Transcript Event Shape Variables and DIS at HERA

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
Event Shapes, A. Everett, U. Wisconsin
Preliminary Exam, August 30, 2002 - 1
Study of Partons
Particle Scattering
• Study charge & magnetic moment distributions
• Scattering via probe exchange

• Wavelength  
Q
h : Plank’s Constant
Q: related to momentum of photon
• Special Case : Deep Inelastic Scattering
• High energy lepton transfers momentum to a nucleon via probe
probe
lepton
Size of proton ~ 1 fm
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HERA can probe to ~ 0.001 fm
Preliminary Exam, August 30, 2002 - 2
Perturbative and
Nonperturbative Regimes
Quantum Chromodynamics (QCD):
• strong interactions mediated by gluon
lepton

photon
quark




S

gluon
S
S
Coupling: as Q2 increases, S(Q2) decreases
Perturbative: Q2 large
Can expand with S
High energy scale
Small distances
Nonperturbative: Q2 small
Can’t expand in S
Low energy scales
 Large distances
Examine: Perturbative  Nonperturbative
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Preliminary Exam, August 30, 2002 - 3
HERA Description
•
•
•
•
920 GeV p+
27.5 GeV e- or e+
318 GeV cms
50 TeV Fixed Target
L
DESY Hamburg, Germany
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Rtot  (
I tot
 is
I0
) R0
Instantaneous
luminosity max:
1.8 x 1031 cm-2s-1
• 220 bunches
• 96 ns crossing time
IP~90mA p+ 
Ie~40mA e+ 
Preliminary Exam, August 30, 2002 - 4
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
Year
ZEUS Luminosities (pb-1)
HERA
ZEUS on-tape
e-: 93-94, 98-99
e+: 94-97, 99-00
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27.37
165.87
18.77
124.54
# events (106)
Physics
32.01
147.55
Preliminary Exam, August 30, 2002 - 5
ZEUS Detector
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Preliminary Exam, August 30, 2002 - 6
ZEUS Angles
 = 1.1  = 36.7o
 = 0.0  = 90.0o
 = 3.0  = 5.7o
 = -0.75  = 129.1o
 = -3.0  = 174.3o

   ln(tan( ))
2
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Preliminary Exam, August 30, 2002 - 7
Kinematic Variables
Center of mass energy of the *P system
W 2  ( q  p) 2
Q2  q 2  k  k 
2
pq
y
pk
2pq
x
Q2
s  ( p  k )2
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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
Preliminary Exam, August 30, 2002 - 8
Kinematic Reconstruction
Four Measured Quantities: Ee’, , Eh, .


Q 2  sxy
DIS Event
Variable
Q2
X
y
(p,E)
conservation
Electron Method
(Ee’,)
2Ee E(1  cos )
Ee
E1  cos 
E p 2 E p  E(1  cos )
E
1
(1  cos )
2 Ee
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JacquetBlondel (Eh,)
Double Angle
(,)
pT2 , h
(1  cos )  sin 
sin   sin   sin(   )
1  y JB
2
QJB
s  y JB
Eh  pz ,h
2Ee
2
QDA
s  y DA
(1  cos )  sin 
4 Ee2
sin   sin   sin(   )
Preliminary Exam, August 30, 2002 - 9
HERA Kinematic Range
Q2 = sxy
0.1 < Q2 < 20000 GeV2
10-6 < x < 0.9
~ 50 TeV Fixed Target
Experiment
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Preliminary Exam, August 30, 2002 - 10
Deep Inelastic Scattering
Cross Section
e(k)
e(k’)
*(q)
p(P)


Jet
2
d 2 (e  p)
2

2
2
E
(
x
,
Q
)


F

y
FL   xF3
 2
2
4
dxdQ
xQ


  1  (1  y) 2
DIS Cross Section:
Given by Structure Functions: F2, F1, xF3
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Preliminary Exam, August 30, 2002 - 11
DIS Event
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Preliminary Exam, August 30, 2002 - 12
Naïve Quark Parton Model
Scattering on proton is sum of elastic scattering
on all of the proton’s constituents (partons)
e(k)
Point-like Partons
e(k’)

*(q)
p(P)

