)] 2  [pb/(GeV/c jj  / dm d -6 10$^{-5}$ 10$^{-4}$ 10$^{-3}$ 10$^{-2}$ 10$^{-1}$ 10 1 10 2 10$^{3}$ 10$^{4}$ 10 ) -1 CDF Run II Data (1.13 fb Fit  = 1) s Excited quark ( f = f’ = f 2 300 GeV/c 2 500 GeV/c 2 700 GeV/c 2 900 GeV/c 2 1100 GeV/c (a) ] 2  [GeV/c jj m 200 400 600 800 1000 1200 1400 (Data - Fit) / Fit -0.4 -0.2 -0 0.2 0.4 0.6 0.8 (b) 200 300 400 500 600 700 -0.04 -0.02 0 0.02 0.04 FIG. 10: (a) CDF’s measured dijet mass spectrum [70]. The dashed curve shows the fit to Equa- tion 9. Also shown are the predicted dijet mass distributions of the excited quark q ∗ for the masses of 300, 500, 700, 900 and 1100 GeV /c 2 respectively. (b) The fractional difference between the measured dijet mass difference and the fit (points) compared to q ∗ signals divided by the fit to the measured dijet mass spectrum (curves). of any resonant structure. The experimental limits are determined for the σ sig ≡ σ · B · A , where σ is the theoretical new particle production rate, B is probability of its decaying into two jets and A is the kinematic acceptance of the resulting particle jets to have | y | < 1 . 0. The upper limits on σ sig are evaluating using a likelihood function L = ∏ i µ n$_{i}$ i exp( − µ$_{i}$ ) /n$_{i}$ ! (10) where µ$_{i}$ = n sig i + n QCD i is the predicted number of events in bin i . The QCD dijet background n QCD i is determined using Equation (9) by evaluating L i · ϵ$_{i}$ · Δ m$_{jj}$ · dσ/dm$_{jj}$ | i where Δ m$_{jj}$ , ϵ$_{i}$ , and L $_{i}$, are the bin width, the trigger efficiency and the integrated luminosity for bin i respectively. The expected signal events n sig i is given by σ sig · L i · ϵ$_{i}$ · ( n$_{i}$/n$_{tot}$ ) where ϵ$_{i}$ is the 29