Schr\"odinger equations for the square root density of an eigenmixture and % the square root of an eigendensity spin matrix

We generalize a "one eigenstate" theorem of Levy, Perdew and Sahni (LPS) to the case of densities coming from eigenmixture density operators. The generalization is of a special interest for the radial density functional theory (RDFT) for nuclei, a consequence of the rotational invariance of the nuclear Hamiltonian; when nuclear ground states (GSs) have a finite spin, the RDFT uses eigenmixture density operators to simplify predictions of GS energies into one-dimensional, radial calculations. We also study Schr\"odinger equations governing spin eigendensity matrices.Comment: 8 page

Open problems in nuclear density functional theory

This note describes five subjects of some interest for the density functional theory in nuclear physics. These are, respectively, i) the need for concave functionals, ii) the nature of the Kohn-Sham potential for the radial density theory, iii) a proper implementation of a density functional for an "intrinsic" rotational density, iv) the possible existence of a potential driving the square root of the density, and v) the existence of many models where a density functional can be explicitly constructed.Comment: 10 page

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 different 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 = 13 TeV collected during 2015–2018 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting quark pairs (qq, bb, , and tb) or third-generation leptons (τν and ττ) are included in this kind of combination for the first time. A simplified model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confidence 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

Combination of searches for resonant Higgs Boson pair production using pp collisions at √s = 13 TeV with the ATLAS detector

A combination of searches for a new resonance decaying into a Higgs boson pair is presented, using up to 139  fb−1 of pp collision data at √s = 13 TeV recorded with the ATLAS detector at the LHC. The combination includes searches performed in three decay channels: b ¯ b ⁢b ¯ b , b⁢ ¯ b ⁢τ+⁢τ−, and b⁢ ¯ bγγ ⁢. No excess above the expected Standard Model background is observed and upper limits are set at the 95% confidence level on the production cross section of Higgs boson pairs originating from the decay of a narrow scalar resonance with mass in the range 251 GeV–5 TeV. The observed (expected) limits are in the range 0.96–600 fb (1.2–390 fb). The limits are interpreted in the type-I two-Higgs-doublet model and the minimal supersymmetric standard model, and constrain parameter space not previously excluded by other searches

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 different 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 ττ) are included in this kind of combination for the first time. A simplified model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confidence 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