Jet
Structure Functions: quantify distribution of
particles and their momentum
F2   ei2 xfi ( x)
i
Fi  Fi (x)
Bjorken Scaling: Only x
dependence
Parton Distribution Functions (PDF)
• Must be derived from experiment
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Preliminary Exam, August 30, 2002 - 13
QCD Theory
Gluons: vector colored bosons carry strong force
• Gluons produce quark and gluon pairs
• Quarks gain transverse momentum
 Small x
• Gluon-driven increase in F2
Bjorken Scaling Violation: Fi(x) Fi(x,Q2)
Observation of QCD effects
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Preliminary Exam, August 30, 2002 - 14
Jets
Colored partons evolve to a roughly collinear
“spray” of colorless hadrons
 JETS
• Partons => Hadrons => Detector: schematically:
As produced
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As observed
Preliminary Exam, August 30, 2002 - 15
Jet Finding
Cone Method
R
• Uses ET and R
• Issues: seed, infrared
unsafe
R  ( ) 2  ( ) 2
i
KT Method
j
di  ET2,i
• Combines jets if dij is
smallest of {di,dij}
• Issues: none known
(( ) 2  ( ) 2 )
dij  min{E , E }
R2
2
T ,i
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2
T, j
Preliminary Exam, August 30, 2002 - 16
Dijets
Direct gluon coupling
• Opportunity to directly examine QCD effects
• Dominant QCD diagrams for dijets:
Boson Gluon Fusion
QCD Compton
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Preliminary Exam, August 30, 2002 - 17
Dijet Event
jet
jet
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Preliminary Exam, August 30, 2002 - 18
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
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Preliminary Exam, August 30, 2002 - 19
Current Hemisphere of Breit
Frame
e-p+ : Breit frame
• photon is space like
Quark’s
hadronization
products in current
hemisphere
PT
Breit Frame
Breit Frame Lab Frame
DIS Event
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PL
Preliminary Exam, August 30, 2002 - 20
Methods to Study QCD
QCD Effects – Gluons
1. Evolution of Quark Distributions
•
•
Gluons change quark distributions
Indirect – inferred from quark distribution
2. Dijets
•
•
Direct – gluons observed as jets
Complexity of jet reconstruction and identification
3. Event Shapes
•
•
•
•
Energy and particle flow
Direct – gluon radiation changes event shapes
Do not need to reconstruct jets
Reduce dependence on hadronization
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Preliminary Exam, August 30, 2002 - 21
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
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Preliminary Exam, August 30, 2002 - 22
Sphericity
Describes isotropy of
energy flow
• Measure of the
summed p2T wrt.
Sphericity axis
3
S  (2  3 )
2


p
p

i
i
S   i
 2
 pi
i
0  S 1
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Preliminary Exam, August 30, 2002 - 23
Aplanarity
Describes energy flow out of Sphericity evt. plane
• Measure of pT out of plane
3
A  3
2
S=A=0
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1
0 A
2
S=3/4 A=0
S=1 A=1/2
Preliminary Exam, August 30, 2002 - 24
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
Tk  max
nˆ k

i pi  nˆk
i pi
nˆ M  zˆ  0 nˆm  zˆ  0
TC axis
TZ axis
k  C, M , m
1
2
TM axis
 T 1
Tm axis
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Preliminary Exam, August 30, 2002 - 25
Thrust and Sphericity
T=1 S=0
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T=3/4 S=1/2
S=1 T=1/2
Preliminary Exam, August 30, 2002 - 26
Broadening
Broadening of particles
in transverse
momentum wrt. thrust
axis
BT  0
Thrust Axis
 BT, BW
 
pi  nT

i
Bk 

i pi
BT  0.5
BT  B1  B2
BW  max{B1 , B2 }
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Preliminary Exam, August 30, 2002 - 27
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
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Preliminary Exam, August 30, 2002 - 28
Out-of-plane Momentum
Energy flow out of
event plane defined
by proton direction
and thrust major axis
'
K out   phout
h
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Preliminary Exam, August 30, 2002 - 29
Azimuthal Correlation
Momentum weighted
function of the
azimuthal angle
around the photonproton axis in the
Breit frame between
pairs of hadrons.
H    
h,h '
pth pth'
    hh ' 
2
Q
 hh '   h   h '     hh '  
 hh '     hh '
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0   
h
h’
pth’
pth
Preliminary Exam, August 30, 2002 - 30
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+eannihilations to measure
the running coupling
e+
e-
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q
q
Preliminary Exam, August 30, 2002 - 31
Thrust and Broadening at
ZEUS
ZEUS: 1995-1997
 48 pb-1 (321K evts.)
 10<Q2<20480 GeV2
 0.0006<x<0.6
Q(GeV)
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Q(GeV)
Preliminary Exam, August 30, 2002 - 32
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
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Preliminary Exam, August 30, 2002 - 33
Background selection: Timing
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Preliminary Exam, August 30, 2002 - 34
Event Selection: E-pz
Photoproduction DIS
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Preliminary Exam, August 30, 2002 - 35
Monte Carlo Description
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Preliminary Exam, August 30, 2002 - 36
Size and Statistics
Selection Cuts
•
•
•
•
•
•
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
cm
First Look: 1999 positron data
• ZEUS on-tape 22 nb-1
• Cuts  6476 events
Monte Carlo
Data
GeV
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Preliminary Exam, August 30, 2002 - 37
Sphericity and Aplanarity
Log plot of 0.5 to 1
• Indicates many planar, back-to-back particles
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Log plot of 0.1 to 0.5
Monte Carlo
Data
Preliminary Exam, August 30, 2002 - 38
Thrust
Log plot of
0.5 to 0.65
• Indicates collimated “Y” particle distribution
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Monte Carlo
Data
Preliminary Exam, August 30, 2002 - 39
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
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Preliminary Exam, August 30, 2002 - 40
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
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Preliminary Exam, August 30, 2002 - 41
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
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Preliminary Exam, August 30, 2002 - 42