Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3 symmetry

We analyse the Higgs sector of an S-3 model with three Higgs doublets and no CP violation. After electroweak breaking there are nine physical Higgs bosons, one of which corresponds to the Standard Model one. We study the scalar and gauge sectors of this model, taking into account the conditions set by the minimisation and stability of the potential. We calculate the masses, trilinear and quartic Higgs-Higgs, and Higgs-gauge couplings. We consider two possible alignment scenarios, where only one of the three neutral scalars has couplings to the gauge bosons and corresponds to the SM Higgs, and whose trilinear and quartic couplings reduce exactly to the SM ones. We also obtain numerically the allowed parameter space for the scalar masses in each of the alignment scenarios. We use the calculated trilinear and quartic couplings to find the analytical structure of the one-loop neutral scalar mass matrix, without fermionic contributions. We show that it is possible to have a compact mass spectrum where the contribution to the oblique parameters might be small. We explore some scenarios for the loop contributions to the neutral scalar masses.