# Presentation: 511248

## Jet finding Algorithms at Tevatron

- B.Andrieu (LPNHE, Paris)
-  On behalf of the             collaboration

- Outline:

- Introduction
- The Ideal Jet Algorithm
- Cone Jet Algorithms: RunII/RunI, D****/CDF
*k* Jet Algorithm
- Summary

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## Jets: from parton to detector level

- Problems of Cone Jet Algorithms using seeds

## Jet definition

- Associate “close” to each other “particles” ****** Clustering (Jet Algorithm)**
- “particles”
- “close” ?  Distance ****** ***R *=    or  *Y * (preferred in RunII) for Cone Algorithm****** **relative *p**T*  for *k* algorithm
- Calculate jet 4 - momentum from “particles” 4 - momenta ****** Recombination scheme**
- invariant under longitudinal boosts
-  Snowmass scheme (RunI): *E**T *-weighted recombination scheme in (,)
-  covariant or *E** *- scheme (preferred for RunII): 4- momenta addition
- used at the end of clustering but also during clustering process(not necessarily the same, still preferable)

- 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)

## The Ideal Jet Algorithm for pp

- 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 *E**T *=** *s*/2)
- factorisation (universal parton densities)
- independence of detector detailed geometry and granularity
- minimal sensitivity to non-perturbative processesand 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

**Theory**

**Experiment**

- -

**General**

- Compare jets at the parton, hadron and detector level
- ****** ****Jet algorithms should ensure**

## Run I Cone Algorithm

- Based on Snowmass Algorithm: *E**T *-weighted recombination scheme in ()
**Preclustering** (D****, similar algorithm for CDF)Note: Tower segmentation in () space: **D******** ******** 0.1 X 0.1****, ****CDF ******** 0.11 X 0.26**
- start from seeds (= towers with *p**T* >1 GeV ordered in decreasing *p**T*)
- cluster (and remove) all contiguous calorimeter towers around seed in a *R*= 0.3 cone
**Clustering**
- start from preclusters (ordered in decreasing *E**T*)
- proto-jet candidate = all particles within *R**cone*  of the precluster axis in () space**CDF:**** keep towers of the original precluster through all iterations (ratcheting)**
- proto-jet direction compared before/after recombination  iterate until it is stable

**Merging/Splitting** (treat overlapping proto-jets)
*E**T,*12 > *f* . Min(*E**T,*1*,** **E**T,*2)  Merge jets
*E**T,*12 < *f* . Min(*E**T,*1*,** **E**T,*2)  Split jets = assign each particle to its closest jet
**D********: *****f***** = 50 %, use only clusters with *****E******T *****> 8 GeV****    -    ****CDF: *****f***** = 75 %**
** ****Final calculation of jet variables** (modified Snowmass scheme)
- scalar addition of ***E******T ***** (D********)** or ***E******  *****(CDF)** of particles to determine jet ***E******T**** * or ***E***** **
- addition of 3-momenta of particles to determine jet direction, then ()Note: this procedure is not Lorentz invariant for boosts along beam axis**CDF: *****E******T *****= *****E *****sin(********)**

## Why new algorithms for Run II?

- different in D**** and CDF
- not infrared and collinear safe due to the use of seeds(collinear safety ensured at sufficiently large *E**T* : ***E******T *****>20 GeV with *****p******T******min *****(seed) = 1 GeV in** **D******)
- preclustering difficult to match at parton or hadron level
- CDF ratcheting not modeled in theory
- ad-hoc parameter (*R**sep* ) in jet algorithm at parton level (S.D. Ellis *et al.*, PRL69, 3615 (1992))
- not invariant under boosts along beam axis
****** ****2 new Cone Algorithms proposed for RunII**    (G.C. Blazey *et al.*, “RunII Jet Physics”, hep-ex/0005012)
- Seedless Cone Algorithm
- RunII (= Improved Legacy or Midpoint) Cone Algorithm
******  ****use**** *****k********* A****lgorithm (already used in RunI)**

**Run I Cone algorithms have many drawbacks**

## Seedless Cone Algorithm

- Streamlined (faster) option
- form cone around seed, recalculate cone direction (Snowmass or *E *- scheme)
- stop processing seed if the cone centroid is outside of the seed tower**CDF: use tower size X 1.1 in 1****st**** step to avoid boundary problems**
- iterate until cone direction after/before recombination is stable
- only miss low *E**T * proto-jets or stable directions within the same tower compared to normal version

