1. Jet Algorithms and Jet Energy Scale at DØ
E. Busato (LPNHE, Paris)
GDR Susy – Lyon - 10/13/2005
Outline:
Introduction
The Ideal Jet Algorithm
DØ Run II Cone Jet Algorithm
Jet Energy Scale
Performances
Summary and Outlook

2. Jet definition QCD partons  jets of hadrons  detector signals
Associate “close” to each other “particles”
“particles” ?
partons (analytical calculations or parton showers MC)
“hadrons” = final state particles
towers (or cells or preclusters) 
“close” ?
 Distance 
DR =  Dh2+Df2 or  DY 2+Df2

3. Recombination scheme
Calculate jet 4-momentum from “particles” 4-momenta
 Recombination scheme
 Invariant under longitudinal boost
 Used at the end of clustering but also during clustering process
(not necessarily the same, still preferable)
 DØ uses the E-scheme :
Note : at Run I, scalar addition of ET (D) or E (CDF) of particles to
determine jet ET or E

4. The Ideal Jet Algorithm
Compare jets at the parton, hadron and detector level
 Jet algorithms should ensure
same algorithm at the parton, hadron and detector level
infrared and collinear safety
invariance under longitudinal boosts
fully specified and straightforward to implement
General
boundary stability (kinematic limit of inclusive jet cross section
at ET = s/2)
Theory
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 vs minimal CPU time
Experiment

5. The DØ Calorimeter Hermetic coverage : || < 4.2
Fine segmentation :
× = 0.1 × 0.1
(0.05 × 0.05 in 3rd EM layer)
Inter-cryostat detector (ICD) :
improves coverage 1.1< || < 1.4
~ 50,000 cells
~ 5,000 pseudo-projective towers

6. The DØ Cone Algorithm
A jet is a stable cone of radius Rcone (except when two cones overlap – merging/splitting issue)
stable means that the cone axis coincides with the direction of the jet, obtained by combining all its particles.
DØ uses Rcone = 0.7 for QCD analyses
Rcone = 0.5 for all other analyses
To find stable cones one needs to :
1) put initial cones (seeds) and let them
drift towards stable positions
2) have a procedure to calculate jet 4-momentum
from “particles” 4-momenta
stable cones are often called “proto-jets” because they are not
always final jets (merging/splitting issue) !

7. Where do we put initial cones ? (1)
Simplest solution : “seedless” algorithm ( = put initial cones at each point on a uniform
and fine enough grid in (Y,φ) space )
 Infrared and collinear safe
BUT, very computationally intensive
 Use an algorithm with seeds
Seeds are preclusters found using a simple cone algorithm :
Input : list of particles ordered by decreasing pT
1) Take the next particle in the list : I
2) If pTI > 500 MeV  form a precluster : P
3) Take the next particle in the list : J
4) If pTJ > 1 MeV and ΔR(P,J) < 0.3  add J to precluster P
(and remove it from
the list of particles)
5) Repeat 3 and 4 until all particles in the list have been tested.
6) Go to 1
particles are combined using
the E-scheme
distance ΔR is calculated
in (η, φ) space (i.e. use η
instead of Y as recommended
in the Run II Jet Physics paper*)
remove preclusters with
pT < 1 GeV
* G. Blazey et al., hep-ex/

8. Where do we put initial cones ? (2)
Quark and gluon jets (partons) can be compared to detector jets
if jet algorithm respects collinear and infrared safety
QCD 
Problems of Cone Jet Algorithms using seeds :
Infrared unsafety
Collinear unsafety
Figures from hep-ex/
How to build a valid 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 ,…)
 in addition to seeds, use “midpoints” i.e. pi+pj , pi+pj+pk ,…

9. How are proto-jets found ?
Input : list of preclusters ordered by decreasing pT
+ list of particles
1) Take the next precluster in the list : P
2) If P is far enough from all existing proto-jets
( ΔR(P, proto-jets) > 0.5 Rcone )
 Form a new proto-jet : PC
3) Recalculate PC direction by combining all its particles until :
- ΔR between ith and (i-1)th iteration <
- or number of iterations = 50 (to avoid  cycles)
4) Add PC to the list of proto-jets if it was not already found
| (pTPC – pTPJ ) / pTPJ | < 0.01
Δ R (PC,PJ) < 0.005
5) Go to 1
particles are combined
using the E-scheme
distance ΔR is calculated
in (Y, φ) space (i.e. as
recommended in the Run II
Jet Physics paper)
after every iteration
(step 3), the iteration
process stops if
pTPC < 3 GeV
(not part of the Run II
Jet Physics paper)
(where PJ is any other proto-jet)

10. Addition of midpoints No midpoints at Run I
Midpoints are added between proto-jets, not seeds
Midpoints are added between pairs of proto-jets, not triplets, ...
Only midpoints between proto-jets satisfying the following conditions are
considered :
Δ R > Rcone and Δ R < 2 . Rcone
(not part of the Run II
Jet Physics paper)
Using the list of midpoints instead of the list of proto-jets, a clustering similar
to the one described on the previous slide is applied, with two differences :
1) No condition on the distance between a midpoint and its closest proto-jet
(step 2 in previous slide)
2) It is not checked whether the proto-jet was already found
(step 4 in previous slide).

