New scenario for aligned Higgs couplings originated from the twisted custodial symmetry at high energies

We investigate a new scenario of the two Higgs doublet model, where the current experimental data for the electroweak rho parameter and those for the Higgs boson couplings can be simultaneously explained. In this scenario, the two Higgs doublet model is supposed to be a low energy effective theory up to a high energy scale $Lambda$, above which a fundamental theory should appear. It is assumed that the Higgs potential respects a global symmetry at $Lambda$ (the twisted custodial symmetry), which is to be given as a consequence of the global symmetry structure of the fundamental theory above $Lambda$. By the analysis using one-loop renormalization group equations, the above experimental data can be explained in a natural way even when the masses of the extra Higgs bosons are near the electroweak scale. We also discuss the predictions on the mass spectrum of the additional Higgs bosons and also those on coupling constants of the standard-model-like Higgs boson, which make it possible to test this scenario at current and future collider experiments.