consequence, gravity appears weak in the three conventional spatial dimensions. The Planck scale, the number of extra dimension n , their size R and an effective Planck scale M$_{S}$ are related by M$_{P l}$ = M$_{S}$R $^{n}$. Experimentally, M$_{S}$ can be measured for different values of n . The Kaluza-Klein excitations of the graviton can be exchanged between partons and thus contribute to jet production, resulting in jets which are central. There are two different formalisms to describe LED models, GRW [77] and HLZ [78]. In the HLZ formalism, the sub-leading dependence on the number n of extra dimensions is also included. In some models [79–81], extra dimensions are assumed to exist at the TeV − 1 distance scale. In these models, Kaluza-Klein excitations of SM bosons modify various production cross sections. In these models, gluons can propagate through the extra dimensions, which changes the jet cross section. The strength of the interaction is given by the model parameter, the compactification scale, M$_{C}$ . To search for new physics, instead of studying the cos θ ∗ distribution directly, it is con- venient to use the χ$_{dijet}$ distribution which removes the Rutherford singularity: χ$_{dijet}$ is defined as exp( | y$_{1}$ − y$_{2}$ | ) where y$_{1}$ and y$_{2}$ are rapidities [19] of the two highest p$_{T}$ jets in an event. For 2 → 2 scattering of massless partons, the variable χ$_{dijet}$ is related to the partonic center-of-momentum frame polar angle θ ∗ by χ$_{dijet}$ = (1 + cos θ $^{∗}$) / (1 − cos θ $^{∗}$). The CDF collaboration studied the dijet angular distributions using 106 pb − 1 of data from Run I [82]. The data excludes at 95% CL a model of quark substructure in which only up and down quarks are composite and the contact interaction scale is Λ + ud ≤ 1 . 6 TeV or Λ − ud ≤ 1 . 4 TeV where the subscript refers to the flavor of quarks assumed to be composite and the superscript ± refers to the sign of the interference. For a model in which all quarks are composite, the excluded regions are Λ + ≤ 1 . 8 TeV and Λ − ≤ 1 . 6 TeV. In Run II, the DØ collaboration measured the χ$_{dijet}$ distribution in the χ$_{dijet}$ ≤ 16 range in 10 dijet mass m$_{jj}$ bins covering the 0 . 25 < m$_{jj}$ < 1 . 1 TeV /c 2 range using up to 0.7 fb − 1 of data collected during 2004 − 2005 [83]. The boost of the two-jet system is required to be y$_{boost}$ ≡ 0 . 5 × | y$_{1}$ + y$_{2}$ | ≤ 1. This requirement, combined with the dijet mass cut and the range of the χ$_{dijet}$ distribution, restricts the highest allowable rapidity to | y$_{1}$$_{,}$$_{2}$ | < 2 . 4 where the DØ detector performance is well understood. The measured distributions are corrected for detector effects using events generated with pythia v6.419 [8] with tune QW [21] and the MSTW2008LO parton distributions functions. This procedure corrects for the migration between dijet mass bins, as well as the shape of the χ$_{dijet}$ distributions in each mass bin. 32