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A Comparison of Three-jet Events in p Collisions to Predictions from a NLO QCD Calculation Sally Seidel QCD’04 July 2004

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Three-jet event cross sections have been measured in CDF Run 1b data to: test models of QCD processes leading to gluon emission, and estimate the magnitude of contributing processes higher than NLO. The data are compared to predictions by Trirad ‡, a complete NLO QCD generator for hadronic three-jet production at hadron colliders. ‡ W. Kilgore and W. Giele, hep-ph/9903361.

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Kinematics and labelling: Define jet transverse energy E T E sin relative to primary event vertex. Sum all calorimeter clusters with uncorrected E T > 10 GeV. Consider events with E T > 175 GeV. Identify the three leading jets in lab system. Boost to their rest frame. Order jets by energy in that rest frame: E 3 > E 4 > E 5.

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A three-jet system in the massless parton approximation can be uniquely described by 5 variables. † We use: m 3J : mass of the three-jet system X 3 E 3 /m 3J : Dalitz variable, leading jet X 4 E 4 /m 3J : Dalitz variable, second jet for the angle between average beam direction and parton 3 in the 3-jet frame, and † S. Geer and T. Akasawa, PRD 53, 4793 (1996).

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for the angle between the plane containing the average beam direction and the plane containing partons 3, 4, and 5.

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Further selection to reject cosmics, beam halo, calorimeter malfunctions — veto if: energy deposited in the Had Cal out of time with the collision E T > 2000 GeV

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Also require: primary vertex has |z| < 60 cm relative to detector origin (to maintain calorimeter projective geometry) and largest p i. reject events with resolved multiple interactions (having a second vertex of 10 tracks separated by 10 cm from primary). apply iterative cone jet algorithm with cone radius reject events with < 3 jets. 3 leading jets must all have E T > 20 GeV and | | < 2.0.

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To avoid collinear instability, cut on cone overlap: reject events if R < 1.0 between any 2 of the 3 leading jets. To exclude regions with geometrical acceptance < 95%, require require full trigger efficiency: 53211 events remain. sort the events into bins of size 0.02 0.02 in the X 3 - X 4 plane.

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Corrections: absolute energy scale, relative energy scale, underlying event z vertex cut efficiency (93%) “unsmear”: simultaneous correction for energy mismeasurement and detector resolution. Generate Herwig events at parton level, hadronize final state, bin in the Dalitz plane, pass through CDF detector simulation, rebin. Compute for each bin: F = #events before sim / #events after Multiply each data bin by F.

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The data, after all selection requirements have been applied but prior to the energy correction:

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Uncertainties: absolute jet energy scale: due to calorimeter calibration resolution (~1.8%), jet fragmentation model (~1.6%), calorimeter stability (1%), and underlying event correction (~1.1GeV) relative ( -dependent) jet energy scale (~6%) total integrated luminosity (4.2%) z-vertex cut efficiency (2%) implementation of simulated events in the correction procedure (<5%).

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The Trirad calculation: 2 3 parton processes at one loop, and 2 4 parton processes at tree level.

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The cross section calculation: uses CTEQ4M, for every bin in the Dalitz plane, multiplies the result by the effective total integrated luminosity of the data to predict a #events in each bin, and excludes bins with X 3 0.98: perturbative expansion is not reliable where 3-jet configuration approaches 2-jet. Compare data to prediction for 215 bins.

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Data NLO prediction Note some shape difference between data and this absolute (normalized to luminosity) prediction. We compare data to theory in 2 ways...

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To compare shapes, normalize theory and data to the same number of events:

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To compare absolute cross sections, normalize data and theory to the same luminosity...

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Using all bins with X 3 0.98, measured cross section: predicted cross section: Using all bins in the Dalitz plane, measured cross section is

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Scale R default is E T. Scale uncertainty is estimated by varying scale from E T /2 to 2E T while maintaining R = F. PDF uncertainty estimated from spread of predictions generated with all members of the CTEQ4A family.

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Summary: Data agree in absolute magnitude with theory and with previous CDF measurements. The shapes of the theoretical and experimental Dalitz distributions differ somewhat. This may indicate the size of higher order corrections and may indicate that up to NLO the theory predicts more soft radiation than the data have in the region where the primary partons are approximately back-to-back. The data may be useful input to theoretical models of gluon emission processes, especially above X 3 = 0.98, where a perturbative expansion is not reliable.

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