DØ Run II jet algorithms E. Busato (LPNHE, Paris) TeV4LHC Workshop 12/1/2004 Outline: Introduction The Ideal Jet Algorithm DØ Run II Cone Jet Algorithm.

DØ Run II jet algorithmsE. Busato (LPNHE, Paris)

TeV4LHC Workshop 12/1/2004

Outline:

Introduction

The Ideal Jet Algorithm

DØ Run II Cone Jet Algorithm

k Jet Algorithm

Summary and Outlook

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partons (analytical calculations or parton showers MC)

“hadrons” = final state particles

towers (or cells or preclusters)

Jet definition

QCD partons jets of hadrons detector signals

Higher orderQCD processes

LO hard process Soft processes

“close” ? Distance relative pT for k algorithm

R = or Y

“particles”

Associate “close” to each other “particles”

Clustering (Jet Algorithm)

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)

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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

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The Ideal Jet Algorithm

same algorithm at the parton, hadron and detector level infrared and collinear safety invariance under longitudinal boosts fully specified and straightforward to implement

Theor

y

Experiment

Gener

al

Compare jets at the parton, hadron and detector level

Jet algorithms should ensure

boundary stability (kinematic limit of inclusive jet cross section at ET = s/2)

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

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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)

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) !

stable means that its axis coincides with the direction of the jet, obtained by combining all its particles.

To find stable cones one needs to :

DØ uses Rcone = 0.7 for QCD analyses

Rcone = 0.5 for all other analyses

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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,φ) (or (η, φ)) space.

Infrared and collinear safe

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

remove preclusters with pT < 1 GeV

for towers : remove preclusters made of only one tower

distance ΔR is calculated in (η, φ) space (i.e. use η instead of Y as recommended in the Run II Jet Physics paper)

particles are combined using the E-scheme

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Where do we put initial cones ? (2)

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 ,…

Problems of Cone Jet Algorithms using seeds :

Infrared unsafety Collinear unsafety Figures from hep-ex/0005012

Quark and gluon jets (partons) can be compared to detector

jets

if jet algorithms respect collinear and infrared safety

QCD

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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 < 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 – pT

PJ ) / pTPJ | < 0.01

Δ R (PC,PJ) < 0.005

5) go to 1

(where PJ is any other proto-jet)

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 pT

PC < 0.5 Min_Jet_Pt (not part of the Run II Jet Physics paper)

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 :

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).

Δ R > Rcone and Δ R < 2 . Rcone (not part of the Run II Jet Physics paper)

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Merging/Splitting

Proto-jets found around preclusters and midpoints can share particles

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-

jetadd P to the list of final jets

no

yes take the highest pT neighbor in the list :

N pT, P N > f . Min( pTP, pT

N ) Merge jets

pT, P N < f . Min( pTP, pT

N ) Split jets (assign each particle to its

closest jet) Recalculate merged/splitted jets

Sort list of proto-jets

3) repeat 1 and 2

particles are combined using the E-scheme

distance ΔR is calculated in (Y, φ) space

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

merging/splitting procedure has to be applied

DØ uses f = 50 %

Keep only final jets with pT > 8 GeV

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k Algorithm

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

D: geometrical 2x2 preclustering pT ordered list of particles form the list of di = (pT

i)2

calculate for all pairs of particles, di j = Min((pTi)2, (pT

j)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

Description of inclusive k algorithm (Ellis&Soper, PRD48, 3160, (1993) )

Remarks

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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)< 0.5 Rcone)

preclustering parameters pT

min cut at the end of preclustering (1 GeV) pT

min 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

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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

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

Remarks