A general search is presented for a low-mass $\tau^-\tau^+$ resonance produced in association with a bottom quark. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The data are consistent with the standard model expectation. Upper limits at 95% confidence level on the cross section times branching fraction are determined for two signal models: a light pseudoscalar Higgs boson decaying to a pair of $\tau$ leptons produced in association with bottom quarks, and a low-mass boson X decaying to a $\tau$-lepton pair that is produced in the decay of a bottom-like quark B such that B $\to$ bX. Masses between 25 and 70 GeV are probed for the light pseudoscalar boson with upper limits ranging from 250 to 44 pb. Upper limits from 20 to 0.3 pb are set on B masses between 170 and 450 GeV for X boson masses between 20 and 70 GeV.

A search is presented for a narrow resonance decaying to a pair of oppositely charged muons using $\sqrt{s} =$ 13 TeV proton-proton collision data recorded at the LHC. In the 45-75 and 110-200 GeV resonance mass ranges, the search is based on conventional triggering and event reconstruction techniques. In the 11.5-45 GeV mass range, the search uses data collected with dimuon triggers with low transverse momentum thresholds, recorded at high rate by storing a reduced amount of trigger-level information. The data correspond to integrated luminosities of 137 fb$^{-1}$ and 96.6 fb$^{-1}$ for conventional and high-rate triggering, respectively. No significant resonant peaks are observed in the probed mass ranges. The search sets the most stringent constraints to date on a dark photon in the $\sim$30-75 and 110-200 GeV mass ranges.

A search for a new $Z'$ gauge boson predicted by $L_{\mu}-L_{\tau}$ models, based on charged-current Drell-Yan production, $pp \rightarrow W^{\pm(*)} \rightarrow Z' \mu^{\pm} \nu \rightarrow \mu^{\pm}\mu^{\mp}\mu^{\pm}\nu$, is presented. The data sample used corresponds to an integrated luminosity of 140 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS detector at the Large Hadron Collider. The search examines a final state of $3\mu$ plus large missing transverse momentum. Upper limits are set on the $Z'$ production cross-section times branching ratio in the mass range of 5-81 GeV. After combining with the previous $Z'$ search using the neutral-current Drell-Yan production with a $4\mu$ final state, the most stringent exclusion limits to date are achieved in the parameter space of the $Z'$ coupling strength and mass.

The results of a search for new heavy $W^\prime$ bosons decaying to an electron or muon and a neutrino using proton-proton collision data at a centre-of-mass energy of $\sqrt{s} = 13$ TeV are presented. The dataset was collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider and corresponds to an integrated luminosity of 36.1 fb$^{-1}$. As no excess of events above the Standard Model prediction is observed, the results are used to set upper limits on the $W^\prime$ boson cross-section times branching ratio to an electron or muon and a neutrino as a function of the $W^\prime$ mass. Assuming a $W^\prime$ boson with the same couplings as the Standard Model $W$ boson, $W^\prime$ masses below 5.1 TeV are excluded at the 95% confidence level.

A search for a new boson X is presented using CERN LHC proton-proton collision data collected by the CMS experiment at $\sqrt{s}$ = 13 TeV in 2016-2018, and corresponding to an integrated luminosity of 138 fb$^{-1}$. The resonance X decays into either a pair of Higgs bosons HH of mass 125 GeV or an H and a new spin-0 boson Y. One H subsequently decays to a pair of photons, and the second H or Y, to a pair of bottom quarks. The explored mass ranges of X are 260-1000 GeV and 300-1000 GeV, for decays to HH and to HY, respectively, with the Y mass range being 90-800 GeV. For a spin-0 X hypothesis, the 95% confidence level upper limit on the product of its production cross section and decay branching fraction is observed to be within 0.90-0.04 fb, depending on the masses of X and Y. The largest deviation from the background-only hypothesis with a local (global) significance of 3.8 (2.8) standard deviations is observed for X and Y masses of 650 and 90 GeV, respectively. The limits are interpreted using several models of new physics.

