Kinematic distributions

The kinematic distributions studied in this section includes various jet $E_T$ , invariant mass and angular correlation variables. These distributions have been measured for the W + jets data but were not corrected for variations in the efficiency of the W selection as a function of the variable under study. For example there is some correlation between the jets and the W transverse energy; this correlation is particularly strong in the events with only one jet where the W is recoiling to the jet. To model this differential efficiency in the theory prediction, Monte Carlo events were passed through the same reconstruction and analysis chain used for data. To extract the theoretical distribution for kinematic variables in $W+\ge n$ jet events, the sample generated with n partons, requiring at least n jet after the reconstruction, have been used.

Figure 11: The one jet rate in the exclusive sample normalized to the inclusive one is shown as a function of the jet $E_T$.

Figure 12: Data to theory comparison for the highest $E_T$ jet distribution in the $W+\ge 1$ jet sample, for the second highest $E_T$ jet distribution in the $W+\ge 2$ jet sample, for the third highest $E_T$ jet distribution in the $W+\ge 3$ jet sample and for the fourth highest $E_T$ jet distribution in the $W+\ge 4$ jet sample. The gray band represent the jet energy systematics. The blue line is a fit to the theoretical distribution calculated with a renormalization scale set to $M_W^2$, while the red dashed line is a fit the theoretical distribution calculated with a renormalization scale set to $<(p_T^{jet})^2>$.

Figure 13: Data to theory comparison for the di-jet invariant mass (left) and angular separation (right). The upper row shows the spectrum of these variables in the $W + ~\ge$ 2 jet samples while the lower row in $W + ~\ge$ 3 jet samples.