Transcript Preliminary Examination

Search for BFKL Dynamics in
Deep Inelastic Scattering at HERA
Preliminary Examination
Sabine Lammers
University of Wisconsin
December 20, 2000
Sabine Lammers, UW Madison
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HERA Collider
HERA: an electron-proton accelerator at DESY
•820/920
GeV proton
•27.5 GeV electrons or positrons
•300/318 GeV center of mass energy
•220 bunches, 96 ns crossing time
•Instantaneous luminosity: 1.8 x 1031 cm-2s-1
•currents: ~90mA protons, ~40mA positrons
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Luminosity
total integrated luminosity: 185 pb-1
A currently undergoing luminosity upgrade
A 1 fb-1 expected by end of 2005
A
 significant yearly improvement
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Zeus Detector
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Zeus Geometry
h=1.1
BCAL
h=-0.75
FCAL
RCAL
h=-3.4
p q=p
h=3.8
q=0 e+
h= -ln[tan(q/2)]
=
Calorimeter: alternating layers of depleted
uranium and scintillator.
· 99.7% solid angle coverage
· Energy resolution: 35%/÷E for hadronic section
18%/E for electromagnetic
=
Central Tracking Detector: drift chamber
· 1.43 T solenoid
· vertex resolution: 1mm transverse, 4mm in z
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Zeus Trigger
= First level
• dedicated hardware
• no deadtime
• global and regional
107 Hz crossing rate
105 Hz background rate
10 Hz physics rate
energy sums
• isolated muon and
positron recognition
• track quality
information
=
Second Level
•
•
•
•
=
timing cuts
E-pz
simple physics filters
vertex information
Third Level
• full event information
available
• advanced physics
filters
• jet and electron finding
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DIS Kinematics
s2 = (p+k)2 ~ 4EpEe = (318 GeV)2 center of mass
energy
Q2 = -q2 = -(k-k')2
the square of the four
momentum tran
2
Q
x=
2pq
fraction of proton's momentum
carried by the struck parton
pq
pk
fraction of positron's energy
transferred to the proton in the
proton's rest frame
y=
Q2 = sxy
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Deep Inelastic Scattering
Event
Q2 ~ 3700
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x ~ .15
y ~ .21
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Kinematic Reconstruction
=
Electron Method - use scattered electron energy, angle
Q2 = 2EE´(1+cosqe)
´
y = 1 - E (1-cosqe)
2E
E´(1+cosqe)
E
x= (
P 2E-E´(1-cosqe)
)
best resolution at high y and low Q2
=
Double Angle Method - use leptonic, hadronic angles
cos Óh =
(Spx)2+(Spy)2-(S(E-pz))2
(Spx)2+(Spy)2+(S(E-pz))2
sin Óh
´
E DA = 2E
sinqe+sinÓh-sin(qe+Óh)
Q2DA
4E2sinÓh(1+cosqe)
sinqe(1-cosÓh)
xDA= sy
Q2DA=sinÓ +sinq -sin(q +Ó ) yDA=
sinÓh+sinqe-sin(qe+Óh)
DA
h
e
e
h
