Transcript No Slide Title

Jet Physics at the
Tevatron
Sally Seidel
University of New Mexico
XXXVII Rencontres de Moriond
For the CDF and D0
Collaborations
An overview of selected jet studies by
CDF and D0 in 2001-2.
1. Jets at CDF and D0
2. Inclusive Jet Production (CDF)
3. Inclusive Jet  and ET Dependence
(D0)
4. s from Inclusive Jet Production
(CDF)
5. Inclusive Jet Cross Section using
the kT Algorithm (D0)
6. Ratios of Multijet Cross Sections (D0)
7. Subjet Multiplicity of g and q Jets
using the kT Algorithm (D0)
8. Charged Jet Evolution and the
Underlying Event (CDF)
Jet distributions at colliders can:
• signal new particles + interactions
• test QCD predictions
• improve parton distribution
functions
CDF (D0) data quality and reconstruction
requirements:
• |zvertex | < 60 (50) cm to maintain projective
geometry of calorimeter towers.
• 0.1 (0.0)  |detector|  0.7 (0.5) for full
containment of energy in central barrel.
• To reject cosmic rays + misvertexed events,
define = missing
E T ET. Require
E T
E
6
(CDF)
T
all
E T< (30 GeV or 0.3ETleading jet,
whichever is larger).
(D0)
• Reconstruct jets using a cone algorithm
2
2
R






 0.7
with cone radius
• Apply EM/HA + jet shape cuts to reject
noise fakes.
Next correct for
•Pre-scaling of triggers.
•Detection efficiencies (typically 94 –100%).
•underlying event + multiple interactions.
•“smearing” of the data: the effects of
detector response and resolution.
•If > 1 primary vertex:
•choose vertex with 2 highest ET jets.
(CDF).
•choose 2 vertices with max track
multiplicity, then choose the one with
 jet
minimum  E .
(D0)
No correction is made for jet energy
deposited outside the cone by the
fragmentation process, as this is included in
the NLO calculations to which the data are
compared.
The Inclusive Jet Cross
Section, E·d3/dp3
CDF
• For jet transverse energies achievable
at the Tevatron, this probes distances
down to 10-17 cm.
•
d 3  1
E 3  
dp
 2ET
 d 2 


 dET d 

N
ET    L
This is what’s measured.
The CDF result for unsmeared
data:
(88.8 pb-1)
(20.0 pb-1)
s  1800GeV
New in this analysis: compare raw data
to smeared theory. This uncouples the
systematic shift in the cross section
associated with smearing from the
statistical uncertainty on the data.
•Consider only uncorrelated
uncertainties first.
•Develop a 2 fitting technique that
includes experimental uncertainties, to
quantify the degree to which each theory
reproduces the data.
Define
nbin
 