A search for flavour-changing neutral-current decays of a top quark into an up-type quark (either up or charm) and a light scalar particle $X$ decaying into a bottom anti-bottom quark pair is presented. The search focuses on top-quark pair production where one top quark decays to $qX$, with $X \rightarrow b\bar{b}$, and the other top quark decays according to the Standard Model, with the $W$ boson decaying leptonically. The final state is thus characterised by an isolated electron or muon and at least four jets. Events are categorised according to the multiplicity of jets and jets tagged as originating from $b$-quarks, and a neural network is used to discriminate between signal and background processes. The data analysed correspond to 139 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of 13 TeV, recorded with the ATLAS detector at the LHC. The 95% confidence-level upper limits between 0.019% and 0.062% are derived for the branching fraction $\mathcal{B}$($t \rightarrow uX$) and between 0.018% and 0.078% for the branching fraction $\mathcal{B}$($t \rightarrow cX$), for masses of the scalar particle $X$ between 20 and 160 GeV.

A search is presented for a right-handed W boson (W$_\mathrm{R}$) and a heavy neutrino (N), in a final state consisting of two same-flavor leptons (ee or $\mu\mu$) and two quarks. The search is performed with the CMS experiment at the CERN LHC using a data sample of proton-proton collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 138 fb$^{-1}$. The search covers two regions of phase space, one where the decay products of the heavy neutrino are merged into a single large-area jet, and one where the decay products are well separated. The expected signal is characterized by an excess in the invariant mass distribution of the final-state objects. No significant excess over the standard model background expectations is observed. The observations are interpreted as upper limits on the product of W$_\mathrm{R}$ production cross sections and branching fractions assuming that couplings are identical to those of the standard model W boson. For N masses $m_\mathrm{N}$ equal to half the W$_\mathrm{R}$ mass $m_\mathrm{W_R}$ ($m_\mathrm{N}$ = 0.2 TeV), $m_\mathrm{W_R}$ is excluded at 95% confidence level up to 4.7 (4.8) and 5.0 (5.4) TeV for the electron and muon channels, respectively. This analysis provides the most stringent limits on the W$_\mathrm{R}$ mass to date.

A search for a right-handed gauge boson $W_{\mathrm{R}}$, decaying into a boosted right-handed heavy neutrino $N_{\mathrm{R}}$, in the framework of Left-Right Symmetric Models is presented. It is based on data from proton-proton collisions with a centre-of-mass energy of 13 TeV collected by the ATLAS detector at the Large Hadron Collider during the years 2015, 2016 and 2017, corresponding to an integrated luminosity of 80 fb$^{-1}$. The search is performed separately for electrons and muons in the final state. A distinguishing feature of the search is the use of large-radius jets containing electrons. Selections based on the signal topology result in smaller background compared with to expected signal. No significant deviation from the Standard Model prediction is observed and lower limits are set in the $W_{\mathrm{R}}$ and $N_{\mathrm{R}}$ mass plane. Mass values of the $W_{\mathrm{R}}$ smaller than 3.8-5 TeV are excluded for $N_{\mathrm{R}}$ in the mass range 0.1-1.8 TeV.

A search is presented for a third-generation leptoquark (LQ) coupled exclusively to a $\tau$ lepton and a b quark. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV recorded with the CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with $\tau$ leptons and a varying number of jets originating from b quarks are considered, targeting the single and pair production of LQs, as well as nonresonant $t$-channel LQ exchange. An excess is observed in the data with respect to the background expectation in the combined analysis of all search regions. For a benchmark LQ mass of 2 TeV and an LQ-b-$\tau$ coupling strength of 2.5, the excess reaches a local significance of up to 2.8 standard deviations. Upper limits at the 95% confidence level are placed on the LQ production cross section in the LQ mass range 0.5-2.3 TeV, and up to 3 TeV for $t$-channel LQ exchange. Leptoquarks are excluded below masses of 1.22-1.88 TeV for different LQ models and varying coupling strengths up to 2.5. The study of nonresonant $\tau\tau$ production through $t$-channel LQ exchange allows lower limits on the LQ mass of up to 2.3 TeV to be obtained.

A search for the electroweak production of a vector-like quark T$'$, decaying to a top quark and a Higgs boson is presented. The search is based on a sample of proton-proton collision events recorded at the LHC at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. This is the first T$'$ search that exploits the Higgs boson decay to a pair of photons. For narrow isospin singlet T$'$ states with masses up to 1.1 TeV, the excellent diphoton invariant mass resolution of 1-2% results in an increased sensitivity compared to previous searches based on the same production mechanism. The electroweak production of a T$'$ quark with mass up to 960 GeV is excluded at 95% confidence level, assuming a coupling strength $\kappa_\mathrm{T}$ = 0.25 and a relative decay width $\Gamma/M_{\mathrm{T}'}$ $\lt$ 5%.