depends only on energy ratios 1
less sensitive to energy scale uncertainties
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Kinematic Range
Q~1/l describes our ability to "see" inside the proton.
Qo
Q > Qo
resolution
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improved resolution
HERA reaches
values of Q that
correspond to
distances of ~.001 fm.
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DIS Cross Section
For neutral current processes, the differential cross section is:
d2s(epeX) 2pa2em
dx dQ2
=
xQ4
[Y+F2(x,Q2) HY-xF3(x,Q2) - y2FL(x,Q2)]
YG = 1G(1-y)2
The structure function F2 parameterizes the interaction between
transversely polarized photon and spin ½ partons.
The structure function FL parameterizes the interaction between
longitudinally polarized photons and the proton.
The structure function xF3 is the parity violating term due to the
presence of the weak interaction.
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Quark Parton Model
The structure function F2 can be expressed in terms of
the quark distributions in the proton:
F2(x,Q2) = S Aq(Q2) ·(xq(x,Q2) + xq(x,Q2))
quarks
parton distribution functions
q(x,Q2) and q(x,Q2) , called parton
distribution functions, are the
For Q2<MZ2, the coefficient
average number of partons
Aq(Q2) approaches eq2, the
with momentum fraction
charge of the quarks, and
between x and x+dx
F2NC reduces to F2EM.
inside the proton.
=
Naive Quark Parton Model
 No interaction between the partons
 Proton structure function independent of Q2
 Interpretation: partons are point-like particles
 Bjorken Scaling F2(x,Q2) F2(x), FL=0
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QCD
Quarks only account for half of the proton's momentum
 introduce gluons
as
(a)
as
as
(b)
(c)
The relevant strong interactions are given by splitting functions,
which are related to the probabilities that
(a) a gluon splits into a quark-antiquark pair
(b) a quark radiates a gluon
(c) a gluon splits into a pair of gluons
Prediction: presence of gluons will break Bjorken scaling
gluon driven scaling violation
Parton-parton interactions are
mediated by gluons, generating
transverse momentum of the
partons.
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Scaling Violation
scaling
violation
scaling
" gluon density can be extracted from fits of F2 along lines
of constant x
2
g x,Q 
dF 2 x,Q 2
dlnQ 2
" gluons account for nearly half the momentum of the proton
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QCD Evolution - DGLAP
A powerful mechanism in QCD is the ability to predict the PDF
at a selected x and Q2, given an initial parton density.
The DGLAP equations evolve the quark and gluon densities in
the proton as follows:
dq i x,Q
d lnQ
2
2
2
s Q

