Searching for direct and indirect signatures of new physics with measurements of the Higgs boson

This thesis describes two searches for new physics using measurements of the Higgs boson at the Compact Muon Solenoid (CMS) experiment. The first search looks for the direct production of a new boson, X, which decays to two Higgs bosons, or a Higgs boson and a new scalar boson, Y. This search is performed in final states including two photons and two tau leptons, and considers mX between 260 and 1000 GeV, and mY between 50 and 800 GeV. The second search considers a scenario where new particles have masses too large to be produced on-shell at the LHC but where their existence can be probed instead by their indirect effects on measurements of single Higgs boson production. In this search, these effects are interpreted in the Standard Model Effective Field Theory (SMEFT). The searches use data collected by the CMS experiment at the LHC between 2016 and 2018 in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb−1. In the direct search, an excess consistent with others seen by the CMS experiment is observed at (mX, mY) = (650, 95) GeV with a local significance of 2.3 standard deviations, and other local excesses are observed up to 3.2 standard deviations, depending on mX and mY. Upper limits are also reported on the production cross sections, and ranges of mX and mY are excluded assuming different theoretical scenarios. In the indirect search, individual constraints on up to 43 SMEFT Wilson coefficients (WCs) are reported, where a discrepancy with respect to the SM prediction is observed for the C(3)Hq WC, corresponding to a p-value of 0.01. Additionally, the simultaneous constraints on up to 17 linear combinations of WCs are reported.