A tagging algorithm to identify jets that are significantly displaced from the proton-proton (pp) collision region in the CMS detector at the LHC is presented. Displaced jets can arise from the decays of long-lived particles (LLPs), which are predicted by several theoretical extensions of the standard model. The tagger is a multiclass classifier based on a deep neural network, which is parameterised according to the proper decay length $\mathrm{c}\tau_0$ of the LLP. A novel scheme is defined to reliably label jets from LLP decays for supervised learning. Samples of pp collision data, recorded by the CMS detector at a centre-of-mass energy of 13 TeV, and simulated events are used to train the neural network. Domain adaptation by backward propagation is performed to improve the simulation modelling of the jet class probability distributions observed in pp collision data. The potential performance of the tagger is demonstrated with a search for long-lived gluinos, a manifestation of split supersymmetric models. The tagger provides a rejection factor of 10 000 for jets from standard model processes, while maintaining an LLP jet tagging efficiency of 30-80% for gluinos with 1 mm $\leq$ $c\tau_0$ $\leq$ 10 m. The expected coverage of the parameter space for split supersymmetry is presented.

Studies of $CP$ violation and anomalous couplings of the Higgs boson to vector bosons and fermions are presented. The data were acquired by the CMS experiment at the LHC and correspond to an integrated luminosity of 137 fb$^{-1}$ at a proton-proton collision energy of 13 TeV. The kinematic effects in the Higgs boson's four-lepton decay H $\to$ 4$\ell$ and its production in association with two jets, a vector boson, or top quarks are analyzed, using a full detector simulation and matrix element techniques to identify the production mechanisms and to increase sensitivity to the Higgs boson tensor structure of the Higgs boson interactions. A simultaneous measurement is performed of up to five Higgs boson couplings to electroweak vector bosons (HVV), two couplings to gluons (Hgg), and two couplings to top quarks (Htt). The $CP$ measurement in the Htt interaction is combined with the recent measurement in the H $\to$ $\gamma\gamma$ channel. The results are presented in the framework of anomalous couplings and are also interpreted in the framework of effective field theory, including the first study of $CP$ properties of the Htt and effective Hgg couplings from a simultaneous analysis of the gluon fusion and top-associated processes. The results are consistent with the standard model of particle physics.

Collinear (small-angle) and large-angle, as well as soft and hard radiations are investigated in three-jet and Z + two-jet events collected in proton-proton collisions at the LHC. The normalized production cross sections are measured as a function of the ratio of transverse momenta of two jets and their angular separation. The measurements in the three-jet and Z + two-jet events are based on data collected at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.8 fb$^{-1}$. The Z + two-jet events are reconstructed in the dimuon decay channel of the Z boson. The three-jet measurement is extended to include $\sqrt{s} =$ 13 TeV data corresponding to an integrated luminosity of 2.3 fb$^{-1}$. The results are compared to predictions from event generators that include parton showers, multiple parton interactions, and hadronization. The collinear and soft regions are in general well described by parton showers, whereas the regions of large angular separation are often best described by calculations using higher-order matrix elements.