Constraints from Heavy Higgs Boson Masses in the two Higgs Doublet Model

Upon the absence of signals of new physics at the Large Hadron Collider, a reasonable strategy is to assume that new particles are very heavy and that the other model parameters are still unknown. In the aligned two Higgs doublet model, however, heavy Higgs boson masses above 500 GeV enhance some couplings in the scalar potential, which causes a breakdown of the perturbative unitarity in general. Some tuning among model parameters is required. We find that one piece of information on the heavy Higgs boson mass, say M H , has significant implications: (i) the other heavy Higgs bosons should have masses similar to M H within ± O (10)%; (ii) the inequalities from the theoretical constraints are practically reduced to an equation such that m 12 2 tan β is constant, where m 12 2 is the soft Z 2 breaking parameter and tan β is the ratio of two vacuum expectation values; (iii) the triple Higgs coupling λ HHh is constant over tan β while λ HHH and λ AAH are linearly proportional to tan β . The double Higgs-strahlung process of e + e − → ZHH is also studied, for which the total cross section is almost constant for a given M H .