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. 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 ~ fm

3. 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

4. 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

5. ZEUS Luminosities (pb-1)
HERA Data
Luminosity upgrade
5x increase in Luminosity
 expect 1 fb-1 by end of
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

6. 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

7. 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.

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

11. 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

12. DIS Event

13. 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

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 => Hadrons => Detector: schematically:
As produced
As observed

16. 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

17. 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

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
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

21. 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.

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
Study distributions of particles in the event
energy flow
angle

23. 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

24. 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

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
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

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

27. 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.

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
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.

30. 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

31. Sphericity and Aplanarity in e+e-: LEP
DELPHI: , 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

32. Thrust and Broadening at ZEUS
Q(GeV)
ZEUS:
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

33. Event Shape Study Collect event sample for 1999 data
22 pb-1 on tape
Extend data to 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?

34. Background selection: Timing

35. Event Selection: E-pz

36. 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

37. Monte Carlo Description

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 to 0.65
Tune the MC:
Only quarks: too collimated
Only gluons: too spherical
Monte Carlo
Data

40. 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

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