Jets Physics at CDF Sally Seidel University of New Mexico Ninth Adriatic Meeting 8 September 2003 for the CDF Collaboration

1. Jets at CDF 2. The Inclusive Jet Cross Section versus E T 3. The Dijet Mass Spectrum 4. Jet Shapes 5. Jet Algorithms

The motivation: Jet distributions at colliders can: signal new particles + interactions test QCD predictions constrain parton distribution functions

What’s new in Run 2? Energy increase: Bunch spacing decrease: to 396 ns Consequences: more precision, better statistics, more jets: the jet cross section is higher shorter distance scales probed: the energy reach per jet is greater

New: tracking system (silicon vertex SVXII, intermediate silicon layers ISL, central outer tracker COT) scintillating tile end plug calorimeter intermediate muon detectors scintillator time of flight system front end electronics pipelined trigger system DAQ Central muon detectors and calorimeters are unchanged.

All detectors inside the solenoid are new. Compare... Run 1 Run 2, inside solenoid

CDF jet energy calibration corrects for: calorimeter response multiple interactions neutrinos + muons underlying event Corrections are based on Monte Carlo tuned on test beam (for 10 GeV  E beam  227 GeV). Drift chamber tracks w/ 400 MeV/c  p T  10 GeV/c. MC fragmentation parameters tuned to match observed particle momenta + numbers. Calorimeter resolution:  = 0.1E T + 1GeV. Forward + plug calorimeter response calibrated by balancing dijets in which 1 jet of the pair is central.

Reconstruction: CDF reconstructs jets using an iterative cone algorithm with cone radius A typical jet crosses 40 calorimeter cells. The algorithm is based on the Snowmass one, which says: if i indexes all towers within cone radius R,

The CDF iterative cone algorithm: Examine all towers with E T > 1 GeV. Form preclusters from continuous groups of towers with monotonically decreasing E T. If a tower is outside a window of 7 x 7 towers from the seed of its cluster, start a new precluster with it. For each precluster, find the E T -weighted centroid for all towers with E T > 100 MeV within R = 0.7. Define the centroid to be the new cluster axis. Iterate until the tower list is stable. If 2 jets overlap – Merge them if  75% of the smaller jet’s E T is in the overlap region; otherwise assign overlap energy to the nearest jet. Recalculate ( ,  ).

, where ….the CDF jets have mass.

The Inclusive Jet Cross Section, E·d 3  /dp 3 For jet transverse energies achievable at the Tevatron, this probes distances smaller than cm. For massless jets + 2  acceptance in ,  This is what we measure.

Data quality requirements: |z vertex | < 60 cm to maintain projective geometry of calorimeter towers. 0.1  |  detector |  0.7 for full containment of energy in central barrel. E total < 2000 to reject accelerator loss events. To reject cosmic rays + misvertexed events, define = missing E T. Require Apply EM/HA + jet shape cuts to reject noise fakes.

Next correct for Pre-scaling of triggers. Detection efficiencies (typically 94 –100%). underlying event + multiple interactions. Run 2-Run 1 jet energy scale (5%). “Smearing”: energy mismeasurement + detector resolution.  No correction is made for jet energy deposited outside the cone by the fragmentation process, as this is included in the NLO calculation to which the data are ultimately compared.

The CDF Unsmearing Procedure: Simultaneous correction for detector response + resolution produces a result that is indepen- dent of binning but preserves the statistical uncertainty on the measured cross section. A smooth function is proposed representing a trial “pre-detector” cross section. This is called the “physics function.” For the inclusive cross section, the physics function has the form:

The physics function is convoluted with measured E T -loss and resolution functions and binned in E T. The response functions have long tails due to uninstrumented regions. The response function is parameterized by an exponential combined with a Gaussian and depends on the choice of cone opening angle. The response function requires Gaussian mean M = C 1 E T 3 + C 2 E T  + C 3 E T 2 + C 4 E T  + C 5 E T + C 6, Gaussian standard deviation  = C 7 (E T + C 8 ) - C 10, and Exponential decay constant S = C 11 E T + C 12 (where C 11 and C 12 depend upon the E T range).

