As the LHC Higgs data persistently suggest the couplings of the observed 125
GeV Higgs boson to be consistent with the Standard Model (SM) expectations, any
extended Higgs sector must lead to the so-called SM alignment limit, where one
of the Higgs bosons behaves exactly like that of the SM. In the context of the
Two Higgs Doublet Model (2HDM), this alignment is often associated with either
decoupling of the heavy Higgs sector or accidental cancellations in the 2HDM
potential. We present a novel symmetry justification for `natural' alignment
without necessarily decoupling or fine-tuning. We show that there exist only
three different symmetry realizations of the natural alignment scenario in
2HDM. We identify the 2HDM parameter space satisfying the natural alignment
condition up to the Planck scale. We also analyze new collider signals for the
heavy Higgs sector in the natural alignment limit, which dominantly lead to
third-generation quarks in the final state and can serve as a useful
observational tool during the Run-II phase of the LHC.Comment: 15 pages, based on a plenary presentation given by A. Pilaftsis at
the Fifth Symposium on Prospects in the Physics of Discrete Symmetries (2016,
Warsaw, Poland), (significant text overlap with arXiv:1408.3405,
arXiv:1503.09140 and arXiv:1510.08790