The result of a search for pair production of the supersymmetric partner of the Standard Model bottom quark ($\tilde{b}_1$) is reported. The search uses 3.2 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}=$13 TeV collected by the ATLAS experiment at the Large Hadron Collider in 2015. Bottom squarks are searched for in events containing large missing transverse momentum and exactly two jets identified as originating from $b$-quarks. No excess above the expected Standard Model background yield is observed. Exclusion limits at 95% confidence level on the mass of the bottom squark are derived in phenomenological supersymmetric $R$-parity-conserving models in which the $\tilde{b}_1$ is the lightest squark and is assumed to decay exclusively via $\tilde{b}_1 \rightarrow b \tilde{\chi}_1^0$, where $\tilde{\chi}_1^0$ is the lightest neutralino. The limits significantly extend previous results; bottom squark masses up to 800 (840) GeV are excluded for the $\tilde{\chi}_1^0$ mass below 360 (100) GeV whilst differences in mass above 100 GeV between the $\tilde{b}_1$ and the $\tilde{\chi}_1^0$ are excluded up to a $\tilde{b}_1$ mass of 500 GeV.

A search for magnetic monopoles and high-electric-charge objects is presented using 34.4 fb$^{-1}$ of 13 TeV $pp$ collision data collected by the ATLAS detector at the LHC during 2015 and 2016. The considered signature is based upon high ionization in the transition radiation tracker of the inner detector associated with a pencil-shape energy deposit in the electromagnetic calorimeter. The data were collected by a dedicated trigger based on the tracker high-threshold hit capability. The results are interpreted in models of Drell-Yan pair production of stable particles with two spin hypotheses (0 and 1/2) and masses ranging from 200 GeV to 4000 GeV. The search improves by approximately a factor of five the constraints on the direct production of magnetic monopoles carrying one or two Dirac magnetic charges and stable objects with electric charge in the range $20\le|z|\le60$ and extends the charge range to $60<|z|\le100$.

A search is performed for the electroweak pair production of charginos and associated production of a chargino and neutralino, each of which decays through an $R$-parity-violating coupling into a lepton and a $W$, $Z$, or Higgs boson. The trilepton invariant-mass spectrum is constructed from events with three or more leptons, targeting chargino decays that include an electron or muon and a leptonically decaying $Z$ boson. The analyzed dataset corresponds to an integrated luminosity of 139 fb$^{-1}$ of proton-proton collision data produced by the Large Hadron Collider at a center-of-mass energy of $\sqrt{s}$ = 13 TeV and collected by the ATLAS experiment between 2015 and 2018. The data are found to be consistent with predictions from the Standard Model. The results are interpreted as limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model. Limits are also set on the production of charginos and neutralinos for a Minimal Supersymmetric Standard Model with an approximate $B$-$L$ symmetry. Charginos and neutralinos with masses between 100 GeV and 1100 GeV are excluded depending on the assumed decay branching fractions into a lepton (electron, muon, or $\tau$-lepton) plus a boson ($W$, $Z$, or Higgs).

Many extensions of the Standard Model predict the existence of charged heavy long-lived particles, such as $R$-hadrons or charginos. These particles, if produced at the Large Hadron Collider, should be moving non-relativistically and are therefore identifiable through the measurement of an anomalously large specific energy loss in the ATLAS pixel detector. Measuring heavy long-lived particles through their track parameters in the vicinity of the interaction vertex provides sensitivity to metastable particles with lifetimes from 0.6 ns to 30 ns. A search for such particles with the ATLAS detector at the Large Hadron Collider is presented, based on a data sample corresponding to an integrated luminosity of 18.4 fb$^{-1}$ of $pp$ collisions at $\sqrt{s}$ = 8 TeV. No significant deviation from the Standard Model background expectation is observed, and lifetime-dependent upper limits on $R$-hadrons and chargino production are set. Gluino $R$-hadrons with 10 ns lifetime and masses up to 1185 GeV are excluded at 95$\%$ confidence level, and so are charginos with 15 ns lifetime and masses up to 482 GeV.

