A spurion-field approach using scale-invariant directions and non-overlapping symmetries constructs all-loop RGIs for bilinear operators in multi-scalar potentials.
Minkowski space structure of the Higgs potential in 2HDM: II. Minima, symmetries, and topology
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abstract
We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of non-contractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/lagrangian and their spontaneous violation from a wider perspective than usual.
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New fermion transformations and all-order renormalization-invariant parameter regions are identified for two-Higgs-doublet models including scalar-fermion interactions.
The r0 symmetry is preserved at one-loop in the r0-invariant two-Higgs Doublet Model if the UV cutoff squared transforms non-trivially under r0; the minimal model requires two real fields.
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Renormalisation Group Invariants from Scaling and Non-overlapping Symmetries
A spurion-field approach using scale-invariant directions and non-overlapping symmetries constructs all-loop RGIs for bilinear operators in multi-scalar potentials.
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GOOFy fermions
New fermion transformations and all-order renormalization-invariant parameter regions are identified for two-Higgs-doublet models including scalar-fermion interactions.
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Imaginary scaling invariance of the one-loop effective potential
The r0 symmetry is preserved at one-loop in the r0-invariant two-Higgs Doublet Model if the UV cutoff squared transforms non-trivially under r0; the minimal model requires two real fields.