Event Shape Variables in Deep Inelastic Scattering at HERA Preliminary Examination Adam Everett Outline Introduction HERA and ZEUS Deep Inelastic Scattering Jets Event Shapes Outlook

Size of proton ~ 1 fm HERA can probe to ~ 0.001 fm Study of Partons Particle Scattering Study charge & magnetic moment distributions Scattering via probe exchange Wavelength Special Case : Deep Inelastic Scattering High energy lepton transfers momentum to a nucleon via probe h : Plank’s Constant Q: related to momentum of photon probe rp  h/2 Size of proton ~ 1 fm HERA can probe to ~ 0.001 fm

Perturbative and Nonperturbative Regimes Quantum Chromodynamics (QCD): strong interactions mediated by gluon Coupling: as Q2 increases, S(Q2) decreases Examine: Perturbative  Nonperturbative S  photon quark lepton gluon Perturbative: Q2 large Nonperturbative: Q2 small Can expand with S Can’t expand in S High energy scale Small distances Low energy scales  Large distances QCD studies strong interactions Coupling : leads to two regimes of QCD

HERA Description 920 GeV p+ 27.5 GeV e- or e+ 318 GeV cms 50 TeV Fixed Target Instantaneous luminosity max: 1.8 x 1031 cm-2s-1 220 bunches 96 ns crossing time IP~90mA p+  Ie~40mA e+  HERA Information: Circumference: 6336 m Energies: e=27.5 GeV p=920 GeV Center of mass energy = 318 GeV Currents: e=40mA p=90mA Fixed target experiments: HERA-B and HERMES HERA-B: CP violation in the B system using p beam on fixed wires HERMES studies spin structure functions using l-polarized e beam on gas target PETRA = pre-accelerator for HERA DESY Hamburg, Germany

ZEUS Luminosities (pb-1) HERA Data Luminosity upgrade 5x increase in Luminosity  expect 1 fb-1 by end of 2006 Measured polarization between 60-70% Spin-rotators for polarized measurement ZEUS Luminosities (pb-1) # events (106) Year HERA ZEUS on-tape Physics e-: 93-94, 98-99 27.37 18.77 32.01 e+: 94-97, 99-00 165.87 124.54 147.55

ZEUS Detector 99.7 % of solid angle covered (not area around beam-pipe) Asymmetrically designed because of boost from p Major Components: CTD, Uranium Calorimeter, small angle rear tracking detector & rear Presampler, hadron electron separator, veto wall and C5 counter, luminosity monitor

ZEUS Angles  = -3.0  = 174.3o  = 1.1  = 36.7o  = -0.75  = 129.1o Pseudorapidity rocks because changes in eta are invariant under Lorentz boosts along the beam direction.

Kinematic Variables Center of mass energy of the *P system Square of momentum transfer Energy transfer to struck parton: 0  y  1 (Momentum fraction of struck parton)/P: 0 x  1 s = Center of mass energy

Kinematic Reconstruction Four Measured Quantities: Ee’, , Eh, . (p,E) conservation   DIS Event Variable Electron Method (Ee’,) Jacquet-Blondel (Eh,) Double Angle (,) Q2 X y

~ 50 TeV Fixed Target Experiment HERA Kinematic Range Q2 = sxy 0.1 < Q2 < 20000 GeV2 10-6 < x < 0.9 ~ 50 TeV Fixed Target Experiment

Deep Inelastic Scattering Cross Section e(k’) e(k)  *(q) p(P) Jet DIS Cross Section: Given by Structure Functions: F2 : parameterizes the interaction between transversely polarized photon and spin ½ partons FL : parameterizes the interaction between longitudinally polarized photons and the proton xF3 : parity violating term due to the Weak interaction DIS Cross Section: Given by Structure Functions: F2, F1, xF3

