D Ø Run II jet algorithms

1. DØ Run II jet algorithms E. Busato (LPNHE, Paris) TeV4LHC Workshop 12/1/2004 Outline: uIntroduction uThe Ideal Jet Algorithm u DØ Run II Cone Jet Algorithm uk Jet Algorithm uSummaryand Outlook

2. Jet definition LO hard process Soft processes Higher order QCD processes 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 =  Dh2+Df2or  DY 2+Df2

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 jetETorE

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

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

6. The DØ Cone Algorithm • A jet is a stable cone of radiusRcone (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 initialcones (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) !

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) (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 : • 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 > 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 • 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 • for towers : remove preclusters made of only one tower

8. Where do we put initial cones ? (2) Quark and gluon jets (partons) can be compared to detector jets if jet algorithms respect collinear and infrared safety QCD Infrared unsafety Collinear unsafety Figures from hep-ex/0005012 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 , pi+pj , pi+pj+pk ,…) •  in addition to seeds, use “midpoints” i.e. pi+pj , pi+pj+pk ,…

9. 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 • ( 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 – pTPJ ) / pTPJ | < 0.01 • Δ R (PC,PJ) < 0.005 • 5) go to 1 • 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 < 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)

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. no yes 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 ΔR is calculated in (Y, φ) 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 > 8 GeV were considered. 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) Recalculate merged/splitted jets Sort list of proto-jets • Keep only final jets with pT > 8 GeV 3) repeat 1 and 2

12. 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, dij = Min((pTi)2, (pTj)2) ΔR/D • find the minimum of all di and dij • 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

13. 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, ...).

14. 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

15. Backup slides

16. 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) • formcone 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