Sphaleron-Bisphaleron bifurcations in a custodial-symmetric two-doublets model

The standard electroweak model is extended by means of a second Brout-Englert-Higgs doublet. The symmetry breaking potential is chosen in such a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a static, spherically symmetric ansatz of the bosonic fields consistently reduces the Euler-Lagrange equations to a set of differential equations. The potential involves, in particular, products of fields of the two doublets, with a coupling constant ?3. Static, finite energy solutions of the classical equations are constructed. The regular, non-trivial solutions with the lowest classical energy can be of two types: sphalerons or bisphalerons, according to the coupling constants. Special emphasis is put on the bifurcation between these two types of solutions which is analyzed in the function of the different constants of the model, namely of ?3.