Jet Algorithms and Jet Energy Scale at D Ø

1. Jet Algorithms and Jet Energy Scale at DØ E. Busato (LPNHE, Paris) GDR Susy – Lyon - 10/13/2005 Outline: • Introduction • The Ideal Jet Algorithm • DØ Run II Cone Jet Algorithm • Jet Energy Scale • Performances • Summaryand Outlook

2. Jet definition QCD partons  jets of hadrons detector signals Associate “close” to each other “particles” “particles” ? partons (analytical calculations or parton showers MC) “hadrons” = final state particles towers (or cells or preclusters)  “close” ?  Distance  DR =  Dh2+Df2or  DY 2+Df2

3. Recombination scheme 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)  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 Experiment

5. The DØ Calorimeter • Hermetic coverage : || < 4.2 • Fine segmentation : • × = 0.1 × 0.1 • (0.05 × 0.05 in 3rd EM layer) • Inter-cryostat detector (ICD) : • improves coverage 1.1< || < 1.4 ~ 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 – merging/splitting issue) stable means that the cone 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 issue) !

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) space )  Infrared and collinear safe BUT, 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 * G. Blazey et al., hep-ex/0005012

8. Where do we put initial cones ? (2) Infrared unsafety Collinear unsafety Figures from hep-ex/0005012 Quark and gluon jets (partons) can be compared to detector jets if jet algorithm respects collinear and infrared safety QCD 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 ? • 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 • 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 pTPC < 3 GeV (not part of the Run II Jet Physics paper) (where PJ is any other proto-jet)

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 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 • DØ uses f = 50 % • particles are combined using the E-scheme add P to the list of final jets take the highest pT neighbor in the list : N • distance ΔR is calculated in (Y, φ) space 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) • Keep only final jets with pT > 6 GeV Recalculate merged/splitted jets Sort list of proto-jets 3)Repeat 1 and 2

12. Jet Energy Scale Goal : correct measured detector energy to particle jet energy • Eoff (Lumi,Rcone,) : Offset •  Energy not associated with hard scatter : • Uranium noise + pile-up • + underlying event + multiple interactions • Rjet (Ejetmeas,Rcone,) : Response •  Calorimeter response to jet •  Determined from ET balance in  +jets events •  EM scale determined using Z  e+e- • Scone (Ejetmeas,Rcone,) : Out of Cone showering •  Fraction of shower energy contained in Rcone • (no correction for particles emitted out of the cone)

13. Offset • Use zero bias and min bias events • ZB = uranium noise and pile-up • MB = ZB + underlying event • and multiple interactions • (For ZB : veto on lumi counters) • As expected, it is found that underlying • event +multiple interactions contribution • scales with # primary vertices. • Once # primary vertices fixed, only small • dependence on L. • (Error bars account for statistics, luminosity and  uncertainties)

14. Jet Response • Deposited energy ≠ Measured energy • Not perfectly compensating • Dead materials, fluctuations between • modules, etc … • Use Missing ET Projection Fraction method : (pT imbalance in +jets events) (Ideal) (Real) Response vs Eta dead materials in inter-cryostat region After em calibration from Z mass : Rem = 1 

15. Out of Cone Showering Correct for shower development out of the jet cone Correction factor = E(r<R) / E(r<rlimit) after baseline (noise+U.E+…) subtraction (rlimit : value of r where the jet is fully contained)  Use di-jets, +jets events For Rcone = 0.5 and 30 < pT < 45 GeV : Correction factor central ~0.99 inter-cryostat ~0.95 forward ~0.95

16. Total Jet Energy Correction

17. Performances – Jet Reconstruction Efficiency • A couple of ID cuts are applied to • reject bad jets. • This picture shows the product • jet reco eff  ID eff as a function • of the pT in +jets events. • Only jets with pT > 8 GeV are kept • Observations : • - Efficiency reaches 100% at ~40 GeV •  Final pT cut lowered to 6 GeV • - Differences between data and MC •  Need to apply correction factors in MC

18. Performances – Jet Resolution Run I • Determined on photon+jets events • (low pT) and di-jets events • (high pT) • Significantly worse than in Run I • Resolution in data worse than in • MC  need to smear MC jets

19. Performances – Inclusive Jet Cross Section Understanding jets is not an easy task, there are a lot of effects to take into account, but once this is done we obtain beautiful results … … ok, but let’s go back to work because this yellow band is dominated by the JES uncertainty !

20. Summary - Outlook • Run II Cone Algorithm midpoints clear improvement over Run I Algorithm • Run II Cone Algorithm used in all DØ analysis • Problems or questions still open (not exhaustive list) : • differences of D implementation w.r.t. recommendations • differences of D implementation w.r.t. CDF • k algorithm less intuitive, but conceptually simpler and theoretically well-behaved • studies needed (sensitivity to experimental effects, underlying event, ...).

21. Backup slides

22. 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

23. 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

24. 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