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Light Jet reconstruction and calibration in

Light Jet reconstruction and calibration in. B.Andrieu (LPNHE, Paris). Introduction: Cone Jet algorithm basics. {. Quark and gluon jets (identified to partons) can be compared to detector jets, if jet algorithms respect collinear and infrared safety (Sterman&Weinberg, 1977). Q C D .

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Light Jet reconstruction and calibration in

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  1. Light Jet reconstruction and calibration in B.Andrieu (LPNHE, Paris)

  2. Introduction: Cone Jet algorithm basics { Quark and gluon jets (identified to partons) can be compared to detector jets, if jet algorithms respect collinear and infrared safety(Sterman&Weinberg, 1977) QCD Infrared unsafety Collinear unsafety Figures from hep-ex/0005012 Cone Jet algorithms • Associate “particles” inside a cone, where particles can be • 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) • Calculate jet 4-momentum from “particles” 4-momenta  Defined by Clustering procedure, Distance and Recombination scheme Cone (proto-) jets are chosen as “stable” cones, i.e. cones whose geometrical position (axis) coincides with jet direction (3-momentum)  How to find all stable cones in minimum CPU time? Problems of “naive” Cone Jet Algorithms using seeds B.AndrieuLight Jet reconstruction and calibration in D∅ -

  3. Introduction: the Ideal Jet Algorithm for Tevatron Compare jets at the parton, hadron and detector level Jet algorithms should ensure General • 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 ET =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 B.AndrieuLight Jet reconstruction and calibration in D∅ -

  4. Introduction: RunII Cone Algorithm (hep-ex/0005012)  2 new Cone Algorithms proposed for RunII(G.C. Blazey et al., “RunII Jet Physics”, hep-ex/0005012)  Seedless Cone Algorithm  Almost ideal, but very computationally intensive  RunII (= Improved Legacy or Midpoint) Cone Algorithm = 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 ,…) • Data: consider seeds used in RunI Cone algorithms as partons in addition to seeds, use ‘midpoints’ i.e. pi+pj , pi+pj+pk ,… • only need to consider seeds all within a distance DR < 2Rcone • only use midpoints between proto-jets (reduce computing time) • otherwise algorithm similar to RunI Other specifications of the suggested RunII cone Algorithm • E -scheme recombination = 4-momenta addition • use true rapidity Y instead of pseudo-rapidity h in DR • use all towers as seeds (pT > 1 GeV) • splitting/merging: pT ordered, f = 50 % B.AndrieuLight Jet reconstruction and calibration in D∅ -

  5. DØ calorimeter reconstruction U/LAr calorimeter • Pseudo-projective geometry • ~ 45 000 cells, ~ 5000 towers • Granularity 0.1 x 0.1 in (h,f) • Cells • Electronics calibration and baseline subtraction • Noise removal: 0-suppression (2.5 s), remove isolated cells (2.5/4 s) • (h,f) intercalibration using jets • EM cal calibrated using Z e+e-  To each cell is associated a massless 4-vector (primary vertexcell center) • Towers • Combine (4-vector addition) all cells with non-0 signal in the same geometrical tower (pointing to detector center) • Towers may be massive  Towers are basic objects used for jet reconstruction From cells to towers B.AndrieuLight Jet reconstruction and calibration in D∅ -

  6. DØ Run II Cone algorithm (I) Algorithm defined in “RunII Jet Physics” (hep- ex/0005012) parameters in green,changes w.r.t. definition in red • Reduce the number of seeds for clustering Preclustering • seeds = pT ordered list of particles with pT >0.5 GeV (1 GeV in RunI) • reduce effect of noise in CH and ECMG  special treatment for towersif highest energy cell of a tower is in CH or ECMG, its energy is removedfrom the tower before applying the above minimum cut for seed selection • precluster = all particles in a cone of r=0.3 around seed (for Cone Jets with Rcone 0.5) • precluster 4-momentum calculated using the E – scheme • Search for stable cones starting from preclusters Clustering • seeds = pT ordered list of preclusters with pT > 1 GeVexcept those close to already found proto-jets: DR (precluster, proto-jet)< 0.5 Rcone • form proto-jet • cluster all towers within Rcone of the precluster axis in (Y ,f) space • recalculate proto-jet 4-momentum (E - scheme) • iterate proto-jet formation (cone drifting) until • cone is stable (cone axis coincides with proto-jet direction) OR • pT< 0.5 pTminOR • # iterations = 50 (to avoid  cycles) • remove duplicates B.AndrieuLight Jet reconstruction and calibration in D∅ -

