Effective Theory of Higgs Sector Vacuum States

The effective field theory description for modifications of Standard Model-like Higgs boson interactions arising from tree-level mixing with heavy Higgs sector vacuum states without conserved quantum numbers is presented. An expansion in terms of effective operator dimension based on powers of the heavy mass scale rather than operator dimension is utilized to systematically organize interactions within the effective theory. Vacuum states arising from electroweak singlet extensions of the Higgs sector yield at leading order only two effective dimension-six operators. One of these uniformly dilutes all the interactions of a single physical Higgs boson as compared with Standard Model expectations, while the combination of the two operators give more general modifications of all remaining interactions with two or more physical Higgs bosons. Vacuum states arising from an additional electroweak doublet yield three types of effective dimension-six operators that modify physical Higgs boson couplings to fermion pairs, self-couplings, and introduce four-fermion interactions. However, in this case modification of physical Higgs boson interactions with massive gauge bosons arise at leading order only from three effective dimension-eight operators. If the underlying Yukawa couplings of the additional electroweak doublet satisfy the Glashow-Weinberg condition then time reversal violation at effective dimension-six depends on a single universal phase appearing only in couplings of physical Higgs bosons to fermion pairs. In all cases the couplings of any three physical states in the effective theory description must be equal to those in a unitary mixing description in order for the long distance non-analytic components of physical on-shell scattering amplitudes to agree, while in contrast couplings of four or more physical states in general differ due to short distance effects.