2
1
dz
z
x
2
qi y,Q P qq
x
x
2
 g y,Q P qg
z
z
splitting functions
-calculable by QCD
dg x,Q 2
d lnQ
2
2
s Q

2
1
dz qi
x
z
2
y,Q P gq
x
x
2
 g y,Q P g g
z
z
The splitting functions are the probabilities for a quark or gluon
to split into a pair of partons.
In the evolution of the PDF's, there are terms proportional to
lnQ2, ln(1/x), and lnQ2 ln(1/x).
DGLAP Approximation:
2
2
" sums terms ln Q , lnQ ln(1/x)
" limited range of validity
s Q 2 ln
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1
 1
x
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Dijet Processes
Direct measurement of the gluon distribution
- how well does perturbative QCD and DGLAP
evolution describe events with jets?
A investigate dijet production in DIS
A kinematic range easily accesible at HERA
Leading Order QCD Diagrams:
Boson-Gluon Fusion
QCD Compton
Now the fraction of the proton's momentum carried
by the parton 2is:
M jj
Mjj = dijet mass
x 1
2
Q
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LO Monte Carlo Models
"Monte Carlos" are event generators that attempt to reproduce
theoretically predicted cross section distributions.
Dijet leading order monte
carlo models include:
LO matrix elements for
two parton final state
" higher order effects
" parton showers
" non-perturbative effects
" hadronization
"
DGLAP Evolution
LO monte carlo programs: ARIADNE, LEPTO, HERWIG
= LO matrix element
" ARIADNE, LEPTO and HERWIG use the Feynman
inspired calculation of the matrix element
= Parton Showers
" LEPTO, HERWIG use parton showers that evolve
according to the DGLAP Equation
" ARIADNE uses the color dipole model, in which each
pair of partons is treated as an independent radiating dipole.
= Hadronization
" LEPTO, ARIADNE use the Lund String Model
" HERWIG uses Cluster Fragmentation
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NLO Calculations
At next to leading order, a single gluon emission is
included in the dijet final state
Next to leading order calculations include:
" matrix elements for three parton final states
" soft/collinear gluon emissions
" virtual loops
They do not include:
" parton showering
" hadronization
Uncertainties:
renormalization scale: scale at which the strong
coupling constant as is evaluated
A factorization scale: scale at which the parton
densities are evaluated
A
NLO calculations: MEPJET, DISENT, DISASTER++
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96/97 Dijet Cross Section
Measurement
Data Sample: 38.4 pb-1 of data taken in 1996 and 1997
Event Selection Cuts: 10 < Q2 < 10,000
y > 0.04
electron energy > 10 GeV
Jet cuts: jet ET > 5 GeV
-2.0 < h < 2.0
leading jet ET > 8 Lab Frame
GeV
subleading jet ET > 5
GeV
Breit Frame
}
}
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Breit Frame
Dijet identification is easier in the Breit Frame
single jet event in
Breit Frame
Definition:
 quark rebounds off photon with
equal and opposite momentum
 axis is the proton-photon axis
 photon is completely space-like:
its 4-momentum has only a zcomponent
 outgoing jet has no ET
In dijet events, the outgoing jets
are balanced in ET
QCD Compton
event in Breit Frame
A cut on the jet ET removes single jet events
from the dijet sample
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Jet Finder
Inclusive mode kT cluster algorithm:
i
j
Combine particles i
and j into a jet if di,j is
smaller of {di,di,j}.
di = ET,i2
di,j = min{ET,i2,ET,j2}(Dh2+Dj2)/R2
Repeat algorithm with all calorimeter cells.
Preferred over cone algorithms because:
"
"
"
"
no seed requirements
same application to cells, hadrons, partons
no overlapping jets
infrared safe to all orders
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Agreement with DGLAP
Comparison of the data with the NLO calculation that uses
a DGLAP model for the PDF's has shown good agreement
- a triumph for pQCD!
Questions remain:
" large renormalization scale uncertainty
" h > 2 region not investigated
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Dijet cross section vs. h
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Why BFKL?
DGLAP: In the perturbative expansion of the parton densities,
only terms proportional to (ln Q2)n are kept and
summed to all orders.
1
At small values of x, terms in the evolution that contain ln x
are no longer negligible.
1/x
BFKL, another evolution of the PDF's, includes
terms1ln in its sum.
x
saturation
non-perturbative
region
BFKL Evolution
high energy limit
limiting case of
large gluon density
DGLAP Evolution
Q2
BFKL provides an evolution in x at fixed Q2,
given a starting distribution at xo.
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BFKL
The BFKL Equation is:
3 s 2  k T f x,k T  f x,k T

kT  ' 2

'2
2
1

kT k T
0 kT
ln
x
2
'2
f x,k T
'2
2
2
f x,k T
'4
4
4k T  k T
where the gluon density is defined to be:
Q
2
dk T2
xg x,Q 2 
0
2
kT
f x,k 2T
The forward jet cross section has been calculated:
forward jet
x jet
x
4ln2 s
N
c

