Three searches are presented for signatures of physics beyond the standard model (SM) in $\tau\tau$ final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay into $\tau$ leptons and the cross sections for the production of a new boson $\phi$, in addition to the H(125) boson, via gluon fusion (gg$\phi$) or in association with b quarks, ranging from $\mathcal{O}$(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5 TeV each. The data reveal two excesses for gg$\phi$ production with local $p$-values equivalent to about three standard deviations at $m_\phi$ = 0.1 and 1.2 TeV. In a search for $t$-channel exchange of a vector leptoquark U$_1$, 95% CL upper limits are set on the dimensionless U$_1$ leptoquark coupling to quarks and $\tau$ leptons ranging from 1 for a mass of 1 TeV to 6 for a mass of 5 TeV, depending on the scenario. In the interpretations of the $M_\mathrm{h}^{125}$ and $M_\mathrm{h, EFT}^{125}$ minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.

A measurement of the jet mass distribution in hadronic decays of Lorentz-boosted top quarks is presented. The measurement is performed in the lepton+jets channel of top quark pair production ($\mathrm{t\bar{t}}$) events, where the lepton is an electron or muon. The products of the hadronic top quark decay are reconstructed using a single large-radius jet with transverse momentum greater than 400 GeV. The data were collected with the CMS detector at the LHC in proton-proton collisions and correspond to an integrated luminosity of 138 fb$^{-1}$. The differential $\mathrm{t\bar{t}}$ production cross section as a function of the jet mass is unfolded to the particle level and is used to extract the top quark mass. The jet mass scale is calibrated using the hadronic W boson decay within the large-radius jet. The uncertainties in the modelling of the final state radiation are reduced by studying angular correlations in the jet substructure. These developments lead to a significant increase in precision, and a top quark mass of 173.06 $\pm$ 0.84 GeV.

A combination of four searches for new physics involving signatures with at least one photon and large missing transverse momentum, motivated by generalized models of gauge-mediated supersymmetry (SUSY) breaking, is presented. All searches make use of proton-proton collision data at $\sqrt{s}=$ 13 TeV, which were recorded with the CMS detector at the LHC in 2016, and correspond to an integrated luminosity of 35.9 fb$^{-1}$. Signatures with at least one photon and large missing transverse momentum are categorized into events with two isolated photons, events with a lepton and a photon, events with additional jets, and events with at least one high-energy photon. No excess of events is observed beyond expectations from standard model processes, and limits are set in the context of gauge-mediated SUSY. Compared to the individual searches, the combination extends the sensitivity to gauge-mediated SUSY in both electroweak and strong production scenarios by up to 100 GeV in neutralino and chargino masses, and yields the first CMS result combining various SUSY searches in events with photons at $\sqrt{s}=$ 13 TeV.

A measurement of the top quark pole mass $m_\mathrm{t}^\text{pole}$ in events where a top quark-antiquark pair ($\mathrm{t\bar{t}}$) is produced in association with at least one additional jet ($\mathrm{t\bar{t}}$+jet) is presented. This analysis is performed using proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment at the CERN LHC, corresponding to a total integrated luminosity of 36.3 fb$^{-1}$. Events with two opposite-sign leptons in the final state (e$^+$e$^-$, $\mu^+\mu^-$, e$^\pm\mu^\mp$) are analyzed. The reconstruction of the main observable and the event classification are optimized using multivariate analysis techniques based on machine learning. The production cross section is measured as a function of the inverse of the invariant mass of the $\mathrm{t\bar{t}}$+jet system at the parton level using a maximum likelihood unfolding. Given a reference parton distribution function (PDF), the top quark pole mass is extracted using the theoretical predictions at next-to-leading order. For the ABMP16NLO PDF, this results in $m_\mathrm{t}^\text{pole}$ = 172.93 $\pm$ 1.36 GeV.

Multijet events at large transverse momentum ($p_\mathrm{T}$) are measured at $\sqrt{s}$ = 13 TeV using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The multiplicity of jets with $p_\mathrm{T}$$>$ 50 GeV that are produced in association with a high-$p_\mathrm{T}$ dijet system is measured in various ranges of the $p_\mathrm{T}$ of the jet with the highest transverse momentum and as a function of the azimuthal angle difference $\Delta\phi_{1,2}$ between the two highest $p_\mathrm{T}$ jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest $p_\mathrm{T}$ jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower.