-  Infrared and collinear safe
-  Probably close to Ideal for a Cone algorithm
-  Very computationally intensive
****** ****Use an approximation of Seedless Algorithm ******** RunII Cone**

**Not really “seedless” **
****** ****use enough seeds (all towers) to find all stable cones**

## RunII Cone Algorithm (hep-ex/0005012)

- QCD calculation at fixed order *N* only 2*N* –1 possible positions for stable cones (*p**i *, *p**i**+p**j *, *p**i**+p**j**+p**k *,...)
- Data: consider seeds used in RunI Cone algorithms as partons in addition to seeds, use ‘midpoints’ i.e. *p**i**+p**j *, *p**i**+p**j**+p**k *,...
- only need to consider seeds all within a distance *R* < 2*R**cone*
- only use midpoints between proto-jets (reduce computing time)
- otherwise algorithm similar to RunI

**How to build a valid approximation of the seedless algorithm?**

*E**  *- scheme recombination = 4-momenta addition
- use true rapidity *Y*  instead of pseudo-rapidity in *R*
- use all towers as seeds (*p**T *> 1 GeV)
- splitting/merging: *p**T*  ordered, *f* = 50 %

**Other specifications of the suggested RunII cone Algorithm**

## D Run II Cone Algorithm

- seeds = *p**T*  ordered list of particles with *p**T* >500 MeV
- precluster = all particles in a cone of *r** *= 0.3 around seed for Cone Jets with *R **** *0.5
- precluster 4-momentum calculated using the *E** *- scheme

- Preclustering similar to RunI except:

- seeds = *p**T* ordered list of preclusters except those close to already found proto-jets: *R* (precluster,proto-jet)< 0.5 *R**cone *
- cone drifting until
- remove duplicates
- repeat same clustering for midpoints***** except

- Clustering

- cone axis coincides with jet direction
*p**T*  < 0.5 Jet *p**T**min*
- # iterations = 50 (to avoid  cycles)

- no condition on close proto-jet
- no removal of duplicates

***** for pairs only, calculated using *p**T* –weighted mean

- Merging/splitting similar to RunI except:

- use *p**T** * ordered list of proto-jets (from seeds and midpoints)
- at each merging/splitting

- recalculate 4-momenta of merged/splitted jets
- re-order list of merged/splitted jets

## The Smaller Search Cone Algorithm

- Jets might be missed by RunII Cone Algorithm (S.D. Ellis *et al.*, hep-ph/0111434) low *p**T * jets
- too close to high *p**T * jet to form a stable cone (cone will drift towards high *p**T * jet)
- too far away from high *p**T * jet to be part of the high *p**T * jet stable cone
- proposed solution
- remove stability requirement of cone
- run cone algorithm with smaller cone radius to limit cone drifting(*R**search * = *R**cone* / ** 2)
- form cone jets of radius *R**cone* around proto-jets found with radius *R**search*

- 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**

## k Algorithm

- originally proposed for *e** *+*e** *- colliders, then adapted to hadron colliders (S. Catani *et al.*, NPB406,187 (1993))
- universal factorisation of initial-state collinear singularities
- 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

- D******:** geometrical 2x2 preclustering, remove preclusters with *E* < 0
*p**T*  ordered list of particles  form the list of *d**i* = (*p**T*i)2
- calculate for all pairs of particles, *d**i* *j *= Min((*p**T*i)2, (*p**T*j)2) *R/D*
- find the minimum of all *d**i*  and *d**i* *j*
- if it is a *d**i* , 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**

## Summary

- RunII (Midpoint) Cone Algorithm clear improvement over RunI Algorithm
- problems or questions still open (not exhaustive list):
- D**** uses RunII Cone (Midpoint) Algorithm (no smaller search cone)
- CDF uses JetClu (RunI) Cone Algorithm + Smaller Search Cone Algorithm
- differences of D**** implementation w.r.t. RunII Cone recommendations
- usefulness of a *p**T* cut on proto-jets before merging/splitting at high luminosity?
- procedure chosen for merging/splitting optimal?
- origin of the difference D**** vs CDF for lost jets problem?
*k* algorithm less intuitive, but conceptually simpler and theoretically well-behaved.
- studies needed, which should be done also for the RunII Cone Algorithm (jet masses, sensitivity to experimental effects, ...).
- 	  shouldn’t we put more effort on using *k* algorithm? (personal statement)