The solution to the Tullock rent-seeking game when R > 2: mixed-strategy equilibria and mean dissipation rates

In Tullock's rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R>2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete, and show that full rent dissipation occurs when the strategy space is continuous. Our results are shown to be consistent with recent experimental evidence on the dissipation of rents. An earlier version of this paper circulated under the title, No, Virginia, There is No Overdissipation of Rents. We are grateful to Dave Furth and Frans van Winden for stimulating conversations, and for comments provided by workshop participants from the CORE-ULB-KUL IUAP project, Purdue University, Pennsylvania State University, Rijksuniversiteit Limburg, and Washington State University. We also thank Max van de Sande Bakhuyzen and Ben Heijdra for useful discussions, and Geert Gielens for computational assistance. An earlier version of the paper was presented at the ESEM 1992 in Brussels and the Mid-West Mathematical Economics Conference in Pittsburgh. All three authors would like to thank CentER for its hospitality during the formative stages of the paper. The second author has also benefited from the financial support of the Katholieke Universitieit Leuven and the Jay N. Ross Young Faculty Scholar Award at Purdue University. The third author benefitted from visiting IGIER where part of the paper was written. The third author also benefitted from grant IUAP 26 of the Belgian Government

Search for the Zγ decay mode of new high-mass resonances in pp collisions at √s = 13 TeV with the ATLAS detector

This letter presents a search for narrow, high-mass resonances in the Zγ final state with the Z boson decaying into a pair of electrons or muons. The √s = 13 TeV pp collision data were recorded by the ATLAS detector at the CERN Large Hadron Collider and have an integrated luminosity of 140 fb−1. The data are found to be in agreement with the Standard Model background expectation. Upper limits are set on the resonance production cross section times the decay branching ratio into Zγ. For spin-0 resonances produced via gluon–gluon fusion, the observed limits at 95% confidence level vary between 65.5 fb and 0.6 fb, while for spin-2 resonances produced via gluon–gluon fusion (or quark–antiquark initial states) limits vary between 77.4 (76.1) fb and 0.6 (0.5) fb, for the mass range from 220 GeV to 3400 GeV

Search for a new heavy scalar particle decaying into a Higgs boson and a new scalar singlet in final states with one or two light leptons and a pair of τ-leptons with the ATLAS detector

A search for a new heavy scalar particle X decaying into a Standard Model (SM) Higgs boson and a new singlet scalar particle S is presented. The search uses a proton-proton (pp) collision data sample with an integrated luminosity of 140 fb−1 recorded at a centre-of-mass energy of s√ = 13 TeV with the ATLAS detector at the Large Hadron Collider. The most sensitive mass parameter space is explored in X mass ranging from 500 to 1500 GeV, with the corresponding S mass in the range 200–500 GeV. The search selects events with two hadronically decaying τ-lepton candidates from H → τ+τ− decays and one or two light leptons (ℓ = e, μ) from S → VV (V = W, Z) decays while the remaining V boson decays hadronically or to neutrinos. A multivariate discriminant based on event kinematics is used to separate the signal from the background. No excess is observed beyond the expected SM background and 95% confidence level upper limits between 72 fb and 542 fb are derived on the cross-section σ(pp → X → SH) assuming the same SM-Higgs boson-like decay branching ratios for the S → VV decay. Upper limits on the visible cross-sections σ(pp → X → SH → WWττ) and σ(pp → X → SH → ZZττ) are also set in the ranges 3–26 fb and 6–33 fb, respectively

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

Search for lepton-favour violation in high-mass dilepton final states using 139 fb−1 of pp collisions at √s = 13 TeV with the ATLAS detector

A search is performed for a heavy particle decaying into different-flavour, dilepton final states, using 139 fb−1 of proton-proton collision data at √s = 13 TeV collected in 2015–2018 by the ATLAS detector at the Large Hadron Collider. Final states with electrons, muons and hadronically decaying tau leptons are considered (eμ, eτ or μτ). No significant excess over the Standard Model predictions is observed. Upper limits on the production cross-section are set as a function of the mass of a Z′ boson, a supersymmetric τ-sneutrino, and a quantum black-hole. The observed 95% CL lower mass limits obtained on a typical benchmark model Z′ boson are 5.0 TeV (eμ), 4.0 TeV (eτ), and 3.9 TeV (μτ), respectively

Search for non-resonant production of semi-visible jets using Run 2 data in ATLAS