Q2

p2t
Expanding,
1
s N c

4ln2log
2
x jet
1 s N c

4ln2log
2

x
x
x jet
2 1 
Q
 ...
p 2t
expansion in ln(1/x)
The first term of this expansion is similar to the NLO
calculation in DGLAP perturbation theory.
The range of applicability is:
s ln Q 2  1
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s ln O 1
x
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Gluon Ladder
HERA
forward
region
DGLAP: x = xn < xn-1 < ... < x1, Q2 = k2T,n >> ... >>
k2T,1
BFKL : x = xn << xn-1 << ... << x1, no ordering in kT
If the BFKL signature is observable, we should
find additional contributions to the hadronic
final state from high transverse momentum
partons going forward in the HERA frame.
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Forward Jets at Zeus
Previous Measurement
Data Sample: 6.36 pb-1 taken in 1995
Analysis done in lab frame
Jet finding with cone algorithm
Selection Cuts
• 4.5 x 10-4 < x < 4.5 x 10-2 range in x limited by resolution and
choice of binning
•
•
•
•
•
•
Ee > 10 GeV good electron
y > 0.1 sufficient hadronic energy away from forward region
0.5 < E2T,Jet / Q2 < 2 selects BFKL phase space
ET,Jet > 5 Gev good reconstruction of the jet
hJet < 2.6 experimental limitations
xJet > 0.036 selects high energy jets at the bottom of the
gluon ladder
• pZ,Jet (Breit) > 0 rejects forward jets with large xBj (QPMevents)
rejects leading order jets from the quark box
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Results of the 1995 Forward
Jets analysis
None of the models used describes the cross section
over the entire x range investigated
Issues:
all monte carlo models understimate the data at low x
" LO monte carlo models are not consistent with each other
" LDC underestimates measured forward jet cross section
"
results inconclusive
LDC, the Linked Dipole Chain model, implements the structure
of the CCFM Equation, intended to reproduce DGLAP and BFKL
in their respective ranges of validity.
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Proposal
Proposal: Test perturbative QCD in a new kinematic
range, applying knowledge acquired from
the dijet analysis.
Challenges: find kinematic region where
"
measurement uncertainties are small
"
theoretical uncertainties are small
"
BFKL effects potentially large
1
forward jet region
We expect a successful measurement because of:
"
Increased statistics by 17x  higher jet ET
1 smaller hadronization corrections
1 improved jet purities and efficiencies
"
Better understanding of DGLAP from dijet analysis
1 Jet finding in Breit Frame using kT algorithm
"
Better understanding of theoretical calculations
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Analysis Method
Plan: Measure the forward jet rate and compare
to QCD based Monte Carlo predictions and
analytical calculations based on DGLAP,
BFKL and CCFM evolution.
Data Sample: 1996,1997,1999,2000 data is available
Use leading order monte carlos for detector corrections
Studies needed:
A jet finding purities and efficiencies
A hadronizationl corrections
A systematic uncertainties
A energy scale uncertainty
Compare forward jet cross section with NLO
calculation, using jets found in the Breit Frame and
reconstructed using the kT method
look for excess above DGLAP prediction
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Data Sample
1996-1997 integrated luminosity = 38.4 pb-1
1999-2000 integrated luminosity = 67.7 pb-1
"
new detector component: Forward Plug Calorimeter
" increases eta range by 1 unit
1996 NC DIS
uncorrected for acceptance
BCAL/FCAL crack
highest ET
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Calorimeter Energy Scale
Uncertainty
Scheme: In QPM events, the scattered positron and the
jet are balanced in ET in the laboratory frame.
Assuming the reconstructed electron energy is reliable, the
jet transverse energy should be the same as the positron's.
uncertainty 
MC
slope data
slope
E vs E
E vs E
jet
t
e
t
jet
t
e
t
MC
jet
vs Eet
t
slope E
uncertainty
Preliminary Conclusion: energy uncertainty is within 3%
h
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Summary
"
"
"
"
A departure from parton evolution described
by DGLAP at low x is theorized
Forward region is the best place to look for
low x, BFKL signature dynamics
96/97 dijets analysis laid out standards with
which to make a solid cross section
measurement
data exists
jet h
reference
frame
jet
finder
DGLAP
order
6.36 pb-1 >5 GeV
<2.6
Lab
cone
LO
106 pb-1 >>5 GeV
>2.6
Breit
kT cluster
NLO
Forward Jet
statistics
95
measurement
proposed
mesurement
jet ET
Conclusion: A measurement of forward jet
cross section is warranted because we have
the possibility to learn more about pQCD.
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Pseudorapidity
E p 
1
rapidity ln
2
E p 
p  p

1
pseudorapidity ln
ln tan
2
p p 
2
Lorentz boost along the beam direction:
h = h + f(v)
h is shifted by an additive constant
Dh is unaffected
The form of the transverse energy distribution
in h-j space is the same in all frames
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Comparison of Data and Monte
Carlo Distributions
Jet quantities
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Preliminary Exam
Comparison of Data and Monte
Carlo Distributions
Event quantities
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3
6
FPC
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