Abstract: We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the aforementioned kinetic term are related by a partial Slavnov-Taylor identity. The main ingredients entering in the solution are projection of the three-gluon vertex and a particular derivative of the ghost-gluon kernel, whose approximate form is derived from a Schwinger-Dyson equation. Crucially, the requirement of a pole-free answer determines the initial condition, whose value is calculated from an integral containing the same ingredients as the solution itself. This feature fixes uniquely, at least in principle, the form of the kinetic term, once the ingredients have been accurately evaluated. In practice, however, due to substantial uncertainties in the computation of the necessary inputs, certain crucial components need be adjusted by hand, in order to obtain self-consistent results. Furthermore, if the gluon propagator has been independently accessed from the lattice, the solution for the kinetic term facilitates the extraction of the momentum-dependent effective gluon mass. The practical implementation of this method is carried out in detail, and the required approximations and theoretical assumptions are duly highlighted.

Abstract: A considerable experimental effort is currently under way to test the persistent hints for oscillations due to an eV-scale sterile neutrino in the data of various reactor neutrino experiments. The assessment of the statistical significance of these hints is usually based on Wilks' theorem, whereby the assumption is made that the log-likelihood is chi 2-distributed. However, it is well known that the preconditions for the validity of Wilks' theorem are not fulfilled for neutrino oscillation experiments. In this work we derive a simple asymptotic form of the actual distribution of the log-likelihood based on reinterpreting the problem as fitting white Gaussian noise. From this formalism we show that, even in the absence of a sterile neutrino, the expectation value for the maximum likelihood estimate of the mixing angle remains non-zero with attendant large values of the log-likelihood. Our analytical results are then confirmed by numerical simulations of a toy reactor experiment. Finally, we apply this framework to the data of the Neutrino-4 experiment and show that the null hypothesis of no-oscillation is rejected at the 2.6 sigma level, compared to 3.2 sigma obtained under the assumption that Wilks' theorem applies.

Abstract: The performance of the ATLAS Inner Detector alignment has been studied using pp collision data at v s = 13 TeV collected by the ATLAS experiment during Run 2 (2015-2018) of the Large Hadron Collider (LHC). The goal of the detector alignment is to determine the detector geometry as accurately as possible and correct for time-dependent movements. The Inner Detector alignment is based on the minimization of track-hit residuals in a sequence of hierarchical levels, from global mechanical assembly structures to local sensors. Subsequent levels have increasing numbers of degrees of freedom; in total there are almost 750,000. The alignment determines detector geometry on both short and long timescales, where short timescales describe movementswithin anLHCfill. The performance and possible track parameter biases originating from systematic detector deformations are evaluated. Momentum biases are studied using resonances decaying to muons or to electrons. The residual sagitta bias and momentum scale bias after alignment are reduced to less than similar to 0.1 TeV-1 and 0.9 x 10(-3), respectively. Impact parameter biases are also evaluated using tracks within jets.