On the origin of Z(2) symmetry in the Two-Higgs Doublet extension of the SM

We argue that the consistent implementation of the multiple point principle (MPP) in the general non-supersymmetric two Higgs doublet model (2HDM) can lead to a set of approximate global custodial symmetries that ensure CP conservation in the Higgs sector and the absence of flavour changing neutral currents (FCNC) in the considered model. In particular the existence of a large set of degenerate vacua at some high energy scale $\Lambda$ caused by the MPP can result in approximate U(1) and Z(2) symmetries that suppress FCNC and CP--violating interactions in the 2HDM. We explore the renormalisation group (RG) flow of the Yukawa and Higgs couplings within the MPP inspired 2HDM with approximate custodial symmetries and show that the solutions of the RG equations are focused near quasi--fixed points at low energies if the MPP scale scale $\Lambda$ is relatively high. We study the Higgs spectrum and couplings near the quasi--fixed point at moderate values of $\tan\beta$ and compute a theoretical upper bound on the lightest Higgs boson mass. When the MPP scale is low, the mass of the lightest Higgs particle can reach $180-220 {GeV}$ while its coupling to the top quark can be significantly larger than in the SM, resulting in the enhanced production of Higgs bosons at the LHC. Other possible scenarios that appear as a result of the implementation of the MPP in the 2HDM are also discussed.