11. Merging/Splitting
Proto-jets found around preclusters and midpoints can share particles
 merging/splitting procedure has to be applied
Input : list of proto-jets ordered by decreasing pT
1) Take next proto-next in the list : P
2) Does P share particles with any neighbor proto-jet
DØ uses f = 50 %
particles are combined
using the E-scheme no
add P to the list of final jets
yes
take the highest pT neighbor in the list : N
distance ΔR is calculated
in (Y, φ) space
pT, P N > f . Min( pTP, pTN )  Merge jets
pT, P N < f . Min( pTP, pTN )  Split jets
(assign each particle to its closest jet)
Keep only final jets
with pT > 6 GeV
Recalculate merged/splitted jets
Sort list of proto-jets
3) Repeat 1 and 2

12. Jet Energy Scale
Goal : correct measured detector energy to particle jet energy
Eoff (Lumi,Rcone,) : Offset
 Energy not associated with hard scatter :
Uranium noise + pile-up
+ underlying event + multiple interactions
Rjet (Ejetmeas,Rcone,) : Response
 Calorimeter response to jet
 Determined from ET balance in  +jets events
 EM scale determined using Z  e+e-
Scone (Ejetmeas,Rcone,) : Out of Cone showering
 Fraction of shower energy contained in Rcone
(no correction for particles emitted out of the cone)

13. Offset Use zero bias and min bias events
ZB = uranium noise and pile-up
MB = ZB + underlying event
and multiple interactions
(For ZB : veto on lumi counters)
As expected, it is found that underlying
event +multiple interactions contribution
scales with # primary vertices.
Once # primary vertices fixed, only small
dependence on L.
(Error bars account for statistics, luminosity and  uncertainties)

14. Jet Response Deposited energy ≠ Measured energy
Not perfectly compensating
Dead materials, fluctuations between
modules, etc …
Use Missing ET Projection Fraction method :
(pT imbalance in +jets events)
(Ideal)
(Real)
Response vs Eta
dead materials in
inter-cryostat region
After em calibration from Z mass : Rem = 1 

15. Out of Cone Showering
Correct for shower development out of the jet cone
Correction factor = E(r<R) / E(r<rlimit)
after baseline (noise+U.E+…) subtraction
(rlimit : value of r where the jet is
fully contained)
 Use di-jets, +jets events
For Rcone = 0.5 and 30 < pT < 45 GeV :
Correction factor
central ~0.99
inter-cryostat ~0.95
forward ~0.95

16. Total Jet Energy Correction

17. Performances – Jet Reconstruction Efficiency
A couple of ID cuts are applied to
reject bad jets.
This picture shows the product
jet reco eff  ID eff as a function
of the pT in +jets events.
Only jets with pT > 8 GeV are kept
Observations :
- Efficiency reaches 100% at ~40 GeV
 Final pT cut lowered to 6 GeV
- Differences between data and MC
 Need to apply correction factors in MC

18. Performances – Jet Resolution
Run I
Determined on photon+jets events
(low pT) and di-jets events
(high pT)
Significantly worse than in Run I
Resolution in data worse than in
MC  need to smear MC jets

19. Performances – Inclusive Jet Cross Section
Understanding jets is not an easy task, there are a lot of effects to take into account, but once this is done we obtain beautiful results …
… ok, but let’s go back to work because this yellow band is dominated by
the JES uncertainty !

20. Summary - Outlook
Run II Cone Algorithm midpoints clear improvement over Run I Algorithm
Run II Cone Algorithm used in all DØ analysis
Problems or questions still open (not exhaustive list) :
differences of D implementation w.r.t. recommendations
differences of D implementation w.r.t. CDF
k algorithm less intuitive, but conceptually simpler and theoretically well-behaved
studies needed (sensitivity to experimental effects, underlying event, ...).

21. Backup slides

22. k Algorithm
Description of inclusive k algorithm (Ellis&Soper, PRD48, 3160, (1993) )
D: geometrical 2x2 preclustering
pT ordered list of particles  form the list of di = (pTi)2
calculate for all pairs of particles, di j = Min((pTi)2, (pTj)2) ΔR/D
find the minimum of all di and di j
if it is a di , form a jet candidate with particle i and remove i from the list
if not, combine i and j according to the E-scheme
use combined particle i + j as a new particle in next iteration
need to reorder list at each iteration  computing time  O(N3) (N particles)
proceed until the list of preclusters is exhausted
Remarks
originally proposed for e +e - colliders, then adapted to hadron colliders (S. Catani et al., NPB406,187 (1993))
infrared safe: soft partons are combined first with harder partons
collinear safe: two collinear partons are combined first in the original parton
no issue with merging/splitting
no issue with unclustered energy

23. The Smaller Search Cone Algorithm
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
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 seen by CDF, not seen by D  A physics or an experimental problem?
Proposed solution unsatisfactory w.r.t. cone jet definition
 D prefers using RunII Cone without Smaller Search Cone

24. Outlook
Suggestions for future studies on cone jets (tentatively ordered by decreasing importance):
Min_Jet_Pt / 2 cut on proto-jets candidates
seeds too close to already found protojets not used
(DR (precluster,proto-jet)< 0.5 Rcone)
preclustering parameters
pTmin cut at the end of preclustering (1 GeV)
pTmin cut on precluster seeds (0.5 GeV)
ΔR cuts for midpoints
no pT cut on proto-jets before merging/splitting  potential problem at high luminosity
use of η instead of Y during preclustering
procedure chosen for merging/splitting