of-plane momentum
LO: Leading order O(alpha_s) correction computed with DISENT
Res: resummation of all leading next-to-leading logarithms of k/Q
NP: leading 1/q non-perturbative corrections
ARIADNE describes data well
indicating significant hadronization corrections

17. Summary
Mean values and differential distributions of event-shape variables have been measured at ZEUS in the kinematic region
80 < Q2 < GeV2 and < x < 0.6
The data are well described by the ARIADNE MC
Power-correction method provides a reasonable description of the data for all event-shape variables with  for most of the variables.
The lack of consistency in the (aS,a0) extraction suggests the importance of high-order processes that are not yet included in the model
Need some theoretical input to proceed with the jets event shapes