1209.0474 (E. Torrente-Lujan)

The Higgs and top masses: why the higgs mass is $m_H^2=m_Z m_t$?    [PDF]

E. Torrente-Lujan

On the light of the recent LHC discovery, we present a simple computation of the the mass ratio $\rho_t=m_Z m_t/m_H^2$. From the LHC combined $m_H$ value, we get $$\rho_t= 1.0022\pm 0.007\pm 0.009.$$ It is tempting to think that a value of $\rho_t$ ratio so close to one, it is not a mere coincidence but, on naturalness grounds, a signal of some more deeper symmetry. In a model independent way, $\rho_t$ can be viewed as the ratio of the highest massive representatives of the spin $(0,1/2,1)$ SM and, to a very good precision the experimental evidence tell us that $$\frac{m_{s=1} m_{s=1/2}}{m_{s=0}^2} \simeq 1.$$ Somehow the mass of the "lowest" scalar particle mass is the geometric mean of the highest spin 1, 1/2 masses. We review the theoretical situation of this ratio in the SM and beyond. In the SM such a ratio hints for a non-casual relation of the type $\lambda\sim g g_t$. Littlest Higgs Models, for example, where $\lambda\sim o(g^2, g_t^2)$ could accomodate such a relation.

View original: http://arxiv.org/abs/1209.0474