In this paper we focus on the notion of robust matrix root-clustering analysis in a union of regions that are possibly disjoint and non symmetric. Indeed this work aims at computing a bound on the size of the uncertainty domain preserving matrix Du-stability. A Linear Fractional Transform (LFT) uncertainty is considered. To reduce conservatism, a new approach, based on some generalized S-proced...

We show that a necessary condition, for the partition function of four-dimensional Yang-Mills theory to satisfy a S-duality property, is that certain functional determinants, generated by the dual change of variables, cancel each other. This result holds up to non-topological boundary terms in the dual action and modulo the problem of field-strength copies for the Bianchi identity constraint.

We present the matching condition for the strong coupling con-tant α (n f) s at a heavy quark threshold to four loops in the modified minimal subtraction scheme. Our results lead to further decrease of the theoretical uncertainty of the evolution of the strong coupling constant through heavy quark thresholds. Using a low energy theorem we furthermore derive the effective coupling of the Higgs b...

We investigate the four-body decays $B_{(s)} \rightarrow (K\pi)_{S/P} (K\pi)_{S/P}$ in $K\pi$-pair invariant mass region around $K^*(892)$ resonance perturbative QCD (PQCD) approach, where $(K\pi)_{S/P}$ denotes a $S$- or $P$-wave $K\pi$ configuration. The contributions from and possible $S$-wave components are included into parametrization of two-meson distribution amplitudes, which nonperturb...