Semi-visible jets, with a significant contribution to the event's missing transverse momentum, can arise in strongly interacting dark sectors. This results in an event topology where one of the jets can be aligned with the direction of the missing transverse momentum. The first search for semi-visible jets produced via a t-channel mediator exchange is presented. The analysis uses proton-proton collisions with an integrated luminosity of 139 fb−1 and a centre-of-mass energy of 13 TeV, collected with the ATLAS detector during the Run 2 of the LHC. No excess over Standard Model predictions is observed. Assuming a coupling strength of unity between the mediator, a Standard Model quark and a dark quark, mediator masses up to 2.7 TeV are excluded at the 95% confidence level. Upper limits on the coupling strength are also derived

Software performance of the ATLAS track reconstruction for LHC run 3

Charged particle reconstruction in the presence of many simultaneous proton–proton (pp) collisions in the LHC is a challenging task for the ATLAS experiment’s reconstruction software due to the combinatorial complexity. This paper describes the major changes made to adapt the software to reconstruct high-activity collisions with an average of 50 or more simultaneous pp interactions per bunch crossing (pileup) promptly using the available computing resources. The performance of the key components of the track reconstruction chain and its dependence on pile-up are evaluated, and the improvement achieved compared to the previous software version is quantified. For events with an average of 60 pp collisions per bunch crossing, the updated track reconstruction is twice as fast as the previous version, without significant reduction in reconstruction efficiency and while reducing the rate of combinatorial fake tracks by more than a factor two

Search for direct production of electroweakinos in final states with one lepton, jets and missing transverse momentum in pp collisions at √s = 13 TeV with the ATLAS detector

Searches for electroweak production of wino-like chargino pairs, χ˜ + 1 χ˜ − 1 , and of wino-like chargino and next-to-lightest neutralino, χ˜ ± 1 χ˜ 0 2 , are presented. The models explored assume that the charginos decay into a W boson and the lightest neutralino, χ˜ ± 1 → W±χ˜ 0 1 . The next-to-lightest neutralinos are degenerate in mass with the chargino and decay to χ˜ 0 1 and either a Z or a Higgs boson, χ˜ 0 2 → Zχ˜ 0 1 or hχ˜ 0 1 . The searches exploit the presence of a single isolated lepton and missing transverse momentum from the W boson decay products and the lightest neutralinos, and the presence of jets from hadronically decaying Z or W bosons or from the Higgs boson decaying into a pair of b-quarks. The searches use 139 fb−1 of √ s = 13 TeV proton-proton collisions data collected by the ATLAS detector at the Large Hadron Collider between 2015 and 2018. No deviations from the Standard Model expectations are found, and 95% confdence level exclusion limits are set. Chargino masses ranging from 260 to 520 GeV are excluded for a massless χ˜ 0 1 in chargino pair production models. Degenerate chargino and next-to-lightest neutralino masses ranging from 260 to 420 GeV are excluded for a massless χ˜ 0 1 for χ˜ 0 2 → Zχ˜ 0 1 . For decays through an on-shell Higgs boson and for mass-splitting between χ˜ ± 1 /χ˜ 0 2 and χ˜ 0 1 as small as the Higgs boson mass, mass limits are improved by up to 40 GeV in the range of 200–260 GeV and 280–470 GeV compared to previous ATLAS constraints

Search for the decay of the Higgs boson to a Z boson and a light pseudoscalar particle decaying to two photons

A search for the decay of the Higgs boson to a Z boson and a light, pseudoscalar particle, a, decaying respectively to two leptons and to two photons is reported. The search uses the full LHC Run 2 proton–proton collision data at √s = 13 TeV, corresponding to 139 fb−1 collected by the ATLAS detector. This is one of the first searches for this specific decay mode of the Higgs boson, and it probes unexplored parameter space in models with axion-like particles (ALPs) and extended scalar sectors. The mass of the a particle is assumed to be in the range 0.1–33 GeV. The data are analysed in two categories: a merged category where the photons from the a decay are reconstructed in the ATLAS calorimeter as a single cluster, and a resolved category in which two separate photons are detected. The main background processes are from Standard Model Z boson production in association with photons or jets. The data are in agreement with the background predictions, and upper limits on the branching ratio of the Higgs boson decay to Za times the branching ratio α = γγ are derived at the 95% confidence level and they range from 0.08% to 2% depending on the mass of the a particle. The results are also interpreted in the context of ALP models