\newcommand{\newc}{\newcommand}
\newc{\del}{\partial}
\newc{\beq}{\begin{equation}}
\newc{\eeq}{\end{equation}}
\newc{\barr}{\begin{eqnarray}}
\newc{\earr}{\end{eqnarray}}
\newc{\ggam}[2]{\Gamma_{#2}^{#1}}
\newc{\ra}{\rightarrow}
\newc{\lam}{\lambda}
\newc{\eps}{\epsilon}
\newc{\half}{\frac{1}{2}}
\newc{\third}{\frac{1}{3}}
\newc{\fourth}{\frac{1}{4}}
\newc{\eighth}{\frac{1}{8}}
\newc{\gev}{\mbox{~GeV}}
\newc{\lra}{\leftrightarrow}
\newc{\Dslash}{\not\!\! D}
\newc{\sg}{{\cal G}}
\newc{\etal}{{\it et al.}\ }
\newc{\Hbar}{{\bar H}}
\newc{\hhbar}{{\overline h}}
\newc{\Ubar}{{\bar U}}
\newc{\Dbar}{{\bar D}}
\newc{\Ebar}{{\bar E}}
\newc{\eg}{{\it e.g.}\ }
\newc{\ie}{{\it i.e.}\ }
\newc{\nonum}{\nonumber}
\newc{\kap}{\kappa}
\newc{\Dt}{\frac{d}{dt}}
\newc{\rpv}{$\not\!\!R_p$}
\newc{\bpv}{$\not\!\!B_p$}
\newc{\mpl}{$M_{Pl}$\ }
\newc{\ol}{\overline}
\newc{\mx}{$M_X$\ }
\newc{\tev}{\mbox{~TeV}}
\newc{\sect}[1]{\ref{sec:#1}}
\newc{\nonr}{\nonumber}
\newc{\eq}[1]{(\ref{eq:#1})}
\newc{\eqs}[2]{(\ref{eq:#1},\ref{eq:#2})}
\newc{\Lam}{{\bf\Large \Lambda}}
\newc{\ltau}{\lambda_\tau}
%\newc{\lt}{\lambda_t}
\newc{\lb}{\lambda_b}
\newc{\lae}{{\Lam}_E}
\newc{\lad}{{\Lam}_D}
\newc{\lau}{{\Lam}_U}
\newc{\lame}[1]{{\Lam}_{E^{#1}}}
\newc{\lamd}[1]{{\Lam}_{D^{#1}}}
\newc{\lamu}[1]{{\Lam}_{U^{#1}}}
\newc{\lamet}[1]{{\Lam}_{E^{#1}}^T}
\newc{\lamdt}[1]{{\Lam}_{D^{#1}}^T}
\newc{\lamut}[1]{{\Lam}_{U^{#1}}^T}
\newc{\lames}[1]{{\Lam}_{E^{#1}}^*}
\newc{\lamds}[1]{{\Lam}_{D^{#1}}^*}
\newc{\lamus}[1]{{\Lam}_{U^{#1}}^*}
\newc{\lamed}[1]{{\Lam}_{E^{#1}}^\dagg}
\newc{\lamdd}[1]{{\Lam}_{D^{#1}}^\dagg}
\newc{\lamud}[1]{{\Lam}_{U^{#1}}^\dagg}
\newc{\Y}{{\bf Y}}
\newc{\ye}{{\Y}_E}
\newc{\yd}{{\Y}_D}
\newc{\yu}{{\Y}_U}
\newc{\yes}{{\Y}_E^*}
\newc{\yds}{{\Y}_D^*}
\newc{\yus}{{\Y}_U^*}
\newc{\yet}{{\Y}_E^T}
\newc{\ydt}{{\Y}_D^T}
\newc{\yut}{{\Y}_U^T}
\newc{\yed}{{\Y}_E^\dagg}
\newc{\ydd}{{\Y}_D^\dagg}
\newc{\yud}{{\Y}_U^\dagg}
\newc{\dagg}{\dagger}

\CTran{Superpotential}

\vspace*{-0.4cm}

\begin{eqnarray} 
W &=& \Green{\epsilon_{ab} \left[ (\ye)_{ij} L_i^a
H_1^b {\bar E}_j + (\yd)_{ij} Q_i^{ax} H_1^b {\bar D}_{jx} +
(\yu)_{ij} Q_i^{ax} H_2^b {\bar U}_{jx} \right]}\nonr \\[0.4cm] &&+~
\Green{\eps_{ab}~ \mu H_1^a H_2^b } \nonr \\[0.4cm] &&+~
\Red{\eps_{ab}\left[ \frac{1}{2}\lambda_{ijk} L_i^a L_j^b{\bar E}_k +
\lambda'_{ijk} L_i^a Q_j^{xb} {\bar D}_{kx} \right]}\;\;\;\ 
\rightarrow  \not \!\! L \; \rm{violation}
 \nonr \\[0.4cm] &&+~
\Red{\frac{1}{2}\eps_{xyz} \lambda^{''}_{ijk} {\bar U}_i^x{\bar
D}_j^y{\bar D}^z_k} \;\;\;\ 
\rightarrow  \not \!\! B \; \rm{violation}
 \nonr\\[0.4cm] && +~ \Red{\eps_{ab} 
\left[\kap^i L_i^a H_2^b \right]} \;\;\;\ 
\rightarrow  \not \!\! L \; \rm{violation}. \nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\centerline{\Blue {$\Downarrow$}}

\vspace*{0.3in}

\centerline{\psfig{figure=proton.eps,height=2.0in}}

\centerline{\Blue{Proton Decay!}}

\vspace*{0.1in}

\Green{$\bullet$}
\Blue{$B$ number is violated by 9 $\lambda^{''}_{ijk}$ couplings}

\vspace*{0.1in}

\Green{$\bullet$}
\Blue{
$L$ bumber is violated by 9 $\lambda_{ijk}$ + 27 $ \lambda'_{ijk}$ +
 3 $\kap_i$ couplings}

 
%\begin{center}
%\Green{$\bullet$} \Red{R-Parity}

%$R  = (-1)^{3B + L +2S}$

%R(SM like particles)=+1   ,  R(SUSY particles)=-1

%\end{center}