  7. DØ Run II Cone algorithm (II) • Ensure infrared and collinear safety Clustering from midpoints • repeat same clustering using midpoints (between previously found proto-jets) as seeds except • no condition on close proto-jet • no removal of duplicates  proto-jets (with possible overlaps) • Treat overlapping proto-jets Merging/Splitting • use pT ordered list of proto-jets (from seeds and midpoints) • a pT cut at 8 GeV was used in RunI and suggested for RunII, but is not applied now • note that pTmin / 2 cut on proto-jets candidates implies a pT cut at 3 GeV (at least) • attribute shared energy exclusively according to shared energy fraction • ET,12 >f. Min(ET,1, ET,2)  Merge jets • ET,12 < f. Min(ET,1, ET,2)  Split jets = assign each particle to its closest jet f = 50 % • at each merging/splitting step • recalculate 4-momenta of merged/splitted jets • re-order list of merged/splitted jets • treat all proto-jets until no shared energy is left  final list of proto-jets (without overlap) • Calculation of jet variables and final pT cut • E-scheme recombination (4-momenta addition) • pT ordering • final pT cut: pTjet > pTmin (pTmin = 6 GeV)  final list of jets B.AndrieuLight Jet reconstruction and calibration in D∅ -

  8. Jet Reconstruction and Identification efficiency (I) Identification Efficiency • Fake jets due to bad noise conditions (especially at the beginning of RunII)  Jet-ID cuts identify “good” jets and reject “fake” jets as efficiently as possible based on:- either topological variables (EMF, CHF, n90,…)- or signal in independent electronic readout (L1 confirmation) • The “true” jet efficiency relates particle jets to detector jets:for particle jets at a given pT and h, it is the fraction of matching detector jets reconstructed and passing ID cuts • Can only be measured in MC • Neglects ambiguous matching between detector and particle level (1->2 or 2->1..) • 3 sources of inefficiency: • ID cuts • Algorithmic • Detector (fixed pT cut + energy response) • In mathematical terms: • Main dependence is on pT_particle (dependence on eta is expected to be less important) • But dependency on pT_min is also important • Due to improper calorimeter response (and trigger) simulation, these 3 sources of inefficiency give 3 possible sources of difference between data and MC B.AndrieuLight Jet reconstruction and calibration in D∅ -

  9. Jet Reconstruction and Identification efficiency (II) • Relative importance of 3 sources of inefficiency • ID cuts  limited effect (few %) in some specific regions, mostly pT independent  most important at high pT • Algorithmic  totally negligible at high pT and O(1-2) % at lowest pT • Energy resolution (+fixed pT cut)  unavoidable!  main pT-dependent effect at low pT (up to 20-25 GeV) and affects reco efficiency  same pT cut must be applied consistently after JES for proper data/MC comparison • Efficiency measurement through Tag & Probe method (assuming reco and ID efficiency factorize) • Tag = Z, g, good jet (+ track jet opposite to Tag to provide Probe h) • Probe = jet (close to track jet) whose efficiency is to be measured • Is there a jet?  reconstruction (reco) efficiency • Is it a good jet (= does it pass ID cuts)?  identification (ID) efficiency • Comparison data/MC • Correct MC to adjust efficiency in MC to that in data • Caveat: Efficiency measured in data is NOT true jet efficiency (pT_Tag ≠pT_true) • At low pT only the effect of pT cut is visible (residual inefficiencies too small) • Issue: Efficiency correction by pT-dependent removal leads to biased distributions for pT-dependent (reconstruction) inefficiency at low pT (energy resolution + pT cut)corrections applied through energy scale and resolution corrections for pT-independent (identification) inefficiency at high pTcorrections applied through removal of a small fraction of jets in MC Measurement Correction B.AndrieuLight Jet reconstruction and calibration in D∅ -

