\CTran{Minimal Supergravity Scenario}

\spa

\Green{$\bullet$} \Blue{Since the most general parametrization
of SUSY breaking introduces more than 100 parameters a construction
of a model with few parameters is needed : \Red{mSUGRA} seems the most 
elegant!}

\spa

\Green{$\bullet$} \Blue{Supergravity $\rightarrow$ local SUSY transformations}

\spa 

Supergravity Scalar Potential :

{\small  H.~P.~Nilles '82, \\
A.~Chamseddine, R.~Arnowitt, P.~Nath, '82 \\
R.~Barbieri, S.~Ferrara, C.~Savoy, '82 \\
L.~Hall, J.~Lykken, S.~Weinberg, '83 \\
S.~K.~Soni, H.~A.~Weldon, '83}


%%%%%%%%%%%%%%%%%
\begin{eqnarray}
 {\cal V} \ =\ e^{(\frac{Z_A^\dagger Z_A}{M^2})}~ 
\Biggl [ F_A^\dagger F_A-3 \frac{f^\dagger f}{M^2} \Biggr ]~+ ~\frac{1}{2} 
D^\alpha D^\alpha\;,
\nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%%

\Green{$\surd$} \Blue{${\cal V}$ not positive definite!
so it could be 
spontaneous SUSY breaking : $<F_A> \ne 0$ with zero vacuum energy, 
$V=0$}

\Green{$\rightarrow$} \Blue{New terms arive!}

\Green{$\bullet$} $m_{ij}^2 =M_0^2~ \delta_{ij}$ $\;\;\;\;\;,\;\;\;\;\;$ 
\Green{$\bullet$} $M_1=M_2=M_3=M_{1/2}$

\Green{$\bullet$} $A_{ijk} =A_0^2$ $\;\;\;\;\;,\;\;\;\;\;\;\;\;\;\;$
\Green{$\bullet$} $\phi_{A_0}$

\Green{$\bullet$} $B_{ij}=B_0 ~\delta_{ij}$ $\;\;\;\;\;,\;\;\;\;\;\;\;$
\Green{$\bullet$} $\phi_{B_0}$



