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Abstract Measuring observables to constrain models using maximum-likelihood estimation is fundamental to many physics experiments. Wilks' theorem provides a simple way to construct confidence intervals on model parameters, but it only applies under certain conditions. These conditions, such as nested hypotheses and unbounded parameters, are often violated in neutrino oscillation measurements and other experimental scenarios. Monte Carlo methods can address these issues, albeit at increased computational cost. In the presence of nuisance parameters, however, the best way to implement a Monte Carlo method is ambiguous. This paper documents the method selected by the NOvA experiment, the profile construction. It presents the toy studies that informed the choice of method, details of its implementation, and tests performed to validate it. It also includes some practical considerations which may be of use to others choosing to use the profile construction. 

Abstract The TOTEM Roman pot detectors are used to reconstruct the transverse momentum of scattered protons and to estimate the transverse location of the primary interaction. This paper presents new methods of track reconstruction, measurements of strip-level detection efficiencies, cross-checks of the LHC beam optics, and detector alignment techniques, along with their application in the selection of signal collision events. The track reconstruction is performed by exploiting hit cluster information through a novel method using a common polygonal area in the intercept-slope plane. The technique is applied in the relative alignment of detector layers with μm precision. A tag-and-probe method is used to extract strip-level detection efficiencies. The alignment of the Roman pot system is performed through time-dependent adjustments, resulting in a position accuracy of 3 μm in the horizontal and 60 μm in the vertical directions. The goal is to provide an optimal reconstruction tool for central exclusive physics analyses based on the high-β* data-taking period at √(s) = 13 TeV in 2018.