First Measurement of the Production of a W Boson in Association with a Single Charm Quark in Proton Anti-proton Collisions at sqrt(s)=1.96 TeV

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We use a ( z , ϕ , θ z,\phi,\theta ) 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 pseudo-rapidity is η ≡ − ln ⁡ ( tan ⁡ θ 2 ) \eta\equiv-\ln(\tan\frac{\theta}{2}) . Transverse energy and momentum are E T ≡ E ​ sin ⁡ θ E_{T}\equiv E\sin\theta and p T ≡ p ​ sin ⁡ θ p_{T}\equiv p\sin\theta respectively, where E E and p p are energy and momentum. The missing transverse energy is E̸ T ≡ | − ∑ i E T i n ^ i | \not{E}_{T}\equiv|-\sum_{i}E_{T}^{i}\hat{n}_{i}| , where E T i E_{T}^{i} is the magnitude of the transverse energy contained in each calorimeter tower i i in the region | η | < 3.6 |\eta|<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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The isolation ( I I ) is defined as the calorimeter transverse energy in a cone of opening Δ ​ R ≡ ( Δ ​ η ) 2 + ( Δ ​ ϕ ) 2 = 0.4 \Delta R\equiv\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}}=0.4 around the lepton (not including the lepton energy itself) divided by the lepton E T E_{T} or p T p_{T}

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