1. Light Jet reconstruction and calibration in
B.Andrieu (LPNHE, Paris)

2. Introduction: Cone Jet algorithm basics
Cone Jet algorithms
Associate “particles” inside a cone, where particles can be
partons (analytical calculations or parton showers MC)
“hadrons” = final state particles (MC particles or charged particles in trackers)
towers (or cells or preclusters or any localized energy deposit)
Calculate jet 4-momentum from “particles” 4-momenta
 Defined by Clustering procedure, Distance and Recombination scheme
Cone (proto-) jets are chosen as “stable” cones, i.e. cones whose geometrical position (axis) coincides with jet direction (3-momentum)
 How to find all stable cones in minimum CPU time?
Quark and gluon jets (identified to partons) can be compared to detector jets,
if jet algorithms respect collinear and infrared safety (Sterman&Weinberg, 1977)
QCD  {
Infrared unsafety
Collinear unsafety
Figures from hep-ex/
Problems of “naive” Cone Jet Algorithms using seeds
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

3. Introduction: the Ideal Jet Algorithm for Tevatron
Compare jets at the parton, hadron and detector level
 Jet algorithms should ensure
infrared and collinear safety
invariance under longitudinal boosts
fully specified and straightforward to implement
same algorithm at the parton, hadron and detector level
boundary stability (kinematic limit of inclusive jet cross section at ET = s/2)
factorisation (universal parton densities)
independence of detector detailed geometry and granularity
minimal sensitivity to non-perturbative processes and pile-up events at high luminosity
minimization of resolution smearing/angle bias
reliable calibration
maximal reconstruction efficiency (find all jets) vs minimal CPU time
replicate RunI cross sections while avoiding theoretical problems
General
Theory
Experiment
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

4. Introduction: RunII Cone Algorithm (hep-ex/0005012)
 2 new Cone Algorithms proposed for RunII (G.C. Blazey et al., “RunII Jet Physics”, hep-ex/ )
 Seedless Cone Algorithm  Almost ideal, but very computationally intensive
 RunII (= Improved Legacy or Midpoint) Cone Algorithm
= approximation of the seedless algorithm
QCD calculation at fixed order N  only 2N –1 possible positions for stable cones (pi , pi+pj , pi+pj+pk ,…)
Data: consider seeds used in RunI Cone algorithms as partons  in addition to seeds, use ‘midpoints’ i.e. pi+pj , pi+pj+pk ,…
only need to consider seeds all within a distance DR < 2Rcone
only use midpoints between proto-jets (reduce computing time)
otherwise algorithm similar to RunI
Other specifications of the suggested RunII cone Algorithm
E -scheme recombination = 4-momenta addition
use true rapidity Y instead of pseudo-rapidity h in DR
use all towers as seeds (pT > 1 GeV)
splitting/merging: pT ordered, f = 50 %
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

5. DØ calorimeter reconstruction
U/LAr calorimeter
Pseudo-projective geometry
~ cells, ~ 5000 towers
Granularity 0.1 x 0.1 in (h,f)
From cells to towers
Cells
Electronics calibration and baseline subtraction
Noise removal: 0-suppression (2.5 s), remove isolated cells (2.5/4 s)
(h,f) intercalibration using jets
EM cal calibrated using Z e+e-
 To each cell is associated a massless 4-vector (primary vertexcell center)
Towers
Combine (4-vector addition) all cells with non-0 signal in the same geometrical tower (pointing to detector center)
Towers may be massive
 Towers are basic objects used for jet reconstruction
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

