Measurement of the ratio of the inclusive 3-jet to 2-jet cross-sections in pp collisions at 7 TeV and first determination of the strong coupling at transverse momenta in the TeV range

A measurement of the ratio of the inclusive 3-jet to 2-jet cross-sections as a function of the average transverse momentum, $\langle p_{T1,2}\rangle$, of the two leading jets in the event is presented. The data have been collected during 2011 at a proton-proton center-of-mass energy of $\sqrt{s}=7\,\text{TeV}$ with the CMS detector at the LHC corresponding to an integrated luminosity of $5.0 {\,\text{fb}^{-1}}$. Comparing the ratio measured in the range $0.4<\langle p_{T1,2}\rangle<1.4{\,\text{TeV}}$ to the predictions of perturbative QCD at next-to-leading order the strong coupling $\alpha_{S}$ is determined. Using the renormalization group equation of QCD this study yields $\alpha_{S}(M_{Z})=0.1143 _{-0.0067}^{+0.0083}$, which is the first derivation of $\alpha_{S}(M_{Z})$ from measurements at momentum scales beyond $0.4 {\,\text{TeV}}$.