Impact of systematic and amplitude model correlations within and between systems of combined input: a case study with ϕ2 (α)

The pursuit of experimental precision in the CP-violating weak phase ϕ2 (α) is not without its challenges, in part due to the need to combine multiple physical observables from various related decay channels, and therein lies a fundamental issue. Similarities in analysis procedures give rise to systematic correlations between the measured inputs constraining ϕ2 that must be taken into account to avoid bias. Specifically, in the case of the irreducible model uncertainty accompanying analyses involving the ρ meson, it is demonstrated that ignoring correlations derived from its pole parameters, or indeed even treating correlations individually contained within each decay channel, can ultimately lead to a bias in ϕ2 of (1°). Correct treatment on the other hand, markedly reduces wandering of its central value as a function of the model uncertainty strength with the added dividend of a further improved overall uncertainty. Bias in the combination of B0 → (ρπ)0 and B → ρρ is also seen to depend on the statistical strength of the former in relation to that of the model uncertainty in the latter. This work can inspire other studies into the points at which systematic correlations beyond those determined in single measurements matter in combinations leading to other CP-violating weak phases such as ϕ1 (β), ϕ3 (γ) and ϕs.

Application of fuzzy soft sets to analyze the statistical strength of S-boxes

For the evaluation of the substitution boxes, the majority logic criterion is used to analyze the statistical strength of the existing substitution boxes. The main objective of this paper is to make a decision on the analysis and selection of the most appropriate S-box based on a fuzzy soft-aggregation operator. Instead of the usual practice in which a single parameter is considered, we are considering several parameters that will definitely give us a comprehensive analysis of the S-boxes.