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

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 98-00 (82.2 pb-1) 80 < Q2 < 20 840 GeV2 0.0024 < x < 0.6 DESY-06-042, hep-ex/0604032

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

Summary Mean values and differential distributions of event-shape variables have been measured at ZEUS in the kinematic region 80 < Q2 < 20 840 GeV2 and 0.0024 < 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 0 0.4-0.5 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