A search for lepton flavour violating decays of the Higgs boson in the $\mu\tau$ and e$\tau$ decay modes is presented. The search is based on a data set corresponding to an integrated luminosity of 35.9 fb$^{-1}$ of proton-proton collisions collected with the CMS detector in 2016, at a centre-of-mass energy of 13 TeV. No significant excess over the standard model expectation is observed. The observed (expected) upper limits on the lepton flavour violating branching fractions of the Higgs boson are $\mathcal{B}$(H$\to\mu\tau$) < 0.25% (0.25%) and $\mathcal{B}$(H$\to$e$\tau$) < 0.61% (0.37%), at 95% confidence level. These results are used to derive upper limits on the off-diagonal $\mu\tau$ and e$\tau$ Yukawa couplings $\sqrt{|{Y_{\mu\tau}}|^{2}+|{Y_{\tau\mu}}|^{2}} < 1.43 \times 10^{-3}$ and $\sqrt{|{Y_{\mathrm{e}\tau}}|^{2}+|{Y_{\tau\mathrm{e}}}|^{2}} < 2.26 \times 10^{-3}$ at 95% confidence level. The limits on the lepton flavour violating branching fractions of the Higgs boson and on the associated Yukawa couplings are the most stringent to date.

Searches for invisible decays of the Higgs boson are presented. The data collected with the CMS detector at the LHC correspond to integrated luminosities of 5.1, 19.7, and 2.3 inverse femtobarns at centre-of-mass energies of 7, 8, and 13 TeV, respectively. The search channels target Higgs boson production via gluon fusion, vector boson fusion, and in association with a vector boson. Upper limits are placed on the branching fraction of the Higgs boson decay to invisible particles, as a function of the assumed production cross sections. The combination of all channels, assuming standard model production, yields an observed (expected) upper limit on the invisible branching fraction of 0.24 (0.23) at the 95% confidence level. The results are also interpreted in the context of Higgs-portal dark matter models.

A search is presented for additional neutral Higgs bosons in the $\tau\tau$ final state in proton-proton collisions at the LHC. The search is performed in the context of the minimal supersymmetric extension of the standard model (MSSM), using the data collected with the CMS detector in 2016 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. To enhance the sensitivity to neutral MSSM Higgs bosons, the search includes production of the Higgs boson in association with b quarks. No significant deviation above the expected background is observed. Model-independent limits at 95% confidence level (CL) are set on the product of the branching fraction for the decay into $\tau$ leptons and the cross section for the production via gluon fusion or in association with b quarks. These limits range from 18 pb at 90 GeV to 3.5 fb at 3.2 TeV for gluon fusion and from 15 pb (at 90 GeV) to 2.5 fb (at 3.2 TeV) for production in association with b quarks, assuming a narrow width resonance. In the m$_{\text{h}}^{\text{mod+}}$ scenario these limits translate into a 95% CL exclusion of $\tan\beta&gt;$ 6 for neutral Higgs boson masses below 250 GeV, where $\tan\beta$ is the ratio of the vacuum expectation values of the neutral components of the two Higgs doublets. The 95% CL exclusion contour reaches 1.6 TeV for $\tan\beta=$ 60.

Measurements of the inclusive and differential fiducial cross sections of the Higgs boson are presented, using the $\tau$ lepton decay channel. The differential cross sections are measured as functions of the Higgs boson transverse momentum, jet multiplicity, and transverse momentum of the leading jet in the event if any. The analysis is performed using proton-proton data collected with the CMS detector at the LHC at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 138 fb$^{-1}$. These are the first differential measurements of the Higgs boson cross section in the final state of two $\tau$ leptons, and they constitute a significant improvement over measurements in other final states in events with a large jet multiplicity or with a Lorentz-boosted Higgs boson.

A search for exotic Higgs boson decays to light pseudoscalars in the final state of two muons and two $\tau$ leptons is performed using proton-proton collision data recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Masses of the pseudoscalar boson between 15.0 and 62.5 GeV are probed, and no significant excess of data is observed above the prediction of the standard model. Upper limits are set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different types of two-Higgs-doublet models extended with a complex scalar singlet.

A search for an exotic decay of the Higgs boson to a pair of light pseudoscalar bosons is performed for the first time in the final state with two b quarks and two $\tau$ leptons. The search is motivated in the context of models of physics beyond the standard model (SM), such as two Higgs doublet models extended with a complex scalar singlet (2HDM+S), which include the next-to-minimal supersymmetric SM (NMSSM). The results are based on a data set of proton-proton collisions corresponding to an integrated luminosity of 35.9 fb$^{-1}$, accumulated by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV. Masses of the pseudoscalar boson between 15 and 60 GeV are probed, and no excess of events above the SM expectation is observed. Upper limits between 3 and 12% are set on the branching fraction $\mathcal{B}$(h $\to$ aa $\to$ 2$\tau$2b) assuming the SM production of the Higgs boson. Upper limits are also set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different 2HDM+S scenarios. Assuming the SM production cross section for the Higgs boson, the upper limit on this quantity is as low as 20% for a mass of the pseudoscalar of 40 GeV in the NMSSM.