A search for the direct production of the supersymmetric partners of $\tau$-leptons (staus) in final states with two hadronically decaying $\tau$-leptons is presented. The analysis uses a dataset of $pp$ collisions corresponding to an integrated luminosity of $139$ fb$^{-1}$, recorded with the ATLAS detector at the Large Hadron Collider at a center-of-mass energy of 13 TeV. No significant deviation from the expected Standard Model background is observed. Limits are derived in scenarios of direct production of stau pairs with each stau decaying into the stable lightest neutralino and one $\tau$-lepton in simplified models where the two stau mass eigenstates are degenerate. Stau masses from 120 GeV to 390 GeV are excluded at 95% confidence level for a massless lightest neutralino.

Narrow resonances decaying into $WW$, $WZ$ or $ZZ$ boson pairs are searched for in 139 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded with the ATLAS detector at the Large Hadron Collider from 2015 to 2018. The diboson system is reconstructed using pairs of high transverse momentum, large-radius jets. These jets are built from a combination of calorimeter- and tracker-inputs compatible with the hadronic decay of a boosted $W$ or $Z$ boson, using jet mass and substructure properties. The search is performed for diboson resonances with masses greater than 1.3 TeV. No significant deviations from the background expectations are observed. Exclusion limits at the 95% confidence level are set on the production cross-section times branching ratio into dibosons for resonances in a range of theories beyond the Standard Model, with the highest excluded mass of a new gauge boson at 3.8 TeV in the context of mass-degenerate resonances that couple predominantly to gauge bosons.

Higgsinos with masses near the electroweak scale can solve the hierarchy problem and provide a dark matter candidate, while detecting them at the LHC remains challenging if their mass-splitting is $\mathcal{O}$(1 GeV). This Letter presents a novel search for nearly mass-degenerate higgsinos in events with an energetic jet, missing transverse momentum, and a low-momentum track with a significant transverse impact parameter using 140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the ATLAS experiment. For the first time since LEP, a range of mass-splittings between the lightest charged and neutral higgsinos from 0.3 GeV to 0.9 GeV is excluded at 95% confidence level, with a maximum reach of approximately 170 GeV in the higgsino mass.

Results are reported of a search for new phenomena, such as supersymmetric particle production, that could be observed in high-energy proton--proton collisions. Events with large numbers of jets, together with missing transverse momentum from unobserved particles, are selected. The data analysed were recorded by the ATLAS experiment during 2015 using the 13 TeV centre-of-mass proton--proton collisions at the Large Hadron Collider, and correspond to an integrated luminosity of 3.2 fb$^{-1}$. The search selected events with various jet multiplicities from $\ge 7$ to $\ge 10$ jets, and with various $b$-jet multiplicity requirements to enhance sensitivity. No excess above Standard Model expectations is observed. The results are interpreted within two supersymmetry models, where gluino masses up to 1400 GeV are excluded at 95% confidence level, significantly extending previous limits.

The problems of neutrino masses, matter-antimatter asymmetry, and dark matter could be successfully addressed by postulating right-handed neutrinos with Majorana masses below the electroweak scale. In this work, leptonic decays of $W$ bosons extracted from 32.9 fb$^{-1}$ to 36.1 fb$^{-1}$ of 13 TeV proton-proton collisions at the LHC are used to search for heavy neutral leptons (HNLs) that are produced through mixing with muon or electron neutrinos. The search is conducted using the ATLAS detector in both prompt and displaced leptonic decay signatures. The prompt signature requires three leptons produced at the interaction point (either $\mu\mu e$ or $e e\mu$) with a veto on same-flavour opposite-charge topologies. The displaced signature comprises a prompt muon from the $W$ boson decay and the requirement of a dilepton vertex (either $\mu\mu$ or $\mu e$) displaced in the transverse plane by 4-300 mm from the interaction point. The search sets constraints on the HNL mixing to muon and electron neutrinos for HNL masses in the range 4.5-50 GeV.

The production of single top quarks and top antiquarks via the $t$-channel exchange of a virtual $W$ boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using $140\,\mathrm{fb^{-1}}$ of ATLAS data. The total cross-sections are determined to be $\sigma(tq)=137^{+8}_{-8}\,\mathrm{pb}$ and $\sigma(\bar{t}q)=84^{+6}_{-5}\,\mathrm{pb}$ for top-quark and top-antiquark production, respectively. The combined cross-section is found to be $\sigma(tq+\bar{t}q)=221^{+13}_{-13}\,\mathrm{pb}$ and the cross-section ratio is $R_{t}=\sigma(tq)/\sigma(\bar{t}q)=1.636^{+0.036}_{-0.034}$. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of $R_{t}$ using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: $-0.37 < C_{Qq}^{3,1}/\Lambda^2 < 0.06$ and $-0.87 < C_{\phi Q}^{3}/\Lambda^2 < 1.42$. The constraint $|V_{tb}|>0.95$ at the 95% confidence level is derived from the measured value of $\sigma(tq+\bar{t}q)$. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confidence contours in the corresponding two-dimensional parameter spaces.

A search for long-lived particles decaying into an oppositely charged lepton pair, $\mu\mu$, $ee$, or $e\mu$, is presented using 32.8 fb$^{-1}$ of $pp$ collision data collected at $\sqrt{s}=13$ TeV by the ATLAS detector at the LHC. Candidate leptons are required to form a vertex, within the inner tracking volume of ATLAS, displaced from the primary $pp$ interaction region. No lepton pairs with an invariant mass greater than 12 GeV are observed, consistent with the background expectations derived from data. The detection efficiencies for generic resonances with lifetimes ($c\tau$) of 100-1000 mm decaying into a dilepton pair with masses between 0.1-1.0 TeV are presented as a function of $p_T$ and decay radius of the resonances to allow the extraction of upper limits on the cross sections for theoretical models. The result is also interpreted in a supersymmetric model in which the lightest neutralino, produced via squark-antisquark production, decays into $\ell^{+}\ell^{'-}\nu$ ($\ell, \ell^{'} = e$, $\mu$) with a finite lifetime due to the presence of R-parity violating couplings. Cross-section limits are presented for specific squark and neutralino masses. For a 700 GeV squark, neutralinos with masses of 50-500 GeV and mean proper lifetimes corresponding to $c\tau$ values between 1 mm to 6 m are excluded. For a 1.6 TeV squark, $c\tau$ values between 3 mm to 1 m are excluded for 1.3 TeV neutralinos.

The results of a search for the stop, the supersymmetric partner of the top quark, in final states with one isolated electron or muon, jets, and missing transverse momentum are reported. The search uses the 2015 LHC $pp$ collision data at a center-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector and corresponding to an integrated luminosity of 3.2 fb${}^{-1}$. The analysis targets two types of signal models: gluino-mediated pair production of stops with a nearly mass-degenerate stop and neutralino; and direct pair production of stops, decaying to the top quark and the lightest neutralino. The experimental signature in both signal scenarios is similar to that of a top quark pair produced in association with large missing transverse momentum. No significant excess over the Standard Model background prediction is observed, and exclusion limits on gluino and stop masses are set at 95% confidence level. The results extend the LHC Run-1 exclusion limit on the gluino mass up to 1460 GeV in the gluino-mediated scenario in the high gluino and low stop mass region, and add an excluded stop mass region from 745 to 780 GeV for the direct stop model with a massless lightest neutralino. The results are also reinterpreted to set exclusion limits in a model of vector-like top quarks.

A measurement of the associated production of a top-quark pair ($t\bar{t}$) with a vector boson ($W$, $Z$) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using $36.1$ fb$^{-1}$ of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The $t\bar{t}Z$ and $t\bar{t}W$ production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are $\sigma_{t\bar{t}Z} = 0.95 \pm 0.08_{\mathrm{stat.}} \pm 0.10_{\mathrm{syst.}}$ pb and $\sigma_{t\bar{t}W} = 0.87 \pm 0.13_{\mathrm{stat.}} \pm 0.14_{\mathrm{syst.}}$ pb in agreement with the Standard Model predictions. The measurement of the $t\bar{t}Z$ cross section is used to set constraints on effective field theory operators which modify the $t\bar{t}Z$ vertex.

The results of a search for direct pair production of top squarks and for dark matter in events with two opposite-charge leptons (electrons or muons), jets and missing transverse momentum are reported, using 139 fb$^{-1}$ of integrated luminosity from proton-proton collisions at $\sqrt{s} = 13$ TeV, collected by the ATLAS detector at the Large Hadron Collider during Run 2 (2015-2018). This search considers the pair production of top squarks and is sensitive across a wide range of mass differences between the top squark and the lightest neutralino. Additionally, spin-0 mediator dark-matter models are considered, in which the mediator is produced in association with a pair of top quarks. The mediator subsequently decays to a pair of dark-matter particles. No significant excess of events is observed above the Standard Model background, and limits are set at 95% confidence level. The results exclude top squark masses up to about 1 TeV, and masses of the lightest neutralino up to about 500 GeV. Limits on dark-matter production are set for scalar (pseudoscalar) mediator masses up to about 250 (300) GeV.

A search is presented for pair-production of long-lived neutral particles using 33 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collision data, collected during 2016 by the ATLAS detector at the LHC. This search focuses on a topology in which one long-lived particle decays in the ATLAS inner detector and the other decays in the muon spectrometer. Special techniques are employed to reconstruct the displaced tracks and vertices in the inner detector and in the muon spectrometer. One event is observed that passes the full event selection, which is consistent with the estimated background. Limits are placed on scalar boson propagators with masses from 125 GeV to 1000 GeV decaying into pairs of long-lived hidden-sector scalars with masses from 8 GeV to 400 GeV. The limits placed on several low-mass scalars extend previous exclusion limits in the range of proper lifetimes $c \tau$ from 5 cm to 1 m.

A search for supersymmetry through the pair production of electroweakinos with mass splittings near the electroweak scale and decaying via on-shell $W$ and $Z$ bosons is presented for a three-lepton final state. The analyzed proton-proton collision data taken at a center-of-mass energy of $\sqrt{s}$ = 13 TeV were collected between 2015 and 2018 by the ATLAS experiment at the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb$^{-1}$. A search, emulating the recursive jigsaw reconstruction technique with easily reproducible laboratory-frame variables, is performed. The two excesses observed in the 2015-2016 data recursive jigsaw analysis in the low-mass three-lepton phase space are reproduced. Results with the full dataset are in agreement with the Standard Model expectations. They are interpreted to set exclusion limits at 95% confidence level on simplified models of chargino-neutralino pair production for masses up to 345 GeV.

The associated production of a Higgs boson and a top-quark pair is measured in events characterised by the presence of one or two electrons or muons. The Higgs boson decay into a $b$-quark pair is used. The analysed data, corresponding to an integrated luminosity of 139 fb$^{-1}$, were collected in proton-proton collisions at the Large Hadron Collider between 2015 and 2018 at a centre-of-mass energy of $\sqrt{s}=13$ TeV. The measured signal strength, defined as the ratio of the measured signal yield to that predicted by the Standard Model, is $0.35^{+0.36}_{-0.34}$. This result is compatible with the Standard Model prediction and corresponds to an observed (expected) significance of 1.0 (2.7) standard deviations. The signal strength is also measured differentially in bins of the Higgs boson transverse momentum in the simplified template cross-section framework, including a bin for specially selected boosted Higgs bosons with transverse momentum above 300 GeV.

A search is reported for long-lived dark photons with masses between 0.1 GeV and 15 GeV, from exotic decays of Higgs bosons produced via vector-boson-fusion. Events that contain displaced collimated Standard Model fermions reconstructed in the calorimeter or muon spectrometer are probed. This search uses the full LHC Run 2 (2015-2018) data sample collected in proton-proton collisions at $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 139 $fb^{-1}$. Dominant backgrounds from Standard Model processes and non-collision sources are estimated by using data-driven techniques. The observed event yields in the signal regions are consistent with the expected background. Upper limits on the Higgs boson to dark photon branching fraction are reported as a function of the dark-photon mean proper decay length or of the dark-photon mass and the coupling between the Standard Model and the potential dark sector. This search is combined with previous ATLAS searches obtained in the gluon-gluon fusion and \textit{WH} production modes. A branching fraction above 10% is excluded at 95% CL for a 125 GeV Higgs boson decaying into two dark photons for dark-photon mean proper decay lengths between 173 and 1296 mm and mass of 10 GeV.

A search for a new heavy boson produced via gluon-fusion in the four-lepton channel with missing transverse momentum or jets is performed. The search uses proton-proton collision data equivalent to an integrated luminosity of 139 fb$^{-1}$ at a centre-of-mass energy of 13 TeV collected by the ATLAS detector between 2015 and 2018 at the Large Hadron Collider. This study explores the decays of heavy bosons: $R\rightarrow SH$ and $A\rightarrow ZH$, where $R$ is a CP-even boson, $A$ is a CP-odd boson, $H$ is a CP-even boson, and $S$ is considered to decay into invisible particles that are candidates for dark matter. In these processes, $S\rightarrow \textrm{invisible}$ and $H\rightarrow ZZ$. The $Z$ boson associated with the heavy scalar boson $H$ decays into all decay channels of the $Z$ boson. The mass range under consideration is 390-1300 (320-1300) GeV for the $R$ ($A$) boson and 220-1000 GeV for the $H$ boson. No significant deviation from the Standard Model backgrounds is observed. The results are interpreted as upper limits at a 95% confidence level on the cross-section times the branching ratio of the heavy resonances.

A search for non-resonant Higgs boson pair production, as predicted by the Standard Model, is presented, where one of the Higgs bosons decays via the $H\rightarrow bb$ channel and the other via one of the $H \rightarrow WW^*/ZZ^*/\tau\tau$ channels. The analysis selection requires events to have at least two $b$-tagged jets and exactly two leptons (electrons or muons) with opposite electric charge in the final state. Candidate events consistent with Higgs boson pair production are selected using a multi-class neural network discriminant. The analysis uses 139 fb$^{-1}$ of $pp$ collision data recorded at a centre-of-mass energy of 13 TeV by the ATLAS detector at the Large Hadron Collider. An observed (expected) upper limit of 1.2 ($0.9^{+0.4}_{-0.3}$) pb is set on the non-resonant Higgs boson pair production cross-section at 95% confidence level, which is equivalent to 40 ($29^{+14}_{-9}$) times the value predicted in the Standard Model.

The results of a search for vector-like top quarks using events with exactly one lepton, at least four jets, and large missing transverse momentum are reported. The search is optimised for pair production of vector-like top quarks in the $Z(\rightarrow \! \! \nu \nu) \, t + X$ decay channel. LHC pp collision data at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector in 2015 and 2016 are used, corresponding to an integrated luminosity of 36.1 $\mathrm{fb}^{-1}$. No significant excess over the Standard Model expectation is seen and upper limits on the production cross-section of a vector-like $T$ quark pair as a function of the $T$ quark mass are derived. The observed (expected) 95% CL lower limits on the $T$ mass are 870 GeV (890 GeV) for the weak-isospin singlet model, 1.05 TeV (1.06 TeV) for the weak-isospin doublet model and 1.16 TeV (1.17 TeV) for the pure $Zt$ decay mode. Limits are also set on the mass as a function of the decay branching ratios, excluding large parts of the parameter space for masses below 1 TeV.

A search for supersymmetry in events with large missing transverse momentum, jets, and at least one hadronically decaying $\tau$-lepton is presented. Two exclusive final states with either exactly one or at least two $\tau$-leptons are considered. The analysis is based on proton-proton collisions at $\sqrt{s}$ = 13 TeV corresponding to an integrated luminosity of 36.1 fb$^{-1}$ delivered by the Large Hadron Collider and recorded by the ATLAS detector in 2015 and 2016. No significant excess is observed over the Standard Model expectation. At 95% confidence level, model-independent upper limits on the cross section are set and exclusion limits are provided for two signal scenarios: a simplified model of gluino pair production with $\tau$-rich cascade decays, and a model with gauge-mediated supersymmetry breaking (GMSB). In the simplified model, gluino masses up to 2000 GeV are excluded for low values of the mass of the lightest supersymmetric particle (LSP), while LSP masses up to 1000 GeV are excluded for gluino masses around 1400 GeV. In the GMSB model, values of the supersymmetry-breaking scale are excluded below 110 TeV for all values of $\tan\beta$ in the range $2 \leq \tan\beta \leq 60$, and below 120 TeV for $\tan\beta>30$.

A search for Higgs boson pair production via vector-boson fusion (VBF) in the $b\bar{b}b\bar{b}$ final state is carried out with the ATLAS experiment using 126 fb$^{-1}$ of proton-proton collision data delivered at $\sqrt{s} = 13$ TeV by the Large Hadron Collider. This search is sensitive to VBF production of additional heavy bosons that may decay into Higgs boson pairs, and in a non-resonant topology it can constrain the quartic coupling between the Higgs bosons and vector bosons. No significant excess relative to the Standard Model expectation is observed, and limits on the production cross-section are set at the 95 % confidence level for a heavy scalar resonance in the context of an extended Higgs sector, and for non-resonant Higgs boson pair production. Interpretation in terms of the coupling between a Higgs boson pair and two vector bosons is also provided: coupling values normalised to the Standard Model expectation of $\kappa_{2V} < -0.43$ and $\kappa_{2V} > 2.56$ are excluded at the 95 % confidence level in data.

A search for the electroweak production of charginos and sleptons decaying into final states with two electrons or muons is presented. The analysis is based on 139 fb$^{-1}$ of proton-proton collisions recorded by the ATLAS detector at the Large Hadron Collider at $\sqrt{s}=13$ TeV. Three $R$-parity-conserving scenarios where the lightest neutralino is the lightest supersymmetric particle are considered: the production of chargino pairs with decays via either $W$ bosons or sleptons, and the direct production of slepton pairs. The analysis is optimised for the first of these scenarios, but the results are also interpreted in the others. No significant deviations from the Standard Model expectations are observed and limits at 95 % confidence level are set on the masses of relevant supersymmetric particles in each of the scenarios. For a massless lightest neutralino, masses up to 420 GeV are excluded for the production of the lightest-chargino pairs assuming $W$-boson-mediated decays and up to 1 TeV for slepton-mediated decays, whereas for slepton-pair production masses up to 700 GeV are excluded assuming three generations of mass-degenerate sleptons.

This search, a type not previously performed at ATLAS, uses a comparison of the production cross sections for $e^+ \mu^-$ and $e^- \mu^+$ pairs to constrain physics processes beyond the Standard Model. It uses $139 \text{fb}^{-1}$ of proton$-$proton collision data recorded at $\sqrt{s} = 13$ TeV at the LHC. Targeting sources of new physics which prefer final states containing $e^{+}\mu^{-}$ to $e^{-}\mu^{+}$, the search contains two broad signal regions which are used to provide model-independent constraints on the ratio of cross sections at the 2% level. The search also has two special selections targeting supersymmetric models and leptoquark signatures. Observations using one of these selections are able to exclude, at 95% confidence level, singly produced smuons with masses up to 640 GeV in a model in which the only other light sparticle is a neutralino when the $R$-parity-violating coupling $\lambda'_{231}$ is close to unity. Observations using the other selection exclude scalar leptoquarks with masses below 1880 GeV when $g_{\text{1R}}^{eu}=g_{\text{1R}}^{\mu c}=1$, at 95% confidence level. The limit on the coupling reduces to $g_{\text{1R}}^{eu}=g_{\text{1R}}^{\mu c}=0.46$ for a mass of 1420 GeV.