The C i are determined by comparing measured calorimeter jet response to jets in Monte Carlo simulation. The Monte Carlo is based on single particle response from test beam data and isolated tracks from minimum bias events. The result of the convolution is compared with the measured cross section. The parameters of the physics function are iterated to obtain the best match between the convoluted function and the data. The ratio of (data):(physics function) for each E T bin is tabulated. The correction factors (typically 10%) are subsequently applied to data to obtain the “unsmeared physics cross section.”

The CDF inclusive jet cross section result for

Systematic uncertainties (all uncorrelated) on inclusive jet cross section measurement: i. Calorimeter response to high-p T charged hadrons (+3.2% -2.2%) ii. Calorimeter response to low-p T charged hadrons (  5%) iii. Energy scale stability (±5%) iv. Jet fragmentation model used in the simulation v. Energy of the underlying event in the jet cone (±30%) vi. Calorimeter response to electrons + photons (  2%) vii. Modelling of the jet energy resolution function (  10%) viii. Normalization (6%)

Theoretical choices Calculation of PDF systematic: CTEQ6.1M includes error info for all its Drell-Yan, DIS, and jet datasets. 20 free parameters used in fit. 20x20 Hessian error matrix computed and diagonalized. Eigenvectors are 20 independent directions in PDF space. Small (large) eigenvalues = directions poorly (well) determined. Direction associated with gluon PDF dominates. Vary each eigenvalue until the  2 for the global fit increases by 100 (= 90% CL). renormalization and factorization scales chosen at E T jet /2. Scale uncertainty small.

Conclusions and status... Good agreement between data and theory Data are below theory at low E T, above theory at high E T ---this was also true for CDF Run 1. Study of systematics is ongoing to quantify the effect.

The Dijet Mass Spectrum A search for new particles Many classes of new particles have a larger branching fraction to just 2 partons than to lepton or Z/W modes. These new particles’ masses could appear as resonances in the spectrum. Search for: Axigluons arise if SU(3) is replaced by SU(3) L  SU(3) R Excited quarks arise in compositeness models Extended Technicolor Coloron Supersymmetry-inspired E6 Scalar Diquarks

Theoretical sources AXIGLUONS P. Frampton and S. Glashow, Phys. Lett. B 190 (1987) 157. EXCITED QUARKS U. Baur, I. Hinchliffe, and D. Zeppenfeld, IJMP A2 (1987) TECHNICOLOR E. Eichten and K. Lane, Phys. Lett. B 327 (1994) 129. E6 DIQUARKS J. Hewitt and T. Rizzo, Phys. Rep. 183 (1989) 193.

Data quality requirements are similar to inclusive cross section study: |z vertex | < 60 cm E total < 2200 GeV Require Correct jet energies. Label highest E T jets after correction “jet 1” and “jet 2” require |  1 | < 2.0 and |  2 | < 2.0 To suppress QCD background require Define dijet mass:

Set mass cuts where jet triggers are 100% efficient: trigger inefficiency < statistical uncertainty lost events are low mass Plot: Fit:

Fit probability 0.66 is good bin width is mass resolution: new particle signal would appear in 2-4 bins No evidence for new particles

To set limits on cross section for new particle production as a function of mass: Assume measured mass spectrum comes from resonance + QCD bkg Predict signal N i sig in bin i: Calculate signal d  /dm using line shape for an excited quark (Gaussian + radiative tails) generated by PYTHIA, smeared by CDF detector simulation Normalize cross section with theory Predict background N i bkg in bin i: Assume QCD spectrum

Float signal normalization: multiply by  Predict total events  i in bin i:  i =  N i sig + N i bkg Poisson probability to observe n i when  i are expected: Likelihood function L for making this observation over all bins in the mass spectrum: Use MINUIT to minimize -ln L for each M in range ( ) GeV/c 2, in 50 GeV/c 2 steps. Fit to signal normalization , bkg normalization p 0, and shape (p 1 -p 3 ).

