Minimizing Higgs Potentials via Numerical Polynomial Homotopy Continuation

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like nonlinearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gr\"obner basis approach.Comment: 9 pages, 4 figure

Supersymmetric QCD corrections to e+e−→tbˉH−e^+e^-\to t\bar{b}H^- and the Bernstein-Tkachov method of loop integration

The discovery of charged Higgs bosons is of particular importance, since their existence is predicted by supersymmetry and they are absent in the Standard Model (SM). If the charged Higgs bosons are too heavy to be produced in pairs at future linear colliders, single production associated with a top and a bottom quark is enhanced in parts of the parameter space. We present the next-to-leading-order calculation in supersymmetric QCD within the minimal supersymmetric SM (MSSM), completing a previous calculation of the SM-QCD corrections. In addition to the usual approach to perform the loop integration analytically, we apply a numerical approach based on the Bernstein-Tkachov theorem. In this framework, we avoid some of the generic problems connected with the analytical method.Comment: 14 pages, 6 figures, accepted for publication in Phys. Rev.

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Prochlo: Strong Privacy for Analytics in the Crowd

The large-scale monitoring of computer users' software activities has become commonplace, e.g., for application telemetry, error reporting, or demographic profiling. This paper describes a principled systems architecture---Encode, Shuffle, Analyze (ESA)---for performing such monitoring with high utility while also protecting user privacy. The ESA design, and its Prochlo implementation, are informed by our practical experiences with an existing, large deployment of privacy-preserving software monitoring. (cont.; see the paper

Flavour physics constraints in the BMSSM

We study the implications of the presence of the two leading-order, non-renormalizable operators in the Higgs sector of the MSSM to flavour physics observables. We identify the constraints of flavour physics on the parameters of the BMSSM when we: a) focus on a region of parameters for which electroweak baryogenesis is feasible, b) use a CMSSM-like parametrization, and c) consider the case of a generic NUHM-type model. We find significant differences as compared to the standard MSSM case.Comment: 22 pages, 7 figure

Comparative analysis of genome-wide association studies signals for lipids, diabetes, and coronary heart disease: Cardiovascular Biomarker Genetics Collaboration

AIMS: To evaluate the associations of emergent genome-wide-association study-derived coronary heart disease (CHD)-associated single nucleotide polymorphisms (SNPs) with established and emerging risk factors, and the association of genome-wide-association study-derived lipid-associated SNPs with other risk factors and CHD events. METHODS AND RESULTS: Using two case–control studies, three cross-sectional, and seven prospective studies with up to 25 000 individuals and 5794 CHD events we evaluated associations of 34 genome-wide-association study-identified SNPs with CHD risk and 16 CHD-associated risk factors or biomarkers. The Ch9p21 SNPs rs1333049 (OR 1.17; 95% confidence limits 1.11–1.24) and rs10757274 (OR 1.17; 1.09–1.26), MIA3 rs17465637 (OR 1.10; 1.04–1.15), Ch2q36 rs2943634 (OR 1.08; 1.03–1.14), APC rs383830 (OR 1.10; 1.02, 1.18), MTHFD1L rs6922269 (OR 1.10; 1.03, 1.16), CXCL12 rs501120 (OR 1.12; 1.04, 1.20), and SMAD3 rs17228212 (OR 1.11; 1.05, 1.17) were all associated with CHD risk, but not with the CHD biomarkers and risk factors measured. Among the 20 blood lipid-related SNPs, LPL rs17411031 was associated with a lower risk of CHD (OR 0.91; 0.84–0.97), an increase in Apolipoprotein AI and HDL-cholesterol, and reduced triglycerides. SORT1 rs599839 was associated with CHD risk (OR 1.20; 1.15–1.26) as well as total- and LDL-cholesterol, and apolipoprotein B. ANGPTL3 rs12042319 was associated with CHD risk (OR 1.11; 1.03, 1.19), total- and LDL-cholesterol, triglycerides, and interleukin-6. CONCLUSION: Several SNPs predicting CHD events appear to involve pathways not currently indexed by the established or emerging risk factors; others involved changes in blood lipids including triglycerides or HDL-cholesterol as well as LDL-cholesterol. The overlapping association of SNPs with multiple risk factors and biomarkers supports the existence of shared points of regulation for these phenotypes