Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

An adaptive finite element method for the infinity Laplacian

We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem are well known to be singular in nature so we have taken the opportunity to conduct an a posteriori analysis of the method deriving residual based estimators to drive an adaptive algorithm. It is numerically shown that optimal convergence rates are regained using the adaptive procedure

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

The ATLAS trigger system for LHC Run 3 and trigger performance in 2022

The ATLAS trigger system is a crucial component of the ATLAS experiment at the LHC. It is responsible for selecting events in line with the ATLAS physics programme. This paper presents an overview of the changes to the trigger and data acquisition system during the second long shutdown of the LHC, and shows the performance of the trigger system and its components in the proton-proton collisions during the 2022 commissioning period as well as its expected performance in proton-proton and heavy-ion collisions for the remainder of the third LHC data-taking period (2022–2025)

Measurement of the charge asymmetry in top-quark pair production in association with a photon with the ATLAS experiment

A measurement of the charge asymmetry in top-quark pair (tt¯) production in association with a photon is presented. The measurement is performed in the single-lepton tt¯ decay channel using proton–proton collision data collected with the ATLAS detector at the Large Hadron Collider at CERN at a centre-of-massenergy of 13 TeV during the years 2015–2018, corresponding to an integrated luminosity of 139 fb−1. The charge asymmetry is obtained from the distribution of the difference of the absolute rapidities of the top quark and antiquark using a profile likelihood unfolding approach. It is measured to be AC = −0.003 ± 0.029 in agreement with the Standard Model expectation

Combination of searches for heavy spin-1 resonances using 139 fb−1 of proton-proton collision data at √s = 13 TeV with the ATLAS detector

A combination of searches for new heavy spin-1 resonances decaying into diferent pairings of W, Z, or Higgs bosons, as well as directly into leptons or quarks, is presented. The data sample used corresponds to 139 fb−1 of proton-proton collisions at √s = 13 TeV collected during 2015–2018 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting quark pairs (qq, bb, tt¯, and tb) or third-generation leptons (τν and τ τ ) are included in this kind of combination for the frst time. A simplifed model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confdence level and are compared with predictions for the benchmark model. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The complementarity of the various analyses increases the sensitivity to new physics, and the resulting constraints are stronger than those from any individual analysis considered. The data exclude a heavy vector-boson triplet with mass below 5.8 TeV in a weakly coupled scenario, below 4.4 TeV in a strongly coupled scenario, and up to 1.5 TeV in the case of production via vector-boson fusion

Search for single production of vector-like T quarks decaying into Ht or Zt in pp collisions at s√ = 13 TeV with the ATLAS detector

This paper describes a search for the single production of an up-type vector-like quark (T) decaying as T → Ht or T → Zt. The search utilises a dataset of pp collisions at s√ = 13 TeV collected with the ATLAS detector during the 2015–2018 data-taking period of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. Data are analysed in final states containing a single lepton with multiple jets and b-jets. The presence of boosted heavy resonances in the event is exploited to discriminate the signal from the Standard Model background. No significant excess above the Standard Model expectation is observed, and 95% CL upper limits are set on the production cross section of T quarks in different decay channels. The results are interpreted in several benchmark scenarios to set limits on the mass and universal coupling strength (κ) of the vector-like quark. For singlet T quarks, κ values above 0.53 are excluded for all masses below 2.3 TeV. At a mass of 1.6 TeV, κ values as low as 0.35 are excluded. For T quarks in the doublet scenario, where the production cross section is much lower, κ values above 0.72 are excluded for all masses below 1.7 TeV, and this exclusion is extended to κ above 0.55 for low masses around 1.0 TeV

Measurement of the cross-sections of the electroweak and total production of a Zγ pair in association with two jets in pp collisions at √s = 13 TeV with the ATLAS detector

This Letter presents the measurement of the fiducial and differential cross-sections of the electroweak production of a Zγ pair in association with two jets. The analysis uses 140 fb−1 of LHC proton–proton collision data taken at √s = 13 TeV recorded by the ATLAS detector during the years 2015–2018. Events with a Z boson candidate decaying into either an e+e− or μ+μ− pair, a photon and two jets are selected. The electroweak component is extracted by requiring a large dijet invariant mass and by using the information about the centrality of the system and is measured with an observed and expected significance well above five standard deviations. The fiducial pp → Zγ jj cross-section for the electroweak production is measured to be 3.6 ± 0.5 fb. The total fiducial cross-section that also includes contributions where the jets arise from strong interactions is measured to be 16.8+2.0 −1.8 fb. The results are consistent with the Standard Model predictions. Differential cross-sections are also measured using the same events and are compared with parton-shower Monte Carlo simulations. Good agreement is observed between data and predictions