2
t
i 1
(nd (i)  nt (i))2

2
t
8
 s
k 1
2
k ,t
where:
nd = observed # jets in bin i
nt = predicted # jets in bin i
t = uncertainty on prediction
sk,t= shift in kth systematic for tth
theoretical prediction
Term 1: uncorrelated scatter of points
about a smooth curve
Term 2: 2 penalty from systematic
uncertainties
Begin with nt0: nominal prediction by
theory t. Smear prediction separately for
each systematic uncertainty k to get
smeared prediction ntk. The systematic
uncertainty in bin i is then
ft (i)  n (i)  n (i)
k
k
t
0
t
Predicted # jets in bin i is
8
nt (i)  n   sk ,t  f t (i)
0
t
k
k 1
Use this nt(i) to calculate (uncorrelated)
statistical uncertainty. The sk are chosen
to minimize total 2 using MINUIT.
Example resulting 2 values:
CTEQ4M: 63.4
CTEQ4HJ: 46.8
MRST: 49.5
This suggests that CTEQ4HJ best
describes the data. But combinations of
the 8 systematics can cancel. To study
this, redo the fit separately for every
combination of systematics. For:
NO systematics:
2 = 94.2
4 systematics:
best 2 = 47.6
8 systematics:
best 2 = 46.8
The normalization systematic can be
cancelled by shape systematics.
To extract confidence levels:
•Generate fake raw data (“pseudoexperiments”) using CTEQ4HJ. Predict
nominal # entries for each of the 33 bins.
Vary each prediction with 33 (statistical)
+ 8 (systematic) random numbers.
Assume systematics are gaussian but ET
dependent. Repeat for other PDF’s.
•Fit each pseudo-experiment to the
nominal PDF prediction using 2.
T itle:
c his qr_s ame_hj_mrst.eps
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Calculate 2 between data and smeared
theory. Integral of the distribution above
this 2 is the CL.
Results, for 33 dof:
CTEQ4HJ: 10% CL
MRST: 7% CL (relatively high value
because normalization systematic is
cancelled by shape systematics).
All other PDF’s: < 5% CL
CTEQ4M: 1.4% CL, change in
agreement with data above 250 GeV
cannot be accounted for.
CDF conclusion on inclusive jet cross
section measurement:
•predictions using CTEQ4HJ have best
agreement with data in both shape and
normalization before considering
systematics.
•when systematics are included, some
combinations cancel out to produce only
small changes in the spectrum shape.
CTEQ4HJ provides the best prediction,
followed by MRST.
•CDF Run Ib data are consistent with
Run Ia and with NLO QCD given the
flexibility allowed by current knowledge
of PDF’s. CDF is also consistent with
D0.
The Inclusive Jet Cross
Section versus
Pseudorapidity and ET
D0
Extends the kinematic range
beyond previous measurements:
T itle:
fi g0.dvi
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D0 result, with cone algorithm, for
95 pb-1 at 1800 GeV:
T itle:
fi g1_new_c ol.dvi
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2 Comparison of D0 data and theory:
i.) Define
 2   Di  Ti  C 1 ij D j  T j  , where
i, j
i  bin #
D  number of jets observedin thedata
T  number of jets predictedby thetheory
C  uncertainty covariancematrix
ii.) Construct the Cij by analyzing the
correlation of uncertainties between
each pair of bins. (Bin-to-bin
correlations for representative bins are
~ 40% + positive.)
iii.) There are 90 -ET bins.
Conclusions:
PDF
2/dof
Probability
CTEQ4HJ
0.66
0.99
MRSTg
0.95
0.63
CTEQ4M
1.03
0.41
MRST
1.26
0.05
Measurement of s from
Inclusive Jet Production
CDF
The cross section and s are related at
NLO by:
d
  s2 Xˆ ( 0) (  F , ET ) 
dET
1   s ( R )k1 ( R ,  F , ET )
In the Tevatron ET regime,
non-perturbative contributions are
negligible.1
1S.D.
Ellis et al., PRL 69, 3615 (1992).
Procedure:
•The Xˆ ( 0) and k1 are calculated with
JETRAD1 for given2 matrix elements, in
the MS scheme. Clustering and cuts are
applied directly to the partons.
•The 33 ET bins provide independent
measurements at 33 values of R = F.
•Evolve the measured s values:
s
 a (M Z ) 
1   s (  R )(b0  b1 s (  R )) ln( R / M Z )
b0 
b1 
1W.
33  2n f
,
6
306  38n f
24 2
Giele et al., PRL 73, 2019 (1994) and Nucl. Phys. B403, 633 (1993)
2R.K. Ellis and J. Sexton, Nucl. Phys. B 269, 445 (1986).
•Result, for 87 pb-1, with CTEQ4M :
•Average of results is s =
0.0081
0.0095
0.1178 0.0001 (stat)
(exp.syst.).
•s evolution verified for 40 < ET <
250 GeV :
27 values of s(MZ) are
ET-independent.
T itle:
plots.dvi
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ET (GeV)
Theoretical uncertainties due to:
ET/2 <  < 2ET:
6%
 4%
PDF:
5%
(extracted s values are consistent with
those in PDF’s.)
1.3 < Rsep < 2.0: 2-3%
T itle:
plots.dvi
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The Inclusive Jet Cross
Section using the kT
Algorithm
D0
The kT algorithm differs from the cone
algorithm because
•Particles with overlapping calorimeter
clusters are assigned to jets
unambiguously.
•Same jet definitions at parton and
detector levels: no Rsep parameter
needed.
•NNLO predictions remain infrared
safe.
The kT algorithm successively merges
pairs of nearby objects (partons,
particles, towers) in order of increasing
relative pT.
Parameter D controls the end of
merging, characterizes jet size.
Every object is uniquely assigned to one
jet.
Infrared + collinear safe to all orders.
D0 kT Algorithm1:
1) For each object i with pTi, define
dii = (pTi)2
2) For each object pair i, j, define
•(Rij)2 = (ij)2 + (ij)2
•dij = min[(pTi)2,(pTj)2]·(Rij)2/D2
3) If the min of all dii and dij is a dij, i
and j are combined; otherwise i is
defined as a jet.
4) Continue until all objects are
combined into jets.
5) Choose D = 1.0 to obtain NLO
prediction identical to that for R = 0.7
cone.
1Based
on S.D. Ellis and D. Soper, PRD 48. 3160 (1993).
kT jets do not have to include all objects
in a cone of radius D, and may include
objects outside cone.
D0 result for 87 pb-1, unsmeared data,
||<0.5, statistical errors only:
T itle:
hc_out.eps
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Theory below data by 50% at low pT,
by (10 - 20)% for pT > 200 GeV/c.
NLO predictions with kT and cone are
within 1%.
Cross section measured with kT is 37%
higher than with cone.
T itle:
este.eps
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Effect of final state hadronization
studied with HERWIG:
T itle:
hc_out.eps
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For 24 d.o.f., 2 calculated with
covariance technique:
PDF
2/dof
Prob.
MRST + hadr.
CTEQ4HJ + hadr.
MRST
MRSTg
CTEQ4M
MRSTg
1.00
1.01
1.12
1.17
1.30
1.38
0.46
0.44
0.31
0.25
0.15
0.10
Ratios of Multijet Cross
Sections
D0
This study measures
 ( pp  n jets  X; n  3)
R32 
 ( pp  m jets  X; m  2)