A search is presented for decays of Z and Higgs bosons to a J$/\psi$ meson and a photon, with the subsequent decay of the J$/\psi$ to $\mu^+\mu^-$. The analysis uses data from proton-proton collisions with an integrated luminosity of 35.9 fb$^{-1}$ at $\sqrt{s} =$ 13 TeV collected with the CMS detector at the LHC. The observed limit on the Z $\to$ J$/\psi \gamma$ decay branching fraction, assuming that the J$/\psi$ meson is produced unpolarized, is 1.4 $\times$ 10$^{-6}$ at 95% confidence level, which corresponds to a rate higher than expected in the standard model by a factor of 15. For extreme-polarization scenarios, the observed limit changes from -13.6 to +8.6% with respect to the unpolarized scenario. The observed upper limit on the branching fraction for H $\to$ J$/\psi \gamma$ where the J$/\psi$ meson is assumed to be transversely polarized is 7.6 $\times$ 10$^{-4}$, a factor of 260 larger than the standard model prediction. The results for the Higgs boson are combined with previous data from proton-proton collisions at $\sqrt{s} =$ 8 TeV to produce an observed upper limit on the branching fraction for H $\to$ J$/\psi \gamma$ that is a factor of 220 larger than the standard model value.

Differential Higgs boson (H) production cross sections are sensitive probes for physics beyond the standard model. New physics may contribute in the gluon-gluon fusion loop, the dominant Higgs boson production mechanism at the LHC, and manifest itself through deviations from the distributions predicted by the standard model. Combined spectra for the H $\to$ $\gamma\gamma$, H $\to$ ZZ, and H $\to$ $\mathrm{b\overline{b}}$ decay channels and the inclusive Higgs boson production cross section are presented, based on proton-proton collision data recorded with the CMS detector at $\sqrt{s} =$ 13 TeV corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The transverse momentum spectrum is used to place limits on the Higgs boson couplings to the top, bottom, and charm quarks, as well as its direct coupling to the gluon field. No significant deviations from the standard model are observed in any differential distribution. The measured total cross section is 61.1 $\pm$ 6.0 (stat) $\pm$ 3.7 (syst) pb, and the precision of the measurement of the differential cross section of the Higgs boson transverse momentum is improved by about 15% with respect to the H $\to$ $\gamma\gamma$ channel alone.

A search for a Higgs boson decaying into a pair of electrons or muons and a photon is described. Higgs boson decays to a Z boson and a photon (H $\to$ Z$\gamma\to\ell\ell\gamma$, $\ell =$ e or $\mu$), or to two photons, one of which has an internal conversion into a muon pair (H $\to\gamma^{*}\gamma\to\mu\mu\gamma$) were considered. The analysis is performed using a data set recorded by the CMS experiment at the LHC from proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. No significant excess above the background prediction has been found. Limits are set on the cross section for a standard model Higgs boson decaying to opposite-sign electron or muon pairs and a photon. The observed limits on cross section times the corresponding branching fractions vary between 1.4 and 4.0 (6.1 and 11.4) times the standard model cross section for H $\to\gamma^{*}\gamma\to\mu\mu\gamma$ (H $\to$ Z$\gamma\to\ell\ell\gamma$) in the 120-130 GeV mass range of the $\ell\ell\gamma$ system. The H $\to\gamma^*\gamma\to\mu\mu\gamma$ and H $\to$ Z$\gamma\to\ell\ell\gamma$ analyses are combined for $m_\mathrm{H} =$ 125 GeV, obtaining an observed (expected) 95% confidence level upper limit of 3.9 (2.0) times the standard model cross section.

A search is presented for massive narrow resonances decaying either into two Higgs bosons, or into a Higgs boson and a W or Z boson. The decay channels considered are HH$\to \mathrm{b\overline{b}}\tau^{+}\tau^{-}$ and VH$ \to \mathrm{q\overline{q}}\tau^{+}\tau^{-}$, where H denotes the Higgs boson, and V denotes the W or Z boson. This analysis is based on a data sample of proton-proton collisions collected at a center-of-mass energy of 13 TeV by the CMS Collaboration, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. For the TeV-scale mass resonances considered, substructure techniques provide ways to differentiate among the hadronization products from vector boson decays to quarks, Higgs boson decays to bottom quarks, and quark- or gluon-induced jets. Reconstruction techniques are used that have been specifically optimized to select events in which the tau lepton pair is highly boosted. The observed data are consistent with standard model expectations and upper limits are set at 95% confidence level on the product of cross section and branching fraction for resonance masses between 0.9 and 4.0 TeV. Exclusion limits are set in the context of bulk radion and graviton models: spin-0 radion resonances are excluded below a mass of 2.7 TeV at 95% confidence level. In the spin-1 heavy vector triplet framework, mass-degenerate W' and Z' resonances with dominant couplings to the standard model gauge bosons are excluded below a mass of 2.8 TeV at 95% confidence level. There are the first limits for these decay channels at $\sqrt{s}=$ 13 TeV.