  10. Jet Reconstruction efficiency in Z+jet • Z+jet sample: • A reconstructed Z (Tag) and at least 1 track jet • Exactly 1 trackjet with ΔΦ(Z,trackjet) > 2.5 • or ≥ 2 trackjets with ΔΦ(Z,leading pT trackjet) > 2.5 • or else, ≥ 2 trackjets with ΔR(leading,next) < 0.7 and ΔΦ(Z,combined trackjet) > 2.6 • ΔR(leading trackjet or each from the combined, e from Z) > 0.5 • Veto jet activity outside the Tag and Probe region (DeltaR> 0.5) • Veto on photon (no EM cluster without an associated track) and on a 3rd electron • Measure efficiency of finding a good jet matched to the probe track jet (DR<0.5) as a function of pT for different |h_det(track-jet)| regions CC ICR pT>15 pT>15 Good agreement after Energy Scale and Resolution corrections B.AndrieuLight Jet reconstruction and calibration in D∅ -

  11. Jet Identification efficiency in g+jet and dijet ID efficiency Scale factor data/MC ID efficiency Plateau values data/MC • MC jet removal according to measuredscale factors as a function of h_jet • Systematics function of pT(ID efficiency lower in MC than in data? not corrected, in systematics) • Detailed systematic studies(bin size, fit procedure,…) Agreement between different methods Closure test Systematics down to 0.5-1% level (except in some specific regions: up to 4% at low pT & ηdet 0-0.4 or 0.8-0.9) B.AndrieuLight Jet reconstruction and calibration in D∅ -

  12. Issue with RunII Cone algorithm: “Dark” jets • 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  Smaller Search Cone Algorithm • 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 first seen by CDF, finally observed by DØ with 2nd-pass algorithm (re-run cone jet algorithm on unclustered energy) • For DØ, maximum effect on inclusive jet cross-section ~ 1% (below 20 GeV) and O(10-5) above 50 GeV  totally negligible • Effect unknown in multi-jet environment? • Proposed solution unsatisfactory w.r.t. cone jet definition anyway D preferred using RunII Cone without Smaller Search Cone CDF decided recently to abandon this option too B.AndrieuLight Jet reconstruction and calibration in D∅ -

  13. Jet Energy Scale: overview Jet energy corrected to the particle level: • Offset (O ): energy not associated with the hard scattering (noise, pileup from previous BC and other interactions in the same BC) measured from zero bias and minimum bias events. • Response (Rjet=RCCx F (h)): calorimeter response to a jet • Jet absolute energy scale for central calorimeter RCC measured from ET balance in g +jet events • h dependence F (h) relative to CC determined by combining g +jet and dijet events for higher statistics and greater energy • High energy extrapolation with modified cell-response MC • Showering (S ): correction for net energy flux through jet cone boundary, measured from energy density around jet • Various k’ s: bias corrections to offset and response estimators. B.AndrieuLight Jet reconstruction and calibration in D∅ -

  14. Jet Energy Scale: Offset correction ZB (LM and PV veto) MB (L~1.6x1032 cm-2s-1) Total Offset Energy 1.2x1032 cm-2s-1 0.5x1032 cm-2s-1 0.1x1032 cm-2s-1 • Correct for multiple interactions (MI), noise and pileup (NP) + energy associated with high pT collision that becomes visible as a combined result of Offset Energy addition in each calorimeter cell AND Zero Suppression (≠ in MB events and in jet area  ZS bias) • Compute energy per i ring (integrated over i) from ZB (noise and pile-up) and MB (multiple interactions) data • Measure separately NP and MI contributions, as a function of , nPV and LO(L, nPV)=OZB(L)+OMB(L,nPV)-OMB(L,nPV=1) • Zero-Suppression bias estimated using g+jet MC w/o and w/ ZB overlay, suppressed and unsuppressed (note: similar bias affects the response measurement, corrected independently. Both corrections cancel almost perfectly.) • Correction determined from average energy per ring within jet area assuming jet is a circle in (h,f)  individual jet shape not taken into account B.AndrieuLight Jet reconstruction and calibration in D∅ -

