D

1
DØ Run II jet algorithms
E. Busato (LPNHE, Paris) TeV4LHC Workshop
12/1/2004
Outline
u Introduction u The Ideal Jet Algorithm u DØ
Run II Cone Jet Algorithm u k? Jet Algorithm u
Summary and Outlook
2
Jet definition
QCD partons ? jets of hadrons ?
detector signals
Associate close to each other particles
Calculate jet 4-momentum from particles
4-momenta ? Recombination scheme
? Clustering (Jet Algorithm)
partons (analytical calculations or parton
showers MC) hadrons final state particles
towers (or cells or preclusters)
? invariant under longitudinal boost ? used at
the end of clustering but also during clustering
process (not necessarily the same, still
preferable)
particles
close ?
? Distance
? ? relative pT for k? algorithm
DR ? Dh2Df2 or ? DY 2Df2
3
Recombination scheme
? At the end of the algorithm, we have to
calculate the jet 4-momemtum from the particles
4-momenta. ? Recombination scheme (also used
during clusterisation, cf next slides) ? 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
• replicate RunI cross sections while avoiding
  theoretical problems

Experiment
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The DØ Calorimeter
50,000 cells 5,000 pseudo-projective towers
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The DØ Cone Algorithm

• A jet is a stable cone of radius Rcone (except
  when two cones overlap)

stable means that its 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 issues) !
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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,f) (or (?, f)) space. ? Infrared and
collinear safe ? Very computationally
intensive ? Use an algorithm with seeds
Seeds are preclusters found using a simple cone
algorithm

• particles are combined using
• the E-scheme

input list of particles ordered by decreasing
pT 1) take the next particle in the list I 2)
if pTI gt 500 MeV ? form a precluster P 3)
take the next particle in the list J 4) if pTJ
gt 1 MeV and ?R(P,J) lt 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

• distance ?R is calculated
• in (?, f) space (i.e. use ?
• instead of Y as recommended
• in the Run II Jet Physics paper)

• remove preclusters with
• pT lt 1 GeV

• for towers
• remove preclusters made
• of only one tower

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Where do we put initial cones ? (2)
Problems of Cone Jet Algorithms using seeds
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 , pipj ,
  pipjpk ,)
• ? in addition to seeds, use midpoints i.e.
  pipj , pipjpk ,

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How are proto-jets found ?

• particles are combined
• using the E-scheme

• 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
• ( ?R(P, proto-jets) gt 0.5 Rcone )
• ? Form a new proto-jet PC
• 3) Recalculate PC direction by combining all its
  particles until
• - ?R between ith and (i-1)th iteration lt
  0.001
• - 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 lt 0.01
• ? R (PC,PJ) lt 0.005
• 5) go to 1

• distance ?R is calculated
• in (Y, f) space (i.e. as
• recommended in the Run II
• Jet Physics paper)

• after every iteration
• (step 3), the iteration
• process stops if
• pTPC lt 0.5 Min_Jet_Pt
• (not part of the Run II
• Jet Physics paper)

(where PJ is any other proto-jet)

• Min_Jet_Pt is the cut
• applied at the very end
• of the reconstruction
• (8 GeV)

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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

? R gt Rcone and ? R lt 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).
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Merging/Splitting
Proto-jets found around preclusters and midpoints
can share particles
? merging/splitting procedure has to be applied

• DØ uses f 50

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

• particles are combined
• using the E-scheme

• distance ?R is calculated
• in (Y, f) space

add P to the list of final jets
take the highest pT neighbor in the list N

• all proto-jets are
• considered (no pT cut
• applied). At Run I, only
• those with pT gt 8 GeV
• were considered.

pT, P? N gt f . Min( pTP, pTN ) ? Merge jets pT,
P? N lt f . Min( pTP, pTN ) ? Split jets
(assign each particle to its closest jet)
Recalculate merged/splitted jets
Sort list of proto-jets

• Keep only final jets
• with pT gt 8 GeV

3) repeat 1 and 2
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k? Algorithm
Description of inclusive k? algorithm
(EllisSoper, 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) ?R/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

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Summary

• RunII Cone Algorithm with midpoints clear
  improvement over RunI Algorithm
• problems or questions still open (not exhaustive
  list)
• D? uses RunII Cone Algorithm with midpoints
• differences of D? implementation w.r.t. RunII
  Cone recommendations
• differences of D? implementation w.r.t. CDF ?
• k? algorithm less intuitive, but conceptually
  simpler and theoretically well-behaved
• studies needed, which should be done also for the
  RunII Cone Algorithm (sensitivity to
  experimental effects, underlying event, ...).

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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)lt 0.5 Rcone)
• preclustering parameters
• pTmin cut at the end of preclustering (1 GeV)
• pTmin cut on precluster seeds (0.5 GeV)
• ?R cuts for midpoints
• no pT cut on proto-jets before merging/splitting
  ? potential problem at high luminosity
• use of ? instead of Y during preclustering
• procedure chosen for merging/splitting

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Backup slides
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The Smaller Search Cone Algorithm

• Jets might be missed by RunII Cone Algorithm
  (S.D. Ellis et al., hep-ph/0111434)? 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