Running of the top quark mass at NNLO in QCD

The running of the top quark mass ($m_{\mathrm{t}}$) is probed at the next-to-next-to-leading order in quantum chromodynamics for the first time. The result is obtained by comparing calculations in the modified minimal subtraction ($\overline{\mathrm{M}\mathrm{S}}$) renormalisation scheme to the CMS result on differential measurement of the top quark-antiquark ($\mathrm{t}\bar{\mathrm{t}}$) production cross section at $\sqrt{s}=13\mathrm{T}\mathrm{e}\mathrm{V}$. The scale dependence of $m_{\mathrm{t}}$ is extracted as a function of the invariant mass of the $\mathrm{t}\bar{\mathrm{t}}$ system, up to an energy scale of about $0.5\mathrm{T}\mathrm{e}\mathrm{V}$. The observed running is found to be in good agreement with the three-loop solution of the renormalisation group equations of quantum chromodynamics.