Measurements of $\alpha_s$ in $pp$ Collisions at the LHC

The coupling of the strong force, $\alpha_s$, is deemed to be a fundamental parameter of Nature, and, beyond the quark masses, constitutes the only free parameter in the QCD Lagrangian. Provided is an overview of CERN Large Hadron Collider (LHC) measurements of $\alpha_s(M_Z)$ evaluated at the $Z$-boson mass and of the running of $\alpha_s(Q)$ as a function of energy-momentum transfer $Q$. The measurements were performed by the ATLAS and CMS Collaborations using proton-proton ($pp$) collisions with centre-of-mass energies of 7 TeV and data samples with time-integrated luminosities of up to 5 fb$^{-1}$. Four different categories of observable were used in the described extractions of $\alpha_s$: inclusive jet cross sections, 3-jet to 2-jet inclusive cross-section ratios, 3-jet mass cross sections, and top-quark pair production cross sections. These results, which include the first NNLO measurement of $\alpha_s$ at a hadron collider and the first determinations of $\alpha_s$ at energy scales above 1 TeV, are consistent with each other, with the world-average value, and with QCD predictions of their running with $Q$.