Abstract: We perform a comprehensive scan of the parameter space of a general singlet scalar extension of the Standard Model to identify the regions which can lead to a strong first-order phase transition, as required by the electroweak baryogenesis mechanism. We find that taking into account bubble nucleation is a fundamental constraint on the parameter space and present a conservative and fast estimate for it so as to enable efficient parameter space scanning. The allowed regions turn out to be already significantly probed by constraints on the scalar mixing from Higgs signal strength measurements. We also consider the addition of new neutrino singlet fields with Yukawa couplings to both scalars and forming heavy (pseudo)-Dirac pairs, as in the linear or inverse Seesaw mechanisms for neutrino mass generation. We find that their inclusion does not alter the allowed parameter space from early universe phenomenology in a significant way. Conversely, there are allowed regions of the parameter space where the presence of the neutrino singlets would remarkably modify the collider phenomenology, yielding interesting new signatures in Higgs and singlet scalar decays.

Abstract: We study a special Schwinger-Dyson equation in the context of a pure SU(3) Yang-Mills theory, formulated in the background field method. Specifically, we consider the corresponding equation for the vertex that governs the interaction of two background gluons with a ghost-antighost pair. By virtue of the background gauge invariance, this vertex satisfies a naive Slavnov-Taylor identity, which is not deformed by the ghost sector of the theory. In the all-soft limit, where all momenta vanish, the form of this vertex may be obtained exactly from the corresponding Ward identity. This special result is subsequently reproduced at the level of the Schwinger-Dyson equation, by making extensive use of Taylor's theorem and exploiting a plethora of key relations, particular to the background field method. This information permits the determination of the error associated with two distinct truncation schemes, where the potential advantage from employing lattice data for the ghost dressing function is quantitatively assessed.

Abstract: We present the details and first results of a new strategy for the determination of alpha s(mZ) (ALPHA Collaboration et al. in Phys. Lett. B 807:135571, 2020). By simultaneously decoupling 3 fictitious heavy quarks we establish a relation between the A-parameters of three-flavor QCD and pure gauge theory. Very precise recent results in the pure gauge theory (Dalla Brida and Ramos in Eur. Phys. J. C 79(8):720, 2019; Nada and Ramos in Eur Phys J C 81(1):1, 2021) can thus be leveraged to obtain the three flavour A-parameter in units of a common decoupling scale. Connecting this scale to hadronic physics in 3-flavour QCD leads to our result in physical units, A(3)/MS = 336(12) MeV, which translates to alpha s(m(Z)) = 0.11823(84). This is compatible with both the FLAG average (Aoki et al. in FLAG review 2021. arXiv:2111.09849 [hep-lat]) and the previous ALPHA result (ALPHA Collaboration et al., Phys. Rev. Lett. 119(10):102001, 2017), with a comparable, yet still statistics dominated, error. This constitutes a highly non-trivial check, as the decoupling strategy is conceptually very different from the 3-flavour QCD step-scaling method, and so are their systematic errors. These include the uncertainties of the combined decoupling and continuum limits, which we discuss in some detail. We also quantify the correlation between both results, due to some common elements, such as the scale determination in physical units and the definition of the energy scale where we apply decoupling.