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 $\sim 125\mathrm{GeV}$. The rest of the Higgses are put above the mass scale of $\sim 600\mathrm{GeV}$, 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.

• Received 10 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.095014