New physics effects in the Higgs trilinear self-coupling through one-loop radiative corrections

We compute the one-loop corrections to the triple Higgs self-interaction $hhh$ in the framework of the Standard Model (SM), the Two Higgs Doublet Model type III (THDM-III) and the Littlest Higgs Model with T parity (LHBM+T). Our results are compared with previous results for the SM. In particular, we find that an imaginary part for the ${\lambda }_{hhh}$ form factor is induced when one of the Higgs boson legs is off-mass shell with 4-momentum magnitude higher than the Higgs boson mass. This contribution is sensitive to virtual effects of the Higgs self-interaction, that induces a radiative correction to the $hhh$ coupling of order 11%. However, the radiative corrections associated to the new degrees of freedom of the THDM-III and the LHBM+T are rather smaller and comparable to the $W^{\pm }$ and $Z^0$ gauge bosons one-loop corrections.