The Two Higgs Doublet Model invariant under the gauge group SU(2)×U(1) is known to have six additional global discrete or continuous symmetries of its scalar sector. We have discovered regions of parameter space of the model which are basis and renormalization group invariant to all orders of perturbation theory in the scalar and gauge sectors, but correspond to none of the hitherto considered symmetries. We therefore identify seven new symmetries of the model and discuss their phenomenology. Soft symmetry breaking is required for some of these models so that electroweak
symmetry breaking can occur. We show that, at least at two-loop level, it is possible to extend some of these symmetries to include fermions.

With support from FCT through project UIDB/00777/2020

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