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\begin{document}

%page-1

\begin{slide}

\begin{center}

{\large\bfseries Higgs sector of the E6 inspired SUSY model 
with an extra $U(1)_N$ factor}

\vspace{3mm}
{\itshape \underline{R.B.Nevzorov} \\[10mm]
{\small in collaboration with}\\[5mm]
{\itshape S.F.King {\small and} S.Moretti }}

\vspace{10mm}
{\bf Contents}
\begin{enumerate}

\item Introduction

\item Exceptional SUSY model

\item Analysis of renormalization group flow

\item Spectrum of the Higgs bosons

\item Collider phenomenology

\item Conclusions

\end{enumerate}
\end{center}
\end{slide}


%page-2

\begin{slide}
{\large\bfseries I. Introduction}
\begin{itemize}
\vspace{-3mm}
\item One of the strongest arguments in favour of SUSY is that the
local version of SUSY (SUGRA) leads to a partial unification of the SM gauge
interactions with gravity.
\vspace{-5mm}
\item However the origin of the $\mu$--term remains unclear in SUGRA models. Indeed
\[
W_{SUGRA}=W_0(h_m)+\mu(h_m)(\hat{H}_d\hat{H}_u)+ ...
\]
where
\[
\mu(h_m)\sim M_{Pl}\qquad \mbox{or}\qquad \mu(h_m)=0.
\]
\vspace{-10mm}
\item The correct pattern of electroweak symmetry breaking requires
\[
\mu(h_m)\sim 100-1000\, \mbox{GeV}\, .
\]
\item Since SUGRA is non--renormalizable theory it should be considered as
an effective one.
\item Nowadays the best candidate for underlying theory is superstring theory.
\end{itemize}
\end{slide}


%page-3

\begin{slide}
\begin{itemize}
\item The enlarged gauge symmetry in the superstring inspired $E_6$ models
forbids any bilinear terms in the superpotential allowing interaction
\[
W_{E_6}=\lambda S(H_d H_u)+...\,.
\]
\item By means of the Hosotani mechanism $E_6$ may be broken to
{\small
\[
E_6\to SU(3)_{C}\times SU(2)_{W}\times U(1)_{Y}\times U(1)_{\psi}\times U(1)_{\chi}\,,
\]
}
where $U(1)_{\psi}$ and $U(1)_{\chi}$ are defined as
{\small
\[
E_6\to SO(10)\times U(1)_{\psi},\qquad SO(10)\to SU(5)\times U(1)_{\chi}.
\]
}
\item The obtained rank--6 model can be reduced further to rank--5 model
that contains only one extra $U(1)'$ factor
\[
U(1)'=U(1)_{\chi}\cos\theta+U(1)_{\psi}\sin\theta\,.
\]
\item At the electroweak or SUSY breaking scale field $S$ acquires VEV
breaking $U(1)'$ and providing natural solution of the $\mu$--problem
\[
\mu_{eff}=\lambda <S>\,.
\]
\end{itemize}
\end{slide}


%page4

\begin{slide}
{\large\bfseries II. Exceptional SUSY model }
\begin{itemize}
\item For a special value of $\theta$
\[
\theta=\arctan\sqrt{15}\,
\]
that corresponds to $U(1)_{N}$ symmetry, right handed neutrino remains
sterile after the breakdown of $E_6$.
\vspace{-0.7cm}
\item Only in this exceptional SUSY model (ESSM) right handed neutrino
can be superheavy.
\vspace{-0.7cm}
\item Anomalies in the ESSM are cancelled automatically if the particle contents form
complete fundamental 27 representations of $E_6$.
\vspace{-1.5cm}
\item To ensure the gauge coupling unification $SU(2)$ doublet and anti doublet from
extra $27$ and $\overline{27}$ ($H'$ and $\overline{H}'$) should be introduced.
\vspace{-0.7cm}
\item Together with survivors the particle contents of the ESSM becomes
\[
\begin{array}{c}
3\biggl[(Q_i,\,u^c_i,\,d^c_i,\,L_i,\,e^c_i)\biggr]+3(D_i,\,\overline{D}_i)+\\[2mm]
+3(H_{2i})+3(H_{1i})+3(S_i)+3(N_i^c)+H'+\overline{H}'\,,
\end{array}
\]
{\small
where $D_i$ and $\overline{D}_i$ are exotic quarks, $H_{1i}$ and $H_{2i}$ are
either Higgs or exotic $SU(2)$ doublets.
}
\end{itemize}
\end{slide}


%page5

\begin{slide}
\begin{itemize}
\item To prevent rapid proton decay the invariance under some discrete
symmetry should be imposed.
\item The straightforward generalization of R--parity definition
\[
R=(-1)^{3(B-L)+2S}
\]
assuming $B_{D}=1/3$ and $B_{\overline{D}}=-1/3$ ensures that the
lightest exotic quark is stable.
\item The existence of stable exotic quarks is ruled out by different experiments.
\item There are two different ways to impose an appropriate $Z_2$ symmetry
leading to the baryon and lepton number conservