An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Search for boosted diphoton resonances in the 10 to 70 GeV mass range using 138 fb−1 of 13 TeV pp collisions with the ATLAS detector

A search for diphoton resonances in the mass range between 10 and 70 GeV with the ATLAS experiment at the Large Hadron Collider (LHC) is presented. The analysis is based on pp collision data corresponding to an integrated luminosity of 138 fb−1 at a centre-of-mass energy of 13 TeV recorded from 2015 to 2018. Previous searches for diphoton resonances at the LHC have explored masses down to 65 GeV, finding no evidence of new particles. This search exploits the particular kinematics of events with pairs of closely spaced photons reconstructed in the detector, allowing examination of invariant masses down to 10 GeV. The presented strategy covers a region previously unexplored at hadron colliders because of the experimental challenges of recording low-energy photons and estimating the backgrounds. No significant excess is observed and the reported limits provide the strongest bound on promptly decaying axion-like particles coupling to gluons and photons for masses between 10 and 70 GeV

Search for heavy resonances decaying into a Z or W boson and a Higgs boson in final states with leptons and b-jets in 139 fb−1 of pp collisions at s√ = 13 TeV with the ATLAS detector

This article presents a search for new resonances decaying into a Z or W boson and a 125 GeV Higgs boson h, and it targets the νν¯¯¯bb¯¯, ℓ+ℓ−bb¯¯, or ℓ±νbb¯¯ final states, where ℓ = e or μ, in proton-proton collisions at s√ = 13 TeV. The data used correspond to a total integrated luminosity of 139 fb−1 collected by the ATLAS detector during Run 2 of the LHC at CERN. The search is conducted by examining the reconstructed invariant or transverse mass distributions of Zh or Wh candidates for evidence of a localised excess in the mass range from 220 GeV to 5 TeV. No significant excess is observed and 95% confidence-level upper limits between 1.3 pb and 0.3 fb are placed on the production cross section times branching fraction of neutral and charged spin-1 resonances and CP-odd scalar bosons. These limits are converted into constraints on the parameter space of the Heavy Vector Triplet model and the two-Higgs-doublet model

Search for flavour-changing neutral current interactions of the top quark and the Higgs boson in events with a pair of τ-leptons in pp collisions at s√ = 13 TeV with the ATLAS detector

A search for flavour-changing neutral current (FCNC) tqH interactions involving a top quark, another up-type quark (q = u, c), and a Standard Model (SM) Higgs boson decaying into a τ-lepton pair (H → τ+τ−) is presented. The search is based on a dataset of pp collisions at s√ = 13 TeV that corresponds to an integrated luminosity of 139 fb−1 recorded with the ATLAS detector at the Large Hadron Collider. Two processes are considered: single top quark FCNC production in association with a Higgs boson (pp → tH), and top quark pair production in which one of top quarks decays into Wb and the other decays into qH through the FCNC interactions. The search selects events with two hadronically decaying τ-lepton candidates (τhad) or at least one τhad with an additional lepton (e, μ), as well as multiple jets. Event kinematics is used to separate signal from the background through a multivariate discriminant. A slight excess of data is observed with a significance of 2.3σ above the expected SM background, and 95% CL upper limits on the t → qH branching ratios are derived. The observed (expected) 95% CL upper limits set on the t → cH and t → uH branching ratios are 9.4×10−4(4.8+2.2−1.4×10−4) and 6.9×10−4(3.5+1.5−1.0×10−4), respectively. The corresponding combined observed (expected) upper limits on the dimension-6 operator Wilson coefficients in the effective tqH couplings are Ccϕ < 1.35 (0.97) and Cuϕ < 1.16 (0.82)

Constraints on spin-0 dark matter mediators and invisible Higgs decays using ATLAS 13 TeV pp collision data with two top quarks and missing transverse momentum in the final state

This paper presents a statistical combination of searches targeting final states with two top quarks and invisible particles, characterised by the presence of zero, one or two leptons, at least one jet originating from a b-quark and missing transverse momentum. The analyses are searches for phenomena beyond the Standard Model consistent with the direct production of dark matter in pp collisions at the LHC, using 139 fb−1 of data collected with the ATLAS detector at a centre-of-mass energy of 13 TeV. The results are interpreted in terms of simplified dark matter models with a spin-0 scalar or pseudoscalar mediator particle. In addition, the results are interpreted in terms of upper limits on the Higgs boson invisible branching ratio, where the Higgs boson is produced according to the Standard Model in association with a pair of top quarks. For scalar (pseudoscalar) dark matter models, with all couplings set to unity, the statistical combination extends the mass range excluded by the best of the individual channels by 50 (25) GeV, excluding mediator masses up to 370 GeV. In addition, the statistical combination improves the expected coupling exclusion reach by 14% (24%), assuming a scalar (pseudoscalar) mediator mass of 10 GeV. An upper limit on the Higgs boson invisible branching ratio of 0.38 (0.30+0.13−0.09) is observed (expected) at 95% confidence level

Measurement of the properties of Higgs boson production at s√ = 13 TeV in the H → γγ channel using 139 fb−1 of pp collision data with the ATLAS experiment

Measurements of Higgs boson production cross-sections are carried out in the diphoton decay channel using 139 fb−1 of pp collision data at s√ = 13 TeV collected by the ATLAS experiment at the LHC. The analysis is based on the definition of 101 distinct signal regions using machine-learning techniques. The inclusive Higgs boson signal strength in the diphoton channel is measured to be 1.04+0.10−0.09 . Cross-sections for gluon-gluon fusion, vector-boson fusion, associated production with a W or Z boson, and top associated production processes are reported. An upper limit of 10 times the Standard Model prediction is set for the associated production process of a Higgs boson with a single top quark, which has a unique sensitivity to the sign of the top quark Yukawa coupling. Higgs boson production is further characterized through measurements of Simplified Template Cross-Sections (STXS). In total, cross-sections of 28 STXS regions are measured. The measured STXS cross-sections are compatible with their Standard Model predictions, with a p-value of 93%. The measurements are also used to set constraints on Higgs boson coupling strengths, as well as on new interactions beyond the Standard Model in an effective field theory approach. No significant deviations from the Standard Model predictions are observed in these measurements, which provide significant sensitivity improvements compared to the previous ATLAS results

Search for direct pair production of sleptons and charginos decaying to two leptons and neutralinos with mass splittings near the W-boson mass in s√ = 13 TeV pp collisions with the ATLAS detector

A search for the electroweak production of pairs of charged sleptons or charginos decaying into two-lepton final states with missing transverse momentum is presented. Two simplified models of R-parity-conserving supersymmetry are considered: direct pair-production of sleptons (ℓ∼ℓ∼), with each decaying into a charged lepton and a χ∼01 neutralino, and direct pair-production of the lightest charginos (χ∼±1χ∼∓1), with each decaying into a W-boson and a χ∼01. The lightest neutralino (χ∼01) is assumed to be the lightest supersymmetric particle (LSP). The analyses target the experimentally challenging mass regions where m(ℓ∼)−m(χ∼01) and m(χ∼±1)−m(χ∼01) are close to the W-boson mass (‘moderately compressed’ regions). The search uses 139 fb−1 of s√ = 13 TeV proton-proton collisions recorded by the ATLAS detector at the Large Hadron Collider. No significant excesses over the expected background are observed. Exclusion limits on the simplified models under study are reported in the (ℓ∼,χ∼01) and (χ∼±1χ∼01) mass planes at 95% confidence level (CL). Sleptons with masses up to 150 GeV are excluded at 95% CL for the case of a mass-splitting between sleptons and the LSP of 50 GeV. Chargino masses up to 140 GeV are excluded at 95% CL for the case of a mass-splitting between the chargino and the LSP down to about 100 GeV

Search for doubly charged Higgs boson production in multi-lepton final states using 139 fb−1 of proton–proton collisions at s√ = 13 TeV with the ATLAS detector

A search for pair production of doubly charged Higgs bosons (H±± ), each decaying into a pair of prompt, isolated, and highly energetic leptons with the same electric charge, is presented. The search uses a proton–proton collision data sample at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb−1 recorded by the ATLAS detector during Run 2 of the Large Hadron Collider (LHC). This analysis focuses on same-charge leptonic decays, H±±→ℓ±ℓ′± where ℓ,ℓ′=e,μ,τ, in two-, three-, and four-lepton channels, but only considers final states which include electrons or muons. No evidence of a signal is observed. Corresponding upper limits on the production cross-section of a doubly charged Higgs boson are derived, as a function of its mass m(H±±), at 95% confidence level. Assuming that the branching ratios to each of the possible leptonic final states are equal, B(H±±→e±e±)=B(H±±→e±μ±)=B(H±±→μ±μ±)=B(H±±→e±τ±)=B(H±±→μ±τ±)=B(H±±→τ±τ±)=1/6, the observed (expected) lower limit on the mass of a doubly charged Higgs boson is 1080 GeV (1065 GeV) within the left-right symmetric type-II seesaw model, which is the strongest limit to date produced by the ATLAS Collaboration. Additionally, this paper provides the first direct test of the Zee–Babu neutrino mass model at the LHC, yielding an observed (expected) lower limit of m(H±±) = 900 GeV (880 GeV)

Diffusion-weighted imaging-based probabilistic segmentation of high- and low-proliferative areas in high-grade gliomas

The apparent diffusion coefficient (ADC) derived from diffusion-weighted imaging (DWI) correlates inversely with tumor proliferation rates. High-grade gliomas are typically heterogeneous and the delineation of areas of high and low proliferation is impeded by partial volume effects and blurred borders. Commonly used manual delineation is further impeded by potential overlap with cerebrospinal fluid and necrosis. Here we present an algorithm to reproducibly delineate and probabilistically quantify the ADC in areas of high and low proliferation in heterogeneous gliomas, resulting in a reproducible quantification in regions of tissue inhomogeneity. We used an expectation maximization (EM) clustering algorithm, applied on a Gaussian mixture model, consisting of pure superpositions of Gaussian distributions. Soundness and reproducibility of this approach were evaluated in 10 patients with glioma. High- and low-proliferating areas found using the clustering correspond well wi th conservative regions of interest drawn using all available imaging data. Systematic placement of model initialization seeds shows good reproducibility of the method. Moreover, we illustrate an automatic initialization approach that completely removes user-induced variability. In conclusion, we present a rapid, reproducible and automatic method to separate and quantify heterogeneous regions in gliomas