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Dijet Transverse Thrust cross sections at DØ Veronica Sorin University of Buenos Aires

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2 Outline Introduction: – Overview – The KT algorithm – Definition of the observable Dijet Transverse Thrust cross section Systematic uncertainties Comparison with theory Conclusions

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3 Theoretical Introduction Quantum Chromodynamics: describe the interaction between quarks and gluons, which carry color charge, conventionally called: blue, red and green. Main QCD characteristics: Confinement: quarks and gluons cannot be seen as isolated particles, partons (q and g) are bound together into hadrons. Fundamental Vertices Asymptotic freedom: as the energy of the interaction increases, the strength of the coupling get smaller, allowing the aplication of perturbative techniques (pQCD). Jet Physics

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4 calorimeter jet Time parton jet particle jet hadrons CH FH EM q q At the final state of an hadronic collision, QCD predicts the appareance of highly collimated sprays of particles, which are called Jets. At the DØ experiment using the Fermilab Laboratory Tevatron collider, we study pp collisions at a c.m. energy of 1.8 TeV. The bunch crossing occurs every 3.5 µs. By identifying these jets, experimental measurements can be compared with pQCD predictions.

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5 Panoramic view of the Fermilab Laboratory

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6 Event Shapes Event shapes have been extensively studied at e + e - and ep experiments to: study spatial distribution of hadronic final states test perturbative QCD predictions extract a precise value of s recently to test QCD developments like resummation calculations and non-perturbative corrections Resummations: needed at small values of the shape variable where fixed-order perturbative calculations are expected to fail.

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7 Thrust : direction which maximizes T The sum is done over all partons/particles/ detector elements/jets in the event T : Pencil-likeness of the event 2 partons in final state N partons in final state T=[1/2,1] (N...NLO) T=1 Jet production rate: s 2 is LO s 3 is NLO Thrust (T ≠ 1): s 3 is LO s 4 is NLO

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8 T in hadron colliders Busy environment: underlying event, pile-up, multiple interactions and noise particles jets We have derived a correction to eliminate on average the energy contributions from sources other than the hard interaction itself. Thrust is not invariant under z boosts Transverse Thrust The pp c.m system is not the parton-parton c.m. – By replacing momenta with transverse momenta Lorentz invariant quantity 3D 2D T

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9 The DØ Calorimeters Liquid argon active medium and uranium absorber Hermetic with full coverage < 4.2 int total) Transverse segmentation ( towers ) x x E / E = 15% / for electrons E / E = 45% / for pions x Z y

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10 Jet Algorithms Parton jet: q and g (before hadronization) Particle jet: final state particles (after hadronization) Calorimeter jet: measured object (after calorimeter shower) Iterative Fixed cone of radius R Overlapping cones: arbitrary criteria to resolve ambiguities Sensitivity to soft radiation Requires ad-hoc parameter for the theory Recombination Distance parameter D Infrared and collinear safe Same algorithm in theory and experiment Fixed Cone (RunI) K T (Ellis-Soper) calorimeter jet Time parton jet particle jet hadrons CH FH EM

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11 RunI DØ Analyses using the K T algorithm “Subjet Multiplicity of Gluon and Quark Jets” Phys. Rev. D 65, 052008 (2002) “The Inclusive Jet Cross Section” Phys. Lett. B 525, 211 (2002) “Dijet Transverse Thrust Cross Sections” paper in preparation

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12 K T Algorithm at DØ (RunI) Cone jetK T jet (Ellis-Soper PRD 48 3160)

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13 K T Algorithm at DØ (RunI) For each particle or pair of particles : Produce list of jets Is less than ? Move i to list of jets Any left? No Yes Merge i+j Beam

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14 Jet Momentum Scale Correction Offset (O): Ur noise, pileup, multiple interactions, underlying event (ue) Response (Rjet): P meas / P true (using transverse momentum balance in -jet events) Calorimeter jet Particle jet

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15 Offset Correction MC Jets MC+Noise O = UE + N Ur noise, pileup, multiple interactions Underlying Event The offset contribution is obtained as the momentum difference between jets. MC events + detector simulation + noise data Noise data can be: Zero bias : random crossing (N) Minimum bias : crossing with a pp interaction (UE) _

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16 O = UE + N Offset Correction Luminosity dependent (L in cm -2 s -1 )..... MC + Overlayed to crossing with inelastic interaction MC + Overlayed to random crossing UE(GeV) N(GeV)

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17 R jet = a + b ln( P jet ) + c ln 2 ( P jet ) R jet Correction Monte Carlo Closure D=1 (K T jets) P ptcl (GeV) P meas / P ptcl

