Boundary triples and Weyl functions for Dirac operators with singular interactions

In this article we develop a systematic approach to treat Dirac operators $A_{\eta, \tau, \lambda}$ with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths $\eta, \tau, \lambda \in \mathbb{R}$, respectively, supported on points in $\mathbb{R}$, curves in $\mathbb{R}^2$, and surfaces in $\mathbb{R}^3$ that is based on boundary triples and their associated Weyl functions. First, we discuss the one-dimensional case which also serves as a motivation for the multidimensional setting. Afterwards, in the two and three-dimensional situation we construct quasi, generalized, and ordinary boundary triples and their Weyl functions, and provide a detailed characterization of the associated Sobolev spaces, trace theorems, and the mapping properties of integral operators which play an important role in the analysis of $A_{\eta, \tau, \lambda}$. We make a substantial step towards more rough interaction supports $\Sigma$ and consider general compact Lipschitz hypersurfaces. We derive conditions for the interaction strengths such that the operators $A_{\eta, \tau, \lambda}$ are self-adjoint, obtain a Krein-type resolvent formula, and characterize the essential and discrete spectrum. These conditions include purely Lorentz scalar and purely non-critical anomalous magnetic interactions as well as the confinement case, the latter having an important application in the mathematical description of graphene. Using a certain ordinary boundary triple, we show the self-adjointness of $A_{\eta, \tau, \lambda}$ for arbitrary combinations of the interaction strengths (including critical ones) under the condition that $\Sigma$ is $C^{\infty}$-smooth and derive its spectral properties. In particular, in the critical case, a loss of Sobolev regularity in the operator domain and a possible additional point of the essential spectrum are observed.Comment: 56 pages; to appear in Reviews in Mathematical Physic

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Measurement of the inclusive isolated-photon cross section in pp collisions at √s = 13 TeV using 36 fb−1 of ATLAS data

The differential cross section for isolated-photon production in pp collisions is measured at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC using an integrated luminosity of 36.1 fb. The differential cross section is presented as a function of the photon transverse energy in different regions of photon pseudorapidity. The differential cross section as a function of the absolute value of the photon pseudorapidity is also presented in different regions of photon transverse energy. Next-to-leading-order QCD calculations from Jetphox and Sherpa as well as next-to-next-to-leading-order QCD calculations from Nnlojet are compared with the measurement, using several parameterisations of the proton parton distribution functions. The predictions provide a good description of the data within the experimental and theoretical uncertainties. [Figure not available: see fulltext.

Genetic modifiers of radon-induced lung cancer risk: a genome-wide interaction study in former uranium miners

PURPOSE: Radon is a risk factor for lung cancer and uranium miners are more exposed than the general population. A genome-wide interaction analysis was carried out to identify genomic loci, genes or gene sets that modify the susceptibility to lung cancer given occupational exposure to the radioactive gas radon. METHODS: Samples from 28 studies provided by the International Lung Cancer Consortium were pooled with samples of former uranium miners collected by the German Federal Office of Radiation Protection. In total, 15,077 cases and 13,522 controls, all of European ancestries, comprising 463 uranium miners were compared. The DNA of all participants was genotyped with the OncoArray. We fitted single-marker and in multi-marker models and performed an exploratory gene-set analysis to detect cumulative enrichment of significance in sets of genes. RESULTS: We discovered a genome-wide significant interaction of the marker rs12440014 within the gene CHRNB4 (OR = 0.26, 95% CI 0.11-0.60, p = 0.0386 corrected for multiple testing). At least suggestive significant interaction of linkage disequilibrium blocks was observed at the chromosomal regions 18q21.23 (p = 1.2 × 10-6), 5q23.2 (p = 2.5 × 10-6), 1q21.3 (p = 3.2 × 10-6), 10p13 (p = 1.3 × 10-5) and 12p12.1 (p = 7.1 × 10-5). Genes belonging to the Gene Ontology term "DNA dealkylation involved in DNA repair" (GO:0006307; p = 0.0139) or the gene family HGNC:476 "microRNAs" (p = 0.0159) were enriched with LD-blockwise significance. CONCLUSION: The well-established association of the genomic region 15q25 to lung cancer might be influenced by exposure to radon among uranium miners. Furthermore, lung cancer susceptibility is related to the functional capability of DNA damage signaling via ubiquitination processes and repair of radiation-induced double-strand breaks by the single-strand annealing mechanism