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 Summary and Outlook

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+Df2 or  DY 2+Df2

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 jet ET or E

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

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

The DØ Cone Algorithm A jet is a stable cone of radius Rcone (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 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 issue) !

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 : 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 particles are combined using the E-scheme 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

Where do we put initial cones ? (2) 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 : Infrared unsafety Collinear unsafety Figures from hep-ex/0005012 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 ,…

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)

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).

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 no add P to the list of final jets yes 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

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)

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)

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 

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

Total Jet Energy Correction

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

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

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 !

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, ...).

Backup slides

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, di j = Min((pTi)2, (pTj)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 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

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 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

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