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18 Dijet TransverseThrust Sum done over jets Jets have been reconstructed with the K T algorithm with D=1 Jet Momentum scale correction does not eliminate low energy jets ( high probability to originate 100% from background) distort the shape of the physical distributions Observable selected to reduce detector effects and maximize the signal in a hadron collider. Only the two leading jets will be used to calculate Thrust The spatial configuration of the two leading jets inherits the information of the other jets in the event

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19 Effects of noise and luminosity on T T The addition of randomly oriented noise jets renders the event more isotropic Use only the 2 leading jets Selection of the observable

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20 Selection of the observable The event energy scale Look for a variable correlated with Q 2 and with low sensitivity to noise HT at parton level: measure of Q 2 HT3 (scalar sum of the transverse momentum of the three leading jets) HT3 vs HT Noise jetsE T3 spectrum Data

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21 Brief Recapitulation Measurement of cross section as a function of HT3 Using jets for which we have derived a correction that eliminates on average the contributions not related with the hard interaction. Test quality of QCD predictions Study significance of resummation calculations O( s 3 ) calculations can not cover the whole physical range: for, the LO calculation is O( s 4 ) 120 o

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22 Observed Dijet Transverse Thrust Cross Sections Systematic Uncertainties: – Momentum Scale Correction – Energy and Angular resolutions – Unfolding Final results and Comparison with Theory Conclusions Coming up now….

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23 Dijet Transverse Thrust cross section K T algorithm (parameter D = 1) Event Selection: Vertex cut (| z | < 50 cm, e ~ 90 %) Cut on missing E T (E T /p T lj < 0.7, e ~ 99.8 %) Jet quality cuts (e ~ 99.5 % ) ( 0.05 < EMF < 0.95, CHF < 0.4 ) Kinematic cuts: | 1,2 | < 1 Jet Selection:

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24 It is presented in four HT3 ranges HT3 : scalar sum of the transverse momentum of the three leading jets. ( use 3rd jet only when | 3 | < 3) Four single jet triggers are used for different HT3 ranges where they are fully efficient. HT3 distributions

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25 Observed cross sections Distributions still distorted due to finite detector resolutions LO O( s 4 ) Resummations ? Theoretical Predictions: Jetrad : QCD event generator O( s 3 ). NLOJET++ : NLO 3 jets generator O( s 4 ).

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26 Momentum scale correction Uncertainty on the Jet Momentum calibration propagates to the thrust via two mechanisms: errors between 10-25% T value changes Migration of events between HT3 bins Dominant Effect Low energy jets : 2-5% uncertainty to take into account reconstruction efficiencies and contamination.

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27 Effect smaller than 5% Affects T via two mechanisms: T value changes Event migration between HT3 ranges Deconvolution Average Momentum (P 1 T + P 2 T )/2 (GeV) 0 100 200 300 σ(P T )/P T 0.02 0.06 1 Measured using P T balance in data, in the limit of no soft radiation. Fractional Resolution Measured in two jet events, assuming : Energy Resolutions

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28 Resolutions Important effect in the limit T 1 MC smeared Calculated from position difference between calorimeter and particle MC jets: MC 10 -6 10 -4 10 -2 1-T 10 -6 10 -4 10 -2 1-Tsme

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29 Unfolding Smear MC at particle level by energy and angular resolutions MC Conservative way: let the contents on each bin vary freely Correlation Matrix 1-T Uncertainty: Correction factor extracted from MC as : generated / smeared

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30 Correction factors

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31 Only statistical errors are shown. DØ preliminary CTEQ4HJ, µ F = µ R = P T max /2

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32 Only statistical errors are shown. DØ preliminary

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33 Sources of systematic uncertainties (2nd Bin) 99.5

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34 Sources of systematic uncertainties Using the full covariance matrix (2nd Bin) 9 9.5

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35 Strong point to point correlations in the uncertainty DØ preliminary Thrust range 10 -4 -10 -1.2 HT3 2 2 160-260 95.08 260-360 81.68 360-430 62.15 430-700 27.69 Comparison with theory (s3)(s3)

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36 Thrust range 10 -4 -10 -1.2 HT3 2 2 160-260 28.86 260-360 8.25 360-430 3.89 430-700 4.54 430<HT3<700 Comparison with theory (s4)(s4) DØ preliminary

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37 Conclusions The first precise measurement of an event shape distribution such as d /dT in a hadron collider. The prediction s 3 (Jetrad) agrees with data except for high T values, 1-T 0.12. Resummation calculations needed in the limit T 1. Between the LO prediction is O( s 4 ). Excellent opportunity to test the recently developed NLO 3-jet generators. This prediction (NLOJET++) agrees with data over the whole T range (T ≠ 1), except in the limit T 1 for low HT3, where higher order corrections are still important.

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