as a function of HT  E Compare
to JETRAD with CTEQ4M for several
choices of renormalization scale using a
2 covariance technique.
jet
T .
Recall F controls infrared divergences;
R controls ultraviolet. Assume R= F.
Test four options:
jet
E
•R =  T for leading 2 jets and
(a) R =  E
jet
T
also for third jet.
(b) R = ET for third jet.
(c) R = 2ET for third jet.
•R = 0.6 ETmax for all 3 jets.
Result, for 10 pb-1:
T itle:
/home/gall as /mul t/eps /r32_ht_203040_nt.eps
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•No prediction accurately describes the
data throughout the full kinematic
region.
•A single R assumption is adequate:
introduction of additional scales does
not improve agreement with data.
• R = 0.3 E
data.
jet
T
is consistent with the
Subjet Multiplicity of Gluon
and Quark Jets Reconstructed
with the kT Algorithm
D0
This study examines
•pT and direction of kT jets
•event-by-event comparison of kT and
cone
•multiplicity structure of quark and
gluon jets
Calibration of jet momentum:
p
true
jet

p
meas
jet
 poffset ( , L, p )
jet
jet
T
R( jet , p jet )
where
poffset  punderlying  penviron
R  detectorresponse
To find penviron (from U noise, multiple
interactions, pile-up) : overlay HERWIG
events with zero-bias (random crossing)
events at various luminosities.
Observation: penviron for (D = 1.0) kT is
50-75% higher (i.e., 1 GeV/jet) than for
(R = 0.7) cone.
To find punderlying:
(1) overlay HERWIG events with
minimum-bias (coincidence in
hodoscopes) data at low luminosity
(negligible environment)
(2) overlay HERWIG events with zerobias events at low luminosity
(3) subtract: (1) - (2).
Observation: punderlying for (D = 1.0) kT is
30% higher than for (R = 0.7) cone.
To find R:
(1) calibrate EM energy scale with Z, J,
0 decays
(2) require pT conservation in -jet
events:
Rcalorimeter  1 