  15. Jet Energy Scale: Absolute Response correction • True response of a particle jet in CC • derived using g+jet events using the MPF(Missing ET Projection Fraction) method.Rrecoil/Rg= 1 + MET/pTg (projected onto g direction)Typically fit: R(E’) = p0+p1log(E’/100)+p2log2(E’/100)E’ = pTg cosh(jet) • biases to be corrected (each at the % level): • Photon energy scale and dijet background contamination • Impact of zero-suppression (similar in size to bias in offset) • Topology bias (difference between response of recoil and response of the jet) Total error at the % level B.AndrieuLight Jet reconstruction and calibration in D∅ -

  16. Jet Energy Scale: Relative Response correction • determine response of a jet at  relative to CC (-dependent corrections) • derived in the whole range (||<3.6) in very fine binning (~0.1). Also E dependent. • use MPF method in g+jet (low ET region) and dijets (higher ET region) events, to extend the kinematic range.Tag object (g or jet) in CC, probe jet anywhere in  • Issues • Discrepancy between g+jet and dijets (up to 10%) • Background contamination in g+jet • g energy bias • different flavor composition(due to difference between quark - and gluon-jet responses) • Resolution bias (effect of resolution + steeply fallingpT spectrum) to be corrected for dijet • Zero-suppression bias and topological bias Uncertainty Results Correction B.AndrieuLight Jet reconstruction and calibration in D∅ -

  17. Jet Energy Scale: Showering correction Rcone=0.5 • Compensate for net energy flow through jet cone boundary • Use same g+jet sample as for absolute response except jet not restricted to CC • True showering correction can be derived using MC without ZB overlay • Alternative method (for both data and MC as a cross-check)- Templates for jet energy profiles (energy in DR annuli) determined in MC • Spatial matching between calorimeter jet and particle jet • One template for “particle-jet” energy profile (1) , one for “not particle-jet” profile (2) • One template for offset energy density - Fit a (1) + b (2) + offset to measured jet energy profiles • Results show good agreement data/MC  common energy dependence B.AndrieuLight Jet reconstruction and calibration in D∅ -

  18. Jet Energy Scale: Results Correction Uncertainty • Results certified for |h|<3.6, pT >25 GeV • 1-2% uncertainty in wide kinematic range for g+jet sample(potential few % change expectedfor other exclusive samples) E E Correction h B.AndrieuLight Jet reconstruction and calibration in D∅ -

  19. Summary • Cone Jet algorithm used by D0 in RunII improvement compared to RunIbut a few problems or questions still open (not exhaustive list): • CDF and D0 use a (slightly, but still...) different Cone Jet algorithm • differences of D implementation w.r.t. RunII Cone recommendations • usefulness of a pT cut on proto-jets before merging/splitting at high luminosity? • even the RunII Cone algorithm is ICS up to NNLO only (G.P. Salam & G. Soyez, hep-ph/0704.0292)  Use SISCone (or even better: use kT!) • Reconstruction and identification efficiency now much better under control • Energy response is the main cause for jet (reconstruction) inefficiency and its improper simulationis the main cause for observed differences in jet efficiency between data and MC • Consistent correction of reconstruction efficiency data/MC differences through JES and JER • Much better understanding and correction of identification efficiency differences systematics to the 0.5%-1% level (except in some specific regions) • Jet Energy Scale correction for RunIIa completed • Many detailed studies of small effects (often O(1%)) • unprecedented level of precision O(1-2%) over a very large kinematic range (|h|<3.6, pT >25 GeV) • However, the absence of a Monte Carlo reproducing data at a fundamental level prevents from extending easily all the knowledge gained on one particular sample to all data: cross checks have to be performed for each analysis using a sample different from the one used for JES derivation.  A good MC simulation helps!  If possible, apply energy calibration of objects before entering jet algorithm B.AndrieuLight Jet reconstruction and calibration in D∅ -

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