Local Supersymmetry

As already seen, the MSSM contains a high number of degrees of freedom.

The impossibility to have guidelines on how build a theory leads to models that consider the Supersymmetry as a local symmetry spontaneously broken at different scales with respect to the weak one. Among these,
the gravity mediated Supersymmetry breaking theories (or briefly SUperGRAvity, or SUGRA) are the most reliable.

The assumption is that the spontaneous breaking concerns a “hidden sector” distinct from the “observable” (the one i.e. populated by the particles and their respective SM superpartner), being the two sectors very weakly interactive with each other. The observable effects of such breaking would depend on the nature of the interactions between these two sectors, taking into account that in Supergravity models the mediator of this interaction is the gravitational interaction.

The promotion of Supersymmetry to local Supersymmetry can be only done by introducing the graviton, a spin-2 field associated with the mediator of the gravitational interaction and its superpartner, the gravitino, a spin $s=\frac{3}{2}$ spinor field, into the theory.
The simplest supergravity model is the mSUGRA and it seems to be one of the most promising to describe the reality, at the present.

The whole $\mathcal{L}_{soft}$, that in the MSSM introduces more than 100 parameters, here is parameterized only by $m_0$ and $A_0$. The free parameters in the mSUGRA Lagrangian so, are only five:

• $m_{\frac{1}{2}}$: universal gaugino mass;
• $m_0$: universal scalar mass;
• $A_0$: universal trilinear coupling;
• $tan\beta$: Higgs fields VEV ratio;
• $sign(\mu)$: higgsino mass parameter sign.

Thus, the superparticles spectrum is a function of these five parameters only.

Direct and indirect supersymmetric particle searches have so far not led to any evidence. The results of the experiments (in particular at $\textsf{LEP}$ and at $\textsf{Tevatron}$) have just set lower limits to the masses of various particles.