E T  nˆT
p T
R consistent for kT and cone jets.
Comparison of kT and cone jet
reconstruction for 2 leading jets in 69k
Run 1b events:
99.94% of jets reconstructed within
R < 0.5.
T itle:
ps/prd/v42/kt_cone_delta_r.eps
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pTkT
jet
systematically higher than ETcone jet
by 3-6%:
T itle:
ps/prd/v43/kt_cone_delta_et.eps
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Subjets
Reapply kT algorithm to each jet, using
its preclusters, until all remaining
objects have
d ij  min(p , p
2
T ,i
2
T, j
)
R
2
ij
D
2
 ycut p ( jet)
2
t
These are subjets, defined by fractional
pT and separation in space. Multiplicity
M depends on:
•color factor (gluon > quark)
• s
•ycut:
ycut = 0  M = # preclusters
ycut = 1  M = 1
Choose ycut = 10-3.
Select gluon-enriched and quarkenriched data samples:
PDF data show that fraction of gluon
jets decreases with x  pT/ s .
•Select jets with same pT at
s = 630 GeV and s = 1800 GeV
for 2-jet events.
•Use HERWIG with CTEQ4M to
predict gluon jet fraction f. LO
calculation is algorithm-independent.
T itle:
ps/prd/v45/isi d34_cut_integ_100_big.eps
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•Identify reconstructed jets with type of
nearest parton. Gluon jet fractions for
55 < pT < 100 GeV/c:
f1800: 0.59
f630: 0.33
Multiplicity M measured in the data is
related to gluon jet multiplicity Mg and
quark jet multiplicity Mq by:
M  fM g  (1  f )M q
For Mg, Mq independent of
s
,
(1  f 630 ) M 1800  (1  f1800 ) M 630
Mg 
f1800  f 630
and
f1800 M 630  f 630 M 1800
Mq 
f1800  f 630
•Correct result for shower detection
effects in calorimeter.
Mean subjet multiplicities:
•gluon jets: 2.21  0.03
•quark jets: 1.69  0.04
after unsmearing,
r
M g 1
M q 1
T itle:
ps/prd/v63_color/d0c qg_color.eps
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 1.84  0.15  00..22
18
Charged Jet Evolution and
the Underlying Event
CDF
A two-part analysis: Data are compared
to HERWIG, ISAJET, and PYTHIA for
• observables associated with the
leading charged jet: the hard scatter.
•global observables used to study the
behavior of the underlying event.
The data:
•minimum bias (one interaction each
with forward + backward beam-beam
counters) and charged jets with ||<1,
50 GeV/c > pT > 0.5 GeV/c.
•measured in the central tracker:
pT/pT2  0.002 (GeV/c)-1
•impact parameter cut, vertex cut, to
ensure 1 primary vertex.
•no correction for track finding
efficiency (92% correction applied to
models).
The models:
•pthard > 3 GeV/c, to guarantee
22 ‹ total inelastic
•All assume superposition of
•the hard scatter
•the underlying event: beam-beam
remnants, initial state radiation, and
multiple parton scattering
•but different models for underlying
event...
•HERWIG: soft collision between 2
beam “clusters.”
•ISAJET: “cut Pomeron” similar to soft
min bias. Independent fragmentation
allows tracing of particles to origin:
beam-beam, initial state rad, hard scatter
+ final state rad.
•PYTHIA: non-radiating beam remnants
+ multiple parton interactions with
different effective minimum pT options:
0, 1.4, and 1.9 GeV/c. No independent
fragmentation: cannot distinguish initial
from final state radiation but can
distinguish beam-beam.
The standard CDF jet algorithm based
on calorimeter towers is not directly
applicable to charged particles. A naive
jet algorithm is used because it can be
applied at low pT:
•define jet as a circular region with
radius
R   2   2  0.7
•Order all charged particles by pT.
•Start with particle with pTmax , include
in the jet all particles within R = 0.7.
Recalculate centroid after each addition.
•Go to next highest pT particle and
construct new jet around its R = 0.7.
•Continue until all particles are in a jet.
•Jet can extend beyond || < 1.
Results on the leading jet:
The QCD hard scattering models
describe these observables for the
leading (highest  pT ) charged jet well:
•multiplicity of charged particles
•size
•radial distribution of charged particles
and pT around jet direction
•momentum distribution of charged
particles
Charged particle clusters evident in the
minimum bias data above pT  2 GeV/c
 a continuation of the high pT jets in
the jet trigger samples.
To study the underlying event, global
observables
<charged multiplicity>
and
<  pT >
are correlated with angle  relative to
axis of leading jet. Region transverse to
leading jet (normal to the plane of the
22 parton hard scatter) is most
sensitive to beam-beam fragments and
initial state radiation.
Observation: <charged multiplicity> and
<  pT > grow rapidly with pTleading,
then plateau at pTleading > 5 GeV/c.
Plateau height in transverse direction is
half height in direction of leading jet.
PYTHIA 6.115 best model for
<charged multiplicity> in tranverse
region but over-estimates in direction of
leading jet. ISAJET shows right activity
but wrong pT dependence:
ISAJET uses independent fragmentation
(too many soft hadrons when partons
overlap) and leading log picture without
color coherence (no angle ordering
within the shower):
HERWIG + PYTHIA model hard scatter
(esp. initial state radiation) component
of underlying event best:
HERWIG lacks adequate pT:
Summary:
Many interesting and significant results
from D0 and CDF in
•Inclusive jets
•s
•kT algorithm
•Multijet production
•Particle evolution
•Underlying event
On to Run II!