Measurement of $$\hbox {t}{\bar{\hbox {t}}}$$tt¯ normalised multi-differential cross sections in $${\text {p}}{\text {p}} $$pp collisions at $$\sqrt{s}=13\,{\text {TeV}} $$s=13TeV , 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 ($$\hbox {t}{\bar{\hbox {t}}}$$) production are measured in proton-proton collisions at a centre-of-mass energy of 13$$\,{\text {TeV}}$$ using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of $$35.9{\,{\text {fb}}^{-1}} $$. The double-differential $$\hbox {t}{\bar{\hbox {t}}}$$ cross section is measured as a function of the kinematic properties of the top quark and of the $$\hbox {t}{\bar{\hbox {t}}}$$ 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 $$\hbox {t}{\bar{\hbox {t}}}$$ system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (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 $$\alpha _{S}$$ and the top quark pole mass ($$m_{{\text {t}}}^{{\text {pole}}}$$) using several sets of parton distribution functions (PDFs). The measurement of $$m_{{\text {t}}}^{{\text {pole}}}$$ exploits the sensitivity of the $$\hbox {t}{\bar{\hbox {t}}}$$ invariant mass distribution to $$m_{{\text {t}}}^{{\text {pole}}}$$ near the production threshold. Furthermore, a simultaneous fit of the PDFs, $$\alpha _{S}$$, and $$m_{{\text {t}}}^{{\text {pole}}}$$ is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of $$\alpha _{S}$$ and $$m_{{\text {t}}}^{{\text {pole}}}$$. The values $$\alpha _{S}(m_{{\text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017}$$ and $$m_{{\text {t}}}^{{\text {pole}}} = 170.5 \pm 0.8 \,{\text {GeV}} $$ are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the $$\hbox {t}{\bar{\hbox {t}}}$$ production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of $$m_{{\text {t}}}^{{\text {pole}}}$$ of the order of $$+1 \,{\text {GeV}} $$, which can be regarded as additional theoretical uncertainty in the current $$m_{{\text {t}}}^{{\text {pole}}}$$ extraction.