Measurements of normalised multi-differential cross$~$sections for top quark pair production in pp collisions at $\sqrt{s}=13~\mathrm{TeV}$ and simultaneous determination of the strong coupling strength, top quark pole mass and parton distribution functions

Normalised multi-differential cross sections for top quark pair (${\mathrm{t}}\bar{\mathrm{t}}$) production are measured in pp collisions at a centre-of-mass energy of $13~\mathrm{TeV}$ using events containing two opposite-sign leptons. The analysed dataset was recorded by the CMS detector in 2016 and corresponds to an integrated luminosity of $35.9~\mathrm{fb}^{-1}$. The ${\mathrm{t}}\bar{\mathrm{t}}$ cross section is measured double-differentially as a function of the kinematic properties of the top quark and the ${\mathrm{t}}\bar{\mathrm{t}}$ system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the ${\mathrm{t}}\bar{\mathrm{t}}$ system and the multiplicity of additional jets at particle level in the event. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) QCD calculations with parton showers. Together with a fixed order NLO QCD calculation the triple-differential measurement is used to extract values of the strong coupling strength ($\alpha_{\mathrm{s}}$) and the top quark pole mass ($m_{\mathrm{t}}^{\mathrm{pole}}$) using several parton distribution function (PDF) sets. Furthermore, a simultaneous fit of PDFs, $\alpha_{\mathrm{s}}$ and $m_{\mathrm{t}}^{\mathrm{pole}}$ is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF and at the same time allow to accurately determine $\alpha_{\mathrm{s}}$ and $m_{\mathrm{t}}^{\mathrm{pole}}$.