Map out L(N i sig ) by varying  holding other parameters constant. Let  95 = 95% CL upper limit on . This is the value of  for which 95% of the area of the likelihood distribution is between 0 and  95. Compute 95% CL upper limit on cross section for production and decay of par ticle M as (total expected cross section)   95.

Systematic uncertainties are under study on absolute jet energy scale background parameterization radiation jet energy resolution luminosity and efficiency

A study of the internal structure of jets. Process dominated by multi-gluon emission, controlled by higher-order QCD. Tests models of parton cascades. Sensitive to: Color structure of the hadronic final state + initial state radiation Underlying event due to interactions between collision remnants Jet Shapes

Define the differential jet shape, the average fraction of the jet’s transverse energy that lies inside an annulus in the  -  plane of inner (outer) radius r-  r/2 (r+  r/2) concentric to the jet cone. Note  (r = R) = 1.

Define the integrated jet shape, the average fraction of the jet’s transverse energy that lies inside a cone of radius r concentric to the jet cone. Note

Data selection: iterative cone jet clustering algorithm R = 0.7 and calorimeter towers with E T > 100 MeV dijet events:  2 jets with uncorrected E T > 30 GeV, |  jet | < 2.3 |z vtx | < 60 cm Compare data to HERWIG and PYTHIA Monte Carlo simulations. Both are (2  2) including initial- and final-state gluon radiation and secondary interactions between remnants.

Typical result for the integrated distribution: HERWIG produces jets narrower than data, especially in forward regions. HERWIG jet description improves with E T.

Typical result for the differential distribution: PYTHIA describes jet shapes fairly well but produces jets slightly narrower at low E T and in the range 1.4 < |  | < 2.3.

Jets narrow as E T jet increases: see the integrated jet shape measured at fixed cone size r =

Algorithm: A method for grouping collimated particle paths in a calorimeter. Needed to provide a common, objective, and unambiguous definition for use by theorists and experimentalists. Ideally should be infrared- and collinear- safe: cross section should not change if parton radiates a soft parton or splits into two collinear ones. Jet direction should correspond with parent parton direction. Run II Jet Algorithms

CDF has compared the cone and k T algorithms and applied both to the Inclusive Jet Cross Section measurement. The k T algorithm successively merges pairs of nearby objects (partons, particles, towers) in order of increasing relative E T. Parameter D controls the end of merging, characterizes jet size. The k T algorithm differs from the cone algorithm because : Particles with overlapping calorimeter clusters are assigned to jets unambiguously. Same jet definitions at parton and detector levels: no R sep parameter needed. NNLO predictions remain infrared safe. k T jets can have more complicated boundaries than do the smooth cones; consequently less E T near their boundaries.

CDF k T Algorithm 1 : 1) For each object i with E Ti, define d ii = (E Ti ) 2 2) For each object pair i, j, define (  R ij ) 2 = (  ij ) 2 + (  ij ) 2 d ij = min[(E Ti ) 2,(E Tj ) 2 ]·(  R ij ) 2 /D 2 3) If the min of all d ii and d ij is a d ij, i and j are combined; otherwise i is defined as a jet. 4) Continue until all objects are combined into jets. 5) Consider various values for D. Show results here for D = 0.7 and Based on S.D. Ellis and D. Soper, PRD (1993).

Analysis: The Inclusive Jet Cross Section analysis cuts were applied to 82 pb -1 of Run 2 data Jets were reconstructed with cone and k T and matches were sought: Define First results...

The k T algorithm typically captures less E T :...and the difference in E T assignment depends upon the E T of the cone jet:

The relative E T captured by the two algorithms depends strongly on the choice of parameter D:

The uncorrected Inclusive Cross Section shape varies slightly with parameter D:...different algorithms may have different corrections.

Summary Inclusive jet cross section shows good agreement with theory; slight disagreement that was present in the Run 1 data persists. New limits set on masses of axigluon, excited quark, coloron, and E6 scalar diquark. Evidence for jet narrowing with increasing E T ; Herwig and Pythia provide adequate models of jet shapes but with typically slightly too narrow jets in some kinematic regions. Studies of k T algorithm implementation are underway.