6. DØ Run II Cone algorithm (I)
Algorithm defined in “RunII Jet Physics” (hep- ex/ )
parameters in green, changes w.r.t. definition in red
Reduce the number of seeds for clustering  Preclustering
seeds = pT ordered list of particles with pT >0.5 GeV (1 GeV in RunI)
reduce effect of noise in CH and ECMG  special treatment for towers if highest energy cell of a tower is in CH or ECMG, its energy is removed from the tower before applying the above minimum cut for seed selection
precluster = all particles in a cone of r = 0.3 around seed (for Cone Jets with Rcone  0.5)
precluster 4-momentum calculated using the E – scheme
Search for stable cones starting from preclusters  Clustering
seeds = pT ordered list of preclusters with pT > 1 GeV except those close to already found proto-jets: DR (precluster, proto-jet)< 0.5 Rcone
form proto-jet
cluster all towers within Rcone of the precluster axis in (Y ,f) space
recalculate proto-jet 4-momentum (E - scheme)
iterate proto-jet formation (cone drifting) until
cone is stable (cone axis coincides with proto-jet direction) OR
pT < 0.5 pTmin OR
# iterations = 50 (to avoid  cycles)
remove duplicates
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

7. DØ Run II Cone algorithm (II)
Ensure infrared and collinear safety  Clustering from midpoints
repeat same clustering using midpoints (between previously found proto-jets) as seeds except
no condition on close proto-jet
no removal of duplicates
 proto-jets (with possible overlaps)
Treat overlapping proto-jets  Merging/Splitting
use pT ordered list of proto-jets (from seeds and midpoints)
a pT cut at 8 GeV was used in RunI and suggested for RunII, but is not applied now
note that pTmin / 2 cut on proto-jets candidates implies a pT cut at 3 GeV (at least)
attribute shared energy exclusively according to shared energy fraction
ET,12 > f . Min(ET,1, ET,2)  Merge jets
ET,12 < f . Min(ET,1, ET,2)  Split jets = assign each particle to its closest jet
f = 50 %
at each merging/splitting step
recalculate 4-momenta of merged/splitted jets
re-order list of merged/splitted jets
treat all proto-jets until no shared energy is left
 final list of proto-jets (without overlap)
Calculation of jet variables and final pT cut
E-scheme recombination (4-momenta addition)
pT ordering
final pT cut: pTjet > pTmin (pTmin = 6 GeV)
 final list of jets
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

8. Jet Reconstruction and Identification efficiency (I)
Fake jets due to bad noise conditions (especially at the beginning of RunII)
 Jet-ID cuts identify “good” jets and reject “fake” jets as efficiently as possible based on: - either topological variables (EMF, CHF, n90,…) - or signal in independent electronic readout (L1 confirmation)
The “true” jet efficiency relates particle jets to detector jets: for particle jets at a given pT and h, it is the fraction of matching detector jets reconstructed and passing ID cuts
Can only be measured in MC
Neglects ambiguous matching between detector and particle level (1->2 or 2->1..)
3 sources of inefficiency:
ID cuts
Algorithmic
Detector (fixed pT cut + energy response)
In mathematical terms:
Main dependence is on pT_particle (dependence on eta is expected to be less important)
But dependency on pT_min is also important
Due to improper calorimeter response (and trigger) simulation, these 3 sources of inefficiency give 3 possible sources of difference between data and MC
Efficiency
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

9. Jet Reconstruction and Identification efficiency (II)
Relative importance of 3 sources of inefficiency
ID cuts  limited effect (few %) in some specific regions, mostly pT independent  most important at high pT
Algorithmic  totally negligible at high pT and O(1-2) % at lowest pT
Energy resolution (+fixed pT cut)  unavoidable!  main pT-dependent effect at low pT (up to GeV) and affects reco efficiency  same pT cut must be applied consistently after JES for proper data/MC comparison
Efficiency measurement through Tag & Probe method (assuming reco and ID efficiency factorize)
Tag = Z, g, good jet (+ track jet opposite to Tag to provide Probe h)
Probe = jet (close to track jet) whose efficiency is to be measured
Is there a jet?  reconstruction (reco) efficiency
Is it a good jet (= does it pass ID cuts)?  identification (ID) efficiency
Comparison data/MC
Correct MC to adjust efficiency in MC to that in data
Caveat: Efficiency measured in data is NOT true jet efficiency (pT_Tag ≠ pT_true)
At low pT only the effect of pT cut is visible (residual inefficiencies too small)
Issue: Efficiency correction by pT-dependent removal leads to biased distributions  for pT-dependent (reconstruction) inefficiency at low pT (energy resolution + pT cut) corrections applied through energy scale and resolution corrections  for pT-independent (identification) inefficiency at high pT corrections applied through removal of a small fraction of jets in MC
Measurement
Correction
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

