Speaker
Description
We analyze the gauge-orbit space in order to derive bounded-from-below (BFB) constraints for models containing two or three SU(2) scalar multiplets. Within this framework, we construct a coordinate system adapted to the symmetries of the scalar potential by recasting the minimization of its quartic part into a geometric problem, namely the analysis of the corresponding shapes in gauge-orbit space.
First, we study an extension of the Standard Model by an SU(2) scalar quadruplet with hypercharge Y=3/2 or Y=1/2. Using exact analytic relations, we determine the boundaries of the phase spaces of the gauge-invariant terms that appear in the scalar potentials. We then develop practical procedures to obtain necessary and sufficient BFB conditions for these potentials.
Second, we consider the SM extended by three SU(2) scalar doublets and endowed with a symmetry under which each doublet independently changes sign. We argue that, in the absence of known necessary and sufficient BFB conditions, it is more effective to build upon necessary conditions. To this end, we present a Mathematica package that implements this strategy with high accuracy for identifying BFB potentials. Furthermore, we propose a machine-learning approach that rapidly and accurately classifies potentials that are both BFB and compatible with perturbative unitarity.
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