We present a consistent renormalization scheme for the CP-conserving TwoHiggs-Doublet Model based on MS renormalization of the mixing angles and the soft-Z 2 -symmetry-breaking scale M sb in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent Smatrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general R ξ -gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the MS renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss their scale dependence.

We consider two approaches to estimate and characterise the theoretical uncertainties stemming from the missing higher orders in perturbative calculations in Quantum Chromodynamics: the traditional one based on renormalisation and factorisation scale variation, and the Bayesian framework proposed by Cacciari and Houdeau. We estimate uncertainties with these two methods for a comprehensive set of more than thirty different observables computed in perturbative Quantum Chromodynamics, and we discuss their performance in properly estimating the size of the higher order terms that are known. We find that scale variation with the conventional choice of varying scales within a factor of two of a central scale gives uncertainty intervals that tend to be somewhat too small to be interpretable as 68% confidence-level-heuristic ones. We propose a modified version of the Bayesian approach of Cacciari and Houdeau which performs well for non-hadronic observables and, after an appropriate choice of the relevant expansion parameter for the perturbative series, for hadronic ones too.

Kinematic edges of cascade decays of new particles produced in high-energy collisions may provide important constraints on the involved particles' masses. For the exemplary case of gluino decay $\tilde{g}\to q\bar q \tilde{\chi}$ into a pair of quarks and a neutralino through a squark resonance, we study the hadronic invariant mass distribution in the vicinity of the kinematic edge. We perform a next-to-leading order calculation in the strong coupling $\alpha_s$ and the ratio of squark width and squark mass $\Gamma_\tilde{q}/m_\tilde{q}$, based on a systematic expansion in $\Gamma_\tilde{q}/m_\tilde{q}$. The separation into hard, collinear and soft contributions elucidates the process dependent and universal features of distributions in the edge region, represented by on-shell decay matrix elements, universal jet functions and a soft function that depends on the resonance propagator and soft Wilson lines.Comment: 15 pages, 5 figure