DIS Event

Naïve Quark Parton Model Scattering on proton is sum of elastic scattering on all of the proton’s constituents (partons) Point-like Partons Structure Functions: quantify distribution of particles and their momentum Parton Distribution Functions (PDF) Must be derived from experiment e(k’) e(k)  *(q) p(P) Jet Scattering on proton is sum of elastic scattering on all of the proton’s constituents (partons) Point-like Partons No transverse momentum Don’t interact with each other Structure Functions: quantify distribution of particles and their momentum How the proton “looks” to the boson F2 is charge weighted sum of parton momentum densities. Parton Distribution Functions (PDF) Must be derived from experiment Momentum distribution of the parts Bjorken Scaling: Only x dependence

QCD Theory Gluons: vector colored bosons carry strong force Gluons produce quark and gluon pairs Quarks gain transverse momentum Gluon-driven increase in F2 Bjorken Scaling Violation: Fi(x) Fi(x,Q2) Observation of QCD effects  Small x

Jets Colored partons evolve to a roughly collinear “spray” of colorless hadrons  JETS Partons => Hadrons => Detector: schematically: As produced As observed

Jet Finding Uses ET and R Issues: seed, infrared unsafe R Combines jets Issues: none known Cone Method R i j KT Method Cone Method Maximize ET within a cone of radius R Conceptually easy Implementation issues Seed requirements Infrared unsafe at NNLO KT Method Combine i and j if dij is the smallest of {di,dij} Smaller hadronization corrections in some regions No known implementation issues

Dijets Direct gluon coupling Opportunity to directly study QCD effects Dominant QCD diagrams for dijets: Boson Gluon Fusion QCD Compton QCD laboratory Can still use kinematic variables Applied slightly differently

Dijet Event jet jet

Study Jets in Breit Frame “The Brick Wall Frame” In leading order: struck quark turns around  Single jet event: jet has no ET Dijet event: jets balanced in ET Breit Frame : helps with multijet identification

Current Hemisphere of Breit Frame DIS Event e-p+ : Breit frame photon is space like Quark’s hadronization products in current hemisphere Lab Frame Breit Frame PT e-e+: photon is timelike no 3-momentum components e-p+ : in the Breit frame the photon is spacelike Final-state particles are assigned to the current region if the longitudinal component of their momentum is negative interpreted as products of the hadronization of the current quark PL Breit Frame

Methods to Study QCD QCD Effects – Gluons Evolution of Quark Distributions Gluons change quark distributions Indirect – inferred from quark distribution Dijets Direct – gluons observed as jets Complexity of jet reconstruction and identification Event Shapes Energy and particle flow Direct – gluon radiation changes event shapes Do not need to reconstruct jets Reduce dependence on hadronization We have already briefly discussed 1 and 2. Now we will focus on 3.

Event Shapes Event Energy Distribution Event Particle Angle Distribution Define Event Shape Variables to examine (next slides) General: Sphericity of the particle distribution Aplanarity Specific: Thrust Broadening wrt. thrust axis Out-of-Plane Momentum Azimuthal Correlation Study distributions of particles in the event energy flow angle

Sphericity Describes isotropy of energy flow Measure of the summed p2T wrt. Sphericity axis 2, 3 are the smallest eigenvalues of the tensor v1 : eigenvector – defines sphericity axis v1,v2: eigenvectors - span sphericity event plane Measure of the summed p2T with respect to the axis minimizing this sum

Aplanarity Describes energy flow out of Sphericity evt. plane Measure of pT out of plane S=A=0 S=3/4 A=0 S=1 A=1/2 S = 2A = 1 for ideal spherical event S = ¾, A = 0 for planar circular event S = A = 0 for linear events

Thrust in DIS Linear collimation of hadronic system along a specified (“thrust”) axis T interpretation depends on choice of axis: Four Thrusts in DIS: TZ, TM, Tm, TC TC axis TZ axis Describes the “pencil-likeness” of the event. Thrusts are longitudinal projections onto a special unit vector (axis). T interpretation depends on choice of axis: TZ: axis = *-proton axis Sum all charged hadrons in current region of Breit Frame TC: axis = “Thrust Axis” chosen so that Thrust is maximized TM: axis = “Thrust Major” chosen to maximize Thrust in plane  to *-proton axis Tm: axis = “Thrust Minor” chosen normal to z axis AND Major axis TM axis Tm axis

Thrust and Sphericity T=1 S=0 T=3/4 S=1/2 S=1 T=1/2

Broadening Broadening of particles in transverse momentum wrt. thrust axis  BT, BW BT  0 BT  1/2 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.

