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  k  Jet Algorithm  Summary and Outlook

1 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 order QCD processes LO hard processSoft 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)

2 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

3 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 Theory Experiment General 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

4 The DØ Calorimeter ~ 50,000 cells ~ 5,000 pseudo-projective towers

5 The DØ Cone Algorithm  A jet is a stable cone of radius R cone (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 R cone = 0.7 for QCD analyses R cone = 0.5 for all other analyses

6 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 p T I > 500 MeV  form a precluster : P 3) take the next particle in the list : J 4) if p T J > 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 p T < 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

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

8 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 R cone )  Form a new proto-jet : PC 3) Recalculate PC direction by combining all its particles until : - ΔR between i th 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 | (p T PC – p T PJ ) / p T PJ | < 0.01 Δ R (PC,PJ) < ) 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 p T 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)

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

10 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-jet add P to the list of final jets no yes take the highest p T neighbor in the list : N p T, P  N > f. Min( p T P, p T N )  Merge jets p T, P  N < f. Min( p T P, p T 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 p T cut applied). At Run I, only those with p T > 8 GeV were considered.  merging/splitting procedure has to be applied DØ uses f = 50 % Keep only final jets with p T > 8 GeV

11 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 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 ) ΔR/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(N 3 ) (N particles) proceed until the list of preclusters is exhausted Description of inclusive k  algorithm ( Ellis&Soper, PRD48, 3160, (1993) ) Remarks

12 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,...).

13 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 R cone ) preclustering parameters p T min cut at the end of preclustering (1 GeV) p T min cut on precluster seeds (0.5 GeV) ΔR cuts for midpoints no p T 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

14 Backup slides

15 The Smaller Search Cone Algorithm Jets might be missed by RunII Cone Algorithm (S.D. Ellis et al., hep-ph/ )  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