Precision measurements constraints on the number of Higgs doublets

Abstract

We consider an extension of the Standard Model with an arbitrary number $N$ of Higgs doublets (NHDM), and calculate their contribution to the oblique parameters $S$ and $T$. We examine the possible limitations on $N$ from precision measurements of these parameters. In view of the complexity of the general case of NHDM, we analyze several benchmark scenarios for the Higgs mass spectrum, identifying the lightest CP-even Higgs with the Higgs-like particle recently observed at the LHC with the mass of $\sim 125$ GeV. The rest of the Higgses are put above the mass scale of $\sim 600$ GeV, below which the LHC experiments do not detect any Higgs-like signals except for the former famous one. We show that, in a scenario, with all the heavy Higgses degenerate at any scale, there are no limitations on the number $N$ of the Higgs doublets. However, upper limits appear for certain not completely degenerate configurations of the heavy Higgses.