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We present a measurement of the $\ttbar$ differential cross section with respect to the $\ttbar$ invariant mass, dSigma/dMttbar, in $\ppbar$ collisions at $\sqrt{s}=1.96$ TeV using an integrated luminosity of $2.7\invfb$ collected by the CDF II experiment.
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Alice Patricia Bridgeman, Measurement of the t t ¯ t\bar{t} Differential Cross Section, d σ / d M t t ¯ d\sigma/dM_{{t\overline{t}}} , in p p ¯ p\bar{p} Collisions at s = 1.96 \sqrt{s}=1.96 TeV, Ph.D Thesis, University of Illinois at Urbana-Champaign, 2008. FERMILAB-THESIS-2008-50
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We use a coordinate system where the z z -axis is in the direction of the proton beam, and ϕ \phi and θ \theta are the azimuthal and polar angles respectively. The pseudorapidity, η \eta , is defined as η = − ln ( tan θ 2 ) \eta=-\ln(\tan\frac{\theta}{2}) . The transverse momentum of a charged particle is P T = P sin θ P_{\mathrm{T}}=P\sin\theta , where P P represents the measured momentum of the charged-particle track. The analogous quantity using calorimeter energies, defined as E T = E sin θ E_{T}=E\sin\theta , is called transverse energy. The missing transverse energy is defined as E / T = − ∣ ∑ i E T i n ^ i ∣ E\!\!\!/_{T}=-\mid\sum_{i}E_{T}^{i}\hat{n}_{i}\mid where E T i E_{T}^{i} is the magnitude of the transverse energy contained in each calorimeter tower i i in the pseudorapidity region ∣ η ∣ < 3.6 \mid\eta\mid<3.6 , and n ^ i \hat{n}_{i} is the direction unit vector of the tower in the plane transverse to the beam direction
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