10. B.Andrieu Light Jet reconstruction and calibration in D∅ -
Jet Reconstruction efficiency in Z+jet
Z+jet sample:
A reconstructed Z (Tag) and at least 1 track jet
Exactly 1 trackjet with ΔΦ(Z,trackjet) > 2.5
or ≥ 2 trackjets with ΔΦ(Z,leading pT trackjet) > 2.5
or else, ≥ 2 trackjets with ΔR(leading,next) < 0.7 and ΔΦ(Z,combined trackjet) > 2.6
ΔR(leading trackjet or each from the combined, e from Z) > 0.5
Veto jet activity outside the Tag and Probe region (DeltaR> 0.5)
Veto on photon (no EM cluster without an associated track) and on a 3rd electron
Measure efficiency of finding a good jet matched to the probe track jet (DR<0.5) as a function of pT for different |h_det(track-jet)| regions CC
ICR
pT>15
pT>15
Good agreement after Energy Scale and Resolution corrections
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

11. Jet Identification efficiency in g+jet and dijet
ID efficiency
Scale factor data/MC
ID efficiency
Plateau values data/MC
Agreement between different methods
MC jet removal according to measured scale factors as a function of h_jet
Systematics function of pT (ID efficiency lower in MC than in data?  not corrected, in systematics)
Detailed systematic studies (bin size, fit procedure,…)
Closure test
Systematics down to 0.5-1% level
(except in some specific regions: up to 4% at low pT & ηdet or )
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

12. Issue with RunII Cone algorithm: “Dark” jets
Jets might be missed by RunII Cone Algorithm (S.D. Ellis et al., hep-ph/ )  low pT jets
too close to high pT jet to form a stable cone (cone will drift towards high pT jet)
too far away from high pT jet to be part of the high pT jet stable cone
proposed solution  Smaller Search Cone Algorithm
remove stability requirement of cone
run cone algorithm with smaller cone radius to limit cone drifting (Rsearch = Rcone /  2)
form cone jets of radius Rcone around proto-jets found with radius Rsearch
Remarks
Problem of lost jets first seen by CDF, finally observed by DØ with 2nd-pass algorithm (re-run cone jet algorithm on unclustered energy)
For DØ, maximum effect on inclusive jet cross-section ~ 1% (below 20 GeV) and O(10-5) above 50 GeV  totally negligible
Effect unknown in multi-jet environment?
Proposed solution unsatisfactory w.r.t. cone jet definition anyway
 D preferred using RunII Cone without Smaller Search Cone
 CDF decided recently to abandon this option too
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

13. Jet Energy Scale: overview
Jet energy corrected to the particle level:
Offset (O ): energy not associated with the hard scattering (noise, pileup from previous BC and other interactions in the same BC) measured from zero bias and minimum bias events.
Response (Rjet=RCC x F (h)): calorimeter response to a jet
Jet absolute energy scale for central calorimeter RCC measured from ET balance in g +jet events
h dependence F (h) relative to CC determined by combining g +jet and dijet events for higher statistics and greater energy
High energy extrapolation with modified cell-response MC
Showering (S ): correction for net energy flux through jet cone boundary, measured from energy density around jet
Various k’ s: bias corrections to offset and response estimators.
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

14. Jet Energy Scale: Offset correction
Correct for multiple interactions (MI), noise and pileup (NP) + energy associated with high pT collision that becomes visible as a combined result of Offset Energy addition in each calorimeter cell AND Zero Suppression (≠ in MB events and in jet area  ZS bias)
Compute energy per i ring (integrated over i) from ZB (noise and pile-up) and MB (multiple interactions) data
Measure separately NP and MI contributions, as a function of , nPV and L O(L, nPV)=OZB(L)+OMB(L,nPV)-OMB(L,nPV=1)
Zero-Suppression bias estimated using g+jet MC w/o and w/ ZB overlay, suppressed and unsuppressed (note: similar bias affects the response measurement, corrected independently. Both corrections cancel almost perfectly.)
Correction determined from average energy per ring within jet area assuming jet is a circle in (h,f)  individual jet shape not taken into account
ZB (LM and PV veto)
MB (L~1.6x1032 cm-2s-1)
Total Offset Energy
1.2x1032 cm-2s-1
0.5x1032 cm-2s-1
0.1x1032 cm-2s-1
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