Event Plane Scattering of two objects occurs in a plane Parton Model Event Plane defined by two vectors Example : lepton-lepton’ Conservation of vector momentum

Out-of-plane Momentum Energy flow out of event plane defined by proton direction and thrust major axis With the photon-proton axis and the Thrust Major axis, we can easily define an event plane. Events with more than two scattered particles will have some amount of momentum out of the event plane.

Azimuthal Correlation Momentum weighted function of the azimuthal angle around the photon-proton axis in the Breit frame between pairs of hadrons. h 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. h’ pth’ pth

Sphericity and Aplanarity in e+e-: LEP DELPHI: 1993-1995, 1997 243 pb-1 (6K evts.) 48 < s < 189 GeV Good agreement between models and data Event shapes used in e+e- annihilations to measure the running coupling e+ e- q

Thrust and Broadening at ZEUS Q(GeV) ZEUS: 1995-1997 48 pb-1 (321K evts.) 10<Q2<20480 GeV2 0.0006<x<0.6 Some models better than others Event shape variables, which have been successful in ee annihilation are now being applied to ep DIS. ZEUS has measured successfully some of these. T-gamma: requires smaller hadronization correction than T-c – contrary to the theoretical expectation of a similar correction B-gamma poorly fitted by DISENT T-c and B-c show smaller x-dependence than B-gamma T-gamma

Event Shape Study Collect event sample for 1999 data 22 pb-1 on tape Extend data to 1996-2000 Sample 114 pb-1 Compare with theoretical Models implemented in Monte Carlo Simulations Choose one model for first look Later compare with other models Improvements Larger event sample Improved understanding of model and data ? Breit Frame?

Background selection: Timing

Event Selection: E-pz

Size and Statistics Selection Cuts First Look: 1999 positron data yJB > 0.04 yel < 0.95 Vertex with |z| < 50 cm |x| > 14 cm or |y| > 14 cm 38 < E-pZ < 65 GeV Good positron with Ee’> 10 GeV First Look: 1999 positron data ZEUS on-tape 22 nb-1 Cuts  6476 events cm yJB > 0.04 to insure good reconstruction of the hadronic system and reject kinematic peak events. KP: due to finite resolution of CAL, the measured energy of the scattered positron in KP events can be larger than kinematically allowed. yEL < 0.95 removes residual events in which a photon or pion fakes a scattered positron in the very forward region of the calorimeter, beyond the acceptance of the CTD. Vertex w/ z-cut: ensures the event is well contained within the CAL and CTD acceptance regions and that vertex available to accurately reconstruct scattering angles. |X| or |Y| impact of scattered positron: avoids low acceptance region near RCAL beam-pipe E-pz: removes background photoproduction Monte Carlo Data GeV

Monte Carlo Description

Sphericity and Aplanarity Indicates many planar, back-to-back particles Log plot of 0.5 to 1 Log plot of 0.1 to 0.5 Monte Carlo Data

Thrust Indicates collimated “Y” particle distribution Log plot of 0.5 to 0.65 Tune the MC: Only quarks: too collimated Only gluons: too spherical Monte Carlo Data

First Look at Out-of-Plane Momentum First look has reasonable agreement More statistics and more work to come! Log plot of 3.5 to 15 Monte Carlo Data

Future Plan of Analysis Enlarge event sample to full data set (’96-’00) 114pb-1 on tape (over 140% increase over previous results) Compare high statistic data to various models with Monte Carlo simulations Study systematic effects

Conclusions Study of Event Shapes in DIS at HERA Should provide a powerful method to study QCD Examine the connection between Perturbative and Nonperturbative regimes Reduce dependence on hadronization and jet reconstruction Provides a direct observation of gluon radiation First look shows acceptable level of agreement Larger sample available for good statistics