Ranks of twists of elliptic curves and Hilbert's Tenth Problem

In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find many twists with trivial Mordell-Weil group, and (assuming the Shafarevich-Tate conjecture) many others with infinite cyclic Mordell-Weil group. Using work of Poonen and Shlapentokh, it follows from our results that if the Shafarevich-Tate conjecture holds, then Hilbert's Tenth Problem has a negative answer over the ring of integers of every number field.Comment: Minor changes. To appear in Inventiones mathematica

A chromosome-level Amaranthus cruentus genome assembly highlights gene family evolution and biosynthetic gene clusters that may underpin the nutritional value of this traditional crop

Traditional crops historically provided accessible and affordable nutrition to millions of rural dwellers but have been neglected, with most modern agricultural systems over reliant on a small number of internationally-traded crops. Traditional crops are typically well-adapted to local agro-ecological conditions and many are nutrient-dense. They can play a vital role in local food systems through enhanced nutrition (especially where diets are dominated by starch crops), food security and livelihoods for smallholder farmers, and a climate-resilient and biodiverse agriculture. Using short-read, long-read and phased sequencing technologies we generated a high-quality chromosome-level genome assembly for Amaranthus cruentus, an under-researched crop with micronutrient- and protein-rich leaves and gluten-free seed, but lacking improved varieties, with respect to productivity and quality traits. The 370.9 MB genome demonstrates a shared whole genome duplication with a related species, Amaranthus hypochondriacus. Comparative genome analysis indicates chromosomal loss and fusion events following genome duplication that are common to both species, as well as fission of chromosome 2 in A. cruentus alone, giving rise to a haploid chromosome number of 17 (versus 16 in A. hypochondriacus). Genomic features potentially underlying the nutritional value of this crop include two A. cruentus-specific genes with a likely role in phytic acid synthesis (an anti-nutrient), expansion of ion transporter gene families, and identification of biosynthetic gene clusters conserved within the amaranth lineage. The A. cruentus genome assembly will underpin much-needed research and global breeding efforts to develop improved varieties for economically viable cultivation and realisation of the benefits to global nutrition security and agrobiodiversity

Inclusive-photon production and its dependence on photon isolation in pp collisions at s√ = 13 TeV using 139 fb−1 of ATLAS data

Measurements of differential cross sections are presented for inclusive isolated-photon production in pp collisions at a centre-of-mass energy of 13 TeV provided by the LHC and using 139 fb−1 of data recorded by the ATLAS experiment. The cross sections are measured as functions of the photon transverse energy in different regions of photon pseudorapidity. The photons are required to be isolated by means of a fixed-cone method with two different cone radii. The dependence of the inclusive-photon production on the photon isolation is investigated by measuring the fiducial cross sections as functions of the isolation-cone radius and the ratios of the differential cross sections with different radii in different regions of photon pseudorapidity. The results presented in this paper constitute an improvement with respect to those published by ATLAS earlier: the measurements are provided for different isolation radii and with a more granular segmentation in photon pseudorapidity that can be exploited in improving the determination of the proton parton distribution functions. These improvements provide a more in-depth test of the theoretical predictions. Next-to-leading-order QCD predictions from JETPHOX and SHERPA and next-to-next-to-leading-order QCD predictions from NNLOJET are compared to the measurements, using several parameterisations of the proton parton distribution functions. The measured cross sections are well described by the fixed-order QCD predictions within the experimental and theoretical uncertainties in most of the investigated phase-space region

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

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

Observation of Wγγ triboson production in proton-proton collisions at √s = 13 TeV with the ATLAS detector

This letter reports the observation of W(ℓν)γγ production in proton-proton collisions. This measurement uses the full Run 2 sample of events recorded at a center-of-mass energy of √s = 13 TeV by the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140 fb−1. Events with a leptonically-decaying W boson and at least two photons are considered. The background-only hypothesis is rejected with an observed and expected significance of 5.6 standard deviations. The inclusive fiducial production cross section of W(eν)γγ and W(μν)γγ events is measured to be σfid=13.8±1.1(stat)+2.1−2.0(syst)±0.1(lumi) fb, in agreement with the Standard Model prediction

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

Charged-hadron production in pp, p+Pb, Pb+Pb, and Xe+Xe collisions at sNN−−−√ = 5 TeV with the ATLAS detector at the LHC

This paper presents measurements of charged-hadron spectra obtained in pp, p+Pb, and Pb+Pb collisions at s√ or sNN−−−√ = 5.02 TeV, and in Xe+Xe collisions at sNN−−−√ = 5.44 TeV. The data recorded by the ATLAS detector at the LHC have total integrated luminosities of 25 pb−1, 28 nb−1, 0.50 nb−1, and 3 μb−1, respectively. The nuclear modification factors RpPb and RAA are obtained by comparing the spectra in heavy-ion and pp collisions in a wide range of charged-particle transverse momenta and pseudorapidity. The nuclear modification factor RpPb shows a moderate enhancement above unity with a maximum at pT ≈ 3 GeV; the enhancement is stronger in the Pb-going direction. The nuclear modification factors in both Pb+Pb and Xe+Xe collisions feature a significant, centrality-dependent suppression. They show a similar distinct pT-dependence with a local maximum at pT ≈ 2 GeV and a local minimum at pT ≈ 7 GeV. This dependence is more distinguishable in more central collisions. No significant |η|-dependence is found. A comprehensive comparison with several theoretical predictions is also provided. They typically describe RAA better in central collisions and in the pT range from about 10 to 100 GeV