Normalised multi-differential cross sections for top quark pair ($$\hbox {t}{\bar{\hbox {t}}}$$tt¯) production are measured in proton-proton collisions at a centre-of-mass energy of 13$$\,{\text {TeV}}$$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 $$35.9{\,{\text {fb}}^{-1}} $$35.9fb-1. The double-differential $$\hbox {t}{\bar{\hbox {t}}}$$tt¯ cross section is measured as a function of the kinematic properties of the top quark and of the $$\hbox {t}{\bar{\hbox {t}}}$$tt¯ 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 $$\hbox {t}{\bar{\hbox {t}}}$$tt¯ 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 $$\alpha _{S}$$αS and the top quark pole mass ($$m_{{\text {t}}}^{{\text {pole}}}$$mtpole) using several sets of parton distribution functions (PDFs). The measurement of $$m_{{\text {t}}}^{{\text {pole}}}$$mtpole exploits the sensitivity of the $$\hbox {t}{\bar{\hbox {t}}}$$tt¯ invariant mass distribution to $$m_{{\text {t}}}^{{\text {pole}}}$$mtpole near the production threshold. Furthermore, a simultaneous fit of the PDFs, $$\alpha _{S}$$αS, and $$m_{{\text {t}}}^{{\text {pole}}}$$mtpole 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 $$\alpha _{S}$$αS and $$m_{{\text {t}}}^{{\text {pole}}}$$mtpole. The values $$\alpha _{S}(m_{{\text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017}$$αS(mZ)=0.1135-0.0017+0.0021 and $$m_{{\text {t}}}^{{\text {pole}}} = 170.5 \pm 0.8 \,{\text {GeV}} $$mtpole=170.5±0.8GeV 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 $$\hbox {t}{\bar{\hbox {t}}}$$tt¯ production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of $$m_{{\text {t}}}^{{\text {pole}}}$$mtpole of the order of $$+1 \,{\text {GeV}} $$+1GeV, which can be regarded as additional theoretical uncertainty in the current $$m_{{\text {t}}}^{{\text {pole}}}$$mtpole extraction.

Using the SU (3) flavor symmetry, we construct the chiral Lagrangians for the light and heavy pentaquarks. The correction from the nonzero quark is taken into account perturbatively. We derive the Gell-Mann−Okubo type relations for various pentaquark multiplet masses and ColemanGlashow relations for anti-sextet heavy pentaquark magnetic moments. We study possible decays of pentaquarks into conventional hadrons. We also study the interactions between and within various pentaquark multiplets and derive their coupling constants in the symmetry limit. Possible kinematically allowed pionic decay modes are pointed out.