15. Jet Energy Scale: Absolute Response correction
True response of a particle jet in CC
derived using g+jet events using the MPF (Missing ET Projection Fraction) method. Rrecoil/Rg= 1 + MET/pTg (projected onto g direction) Typically fit: R(E’) = p0+p1log(E’/100)+p2log2(E’/100) E’ = pTg cosh(jet)
biases to be corrected (each at the % level):
Photon energy scale and dijet background contamination
Impact of zero-suppression (similar in size to bias in offset)
Topology bias (difference between response of recoil and response of the jet)
Total error at the % level
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

16. Jet Energy Scale: Relative Response correction
determine response of a jet at  relative to CC (-dependent corrections)
derived in the whole range (||<3.6) in very fine  binning (~0.1). Also E dependent.
use MPF method in g+jet (low ET region) and dijets (higher ET region) events, to extend the kinematic range. Tag object (g or jet) in CC, probe jet anywhere in 
Issues
Discrepancy between g+jet and dijets (up to 10%)
Background contamination in g+jet
g energy bias
different flavor composition (due to difference between quark - and gluon-jet responses)
Resolution bias (effect of resolution + steeply falling pT spectrum) to be corrected for dijet
Zero-suppression bias and topological bias
Uncertainty
Results
Correction
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

17. Jet Energy Scale: Showering correction
Compensate for net energy flow through jet cone boundary
Use same g+jet sample as for absolute response except jet not restricted to CC
True showering correction can be derived using MC without ZB overlay
Alternative method (for both data and MC as a cross-check) - Templates for jet energy profiles (energy in DR annuli) determined in MC
Spatial matching between calorimeter jet and particle jet
One template for “particle-jet” energy profile (1) , one for “not particle-jet” profile (2)
One template for offset energy density
- Fit a (1) + b (2) + offset to measured jet energy profiles
Results show good agreement data/MC  common energy dependence
Rcone=0.5
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

18. Jet Energy Scale: Results
Correction
Uncertainty E E
Correction
Results certified for |h|<3.6, pT >25 GeV
1-2% uncertainty in wide kinematic range for g+jet sample (potential few % change expected for other exclusive samples) h
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -

19. B.Andrieu Light Jet reconstruction and calibration in D∅ -
Summary
Cone Jet algorithm used by D0 in RunII improvement compared to RunI but a few problems or questions still open (not exhaustive list):
CDF and D0 use a (slightly, but still...) different Cone Jet algorithm
differences of D implementation w.r.t. RunII Cone recommendations
usefulness of a pT cut on proto-jets before merging/splitting at high luminosity?
even the RunII Cone algorithm is ICS up to NNLO only (G.P. Salam & G. Soyez, hep-ph/ )
 Use SISCone (or even better: use kT!)
Reconstruction and identification efficiency now much better under control
Energy response is the main cause for jet (reconstruction) inefficiency and its improper simulation is the main cause for observed differences in jet efficiency between data and MC
Consistent correction of reconstruction efficiency data/MC differences through JES and JER
Much better understanding and correction of identification efficiency differences  systematics to the 0.5%-1% level (except in some specific regions)
Jet Energy Scale correction for RunIIa completed
Many detailed studies of small effects (often O(1%))
unprecedented level of precision O(1-2%) over a very large kinematic range (|h|<3.6, pT >25 GeV)
However, the absence of a Monte Carlo reproducing data at a fundamental level prevents from extending easily all the knowledge gained on one particular sample to all data: cross checks have to be performed for each analysis using a sample different from the one used for JES derivation.
 A good MC simulation helps!
 If possible, apply energy calibration of objects before entering jet algorithm
Workshop on Top Physics: From the TeVatron to the LHC , 18 October 2007
B.Andrieu Light Jet reconstruction and calibration in D∅ -