A search is reported for near-threshold structures in the J/$\psi$J/$\psi$ invariant mass spectrum produced in proton-proton collisions at $\sqrt{s}$ = 13 TeV from data collected by the CMS experiment, corresponding to an integrated luminosity of 135 fb$^{-1}$. Three structures are found, and a model with quantum interference among these structures provides a good description of the data. A new structure is observed with a significance above 5 standard deviations at a mass of 6638 $^{+43}_{-38}$ (stat) $^{+16}_{-31}$ (syst) MeV. Another structure with even higher significance is found at a mass of 6847 $^{+44}_{-28}$ (stat) $^{+48}_{-20}$ (syst) MeV, which is consistent with the X(6900) resonance reported by the LHCb experiment and confirmed by the ATLAS experiment. Evidence for another new structure, with a local significance of 4.7 standard deviations, is found at a mass of 7134 $^{+48}_{-25}$ (stat) $^{+41}_{-15}$ (syst) MeV. Results are also reported for a model without interference, which does not fit the data as well and shows mass shifts up to 150 MeV relative to the model with interference.

A search for Kaluza-Klein excited vector boson resonances, $W_\mathrm{KK}$, decaying in cascade to three W bosons via a scalar radion $R, W_\mathrm{KK}\to WR \to WWW$, with two or three massive jets is presented. The search is performed with proton-proton collision data recorded at $\sqrt{s} =$ 13 TeV, collected by the CMS experiment at the CERN LHC, during 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. Two final states are simultaneously probed, one where the two W bosons produced by the R decay are reconstructed as separate, large-radius, massive jets, and one where they are merged in a single large-radius jet. The observed data are in agreement with the standard model expectations. Limits are set on the product of the $W_\mathrm{KK}$ resonance cross section and branching fraction to three W bosons in an extended warped extra-dimensional model and are the first of their kind at the LHC.

A measurement of the cross section of the associated production of a single top quark and a W boson in final states with a muon or electron and jets in proton-proton collisions at $\sqrt{s}$ = 13 TeV is presented. The data correspond to an integrated luminosity of 36 fb$^{-1}$ collected with the CMS detector at the CERN LHC in 2016. A boosted decision tree is used to separate the tW signal from the dominant $\mathrm{t\bar{t}}$ background, whilst the subleading W+jets and multijet backgrounds are constrained using data-based estimates. This result is the first observation of the tW process in final states containing a muon or electron and jets, with a significance exceeding 5 standard deviations. The cross section is determined to be 89 $\pm$ 4 (stat) $\pm$ 12 (syst) pb, consistent with the standard model.

A search for resonances decaying into a W boson and a radion, where the radion decays into two W bosons, is presented. The data analyzed correspond to an integrated luminosity of 138 fb$^{-1}$ recorded in proton-proton collisions with the CMS detector at $\sqrt{s} =$ 13 TeV. One isolated charged lepton is required, together with missing transverse momentum and one or two massive large-radius jets, containing the decay products of either two or one W bosons, respectively. No excess over the background estimation is observed. The results are combined with those from a complementary channel with an all-hadronic final state, described in an accompanying paper. Limits are set on parameters of an extended warped extra-dimensional model. These searches are the first of their kind at the LHC.

The dependence of the ratio between the B$_\mathrm{s}^0$ and B$^+$ hadron production fractions, $f_\mathrm{s} / f_\mathrm{u}$, on the transverse momentum ($p_\mathrm{T}$) and rapidity of the B mesons is studied using the decay channels B$_\mathrm{s}^0$$\to$ J$/\psi\,\phi$ and B$^+$$\to$ J$/\psi$ K$^+$. The analysis uses a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of 61.6 fb$^{-1}$. The $f_\mathrm{s} / f_\mathrm{u}$ ratio is observed to depend on the B $p_\mathrm{T}$ and to be consistent with becoming asymptotically constant at large $p_\mathrm{T}$. No rapidity dependence is observed. The ratio of the B$^0$ to B$^+$ hadron production fractions, $f_\mathrm{d} / f_\mathrm{u}$, measured using the B$^0$$\to$ J$/\psi$ K$^{*0}$ decay channel, is found to be consistent with unity and independent of $p_\mathrm{T}$ and rapidity, as expected from isospin invariance.