Event Shape Variables in Deep Inelastic Scattering at HERA

1

• 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

2
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 Planks Constant Q related to momentum of
photon
Size of proton 1 fm HERA can probe to
0.001 fm
3
Perturbative and Nonperturbative Regimes

• Quantum Chromodynamics (QCD)
• strong interactions mediated by gluon
• Coupling as Q2 increases, ?S(Q2) decreases
• Examine Perturbative ? Nonperturbative

Perturbative Q2 large Nonperturbative Q2 small
Can expand with ?S Cant expand in ?S
High energy scale ?Small distances Low energy scales ? Large distances
4
HERA Description

• 920 GeV p
• 27.5 GeV e- or e
• 318 GeV cms
• 50 TeV Fixed Target
• Instantaneousluminosity max 1.8 x 1031 cm-2s-1
• 220 bunches
• 96 ns crossing time
• IP90mA p ?
• Ie40mA e ?

DESY Hamburg, Germany
5
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) ZEUS Luminosities (pb-1) 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
6
ZEUS Detector
7
ZEUS Angles
8
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
9
Kinematic Reconstruction

• Four Measured Quantities Ee, ?, Eh, ?.

(p,E) conservation
?
?
DIS Event
Variable Electron Method (Ee,?) Jacquet-Blondel (Eh,?) Double Angle (?,?)
Q2
X
y
10
HERA Kinematic Range

• Q2 sxy
• 0.1 lt Q2 lt 20000 GeV2
• 10-6 lt x lt 0.9
• 50 TeV Fixed Target Experiment

11
Deep Inelastic Scattering Cross Section

• DIS Cross Section Given by Structure Functions
  F2, F1, xF3

12
DIS Event
13
Naïve Quark Parton Model

• Scattering on proton is sum of elastic scattering
  on all of the protons constituents (partons)
• Point-like Partons
• Structure Functions quantify distribution of
  particles and their momentum
• Parton Distribution Functions (PDF)
• Must be derived from experiment

Bjorken Scaling Only x dependence
14
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
15
Jets

• Colored partons evolve to a roughly collinear
  spray of colorless hadrons
• ? JETS
• Partons gt Hadrons gt Detector schematically

As observed
As produced
16
Jet Finding

• Uses ET and R
• Issues seed, infrared unsafe
• Combines jets if dij is smallest of di,dij
• Issues none known

Cone Method
KT Method
17
Dijets

• Direct gluon coupling
• Opportunity to directly examine QCD effects
• Dominant QCD diagrams for dijets

Boson Gluon Fusion
QCD Compton
18
Dijet Event
jet
jet
19
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

20
Current Hemisphere of Breit Frame
DIS Event

• e-p Breit frame
• photon is space like
• ?Quarks hadronization products in current
  hemisphere

Lab Frame
Breit Frame
PT
PL
Breit Frame
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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

22
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

23
Sphericity

• Describes isotropy of energy flow
• Measure of the summed p2T wrt. Sphericity axis

24
Aplanarity

• Describes energy flow out of Sphericity evt.
  plane
• Measure of pT out of plane

25
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
TM axis
Tm axis
26
Thrust and Sphericity
27
Broadening

• Broadening of particles in transverse momentum
  wrt. thrust axis
• ? BT, BW

28
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

29
Out-of-plane Momentum

• Energy flow out of event plane defined by proton
  direction and thrust major axis

30
Azimuthal Correlation

• Momentum weighted function of the azimuthal angle
  around the photon-proton axis in the Breit frame
  between pairs of hadrons.

?h
?h
pth
pth
31
Sphericity and Aplanarity in ee- LEP

• DELPHI 1993-1995, 1997
• 243 pb-1 (6K evts.)
• 48 lt ?s lt 189 GeV
• Good agreement between models and data
• Event shapes used in ee- annihilations to
  measure the running coupling

32
Thrust and Broadening at ZEUS

• ZEUS 1995-1997
• 48 pb-1 (321K evts.)
• 10ltQ2lt20480 GeV2
• 0.0006ltxlt0.6

33
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
• Study other frames

34
Background selection Timing
35
Event Selection E-pz
36
Monte Carlo Description
37
Size and Statistics

• Selection Cuts
• yJB gt 0.04
• yel lt 0.95
• Vertex with z lt 50 cm
• x gt 14 cm or y gt 14 cm
• 38 lt E-pZ lt 65 GeV
• Good positron with Eegt 10 GeV
• First Look 1999 positron data
• ZEUS on-tape 22 nb-1
• Cuts ? 6476 events

cm
Monte Carlo Data
GeV
38
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
39
Thrust

• Indicates collimated Y particle distribution

Log plot of 0.5 to 0.65
Monte Carlo Data
40
First Look at Out-of-Plane Momentum

• Plausible for a first pass
• More statistics and more work to come!

Log plot of 3.5 to 15
Monte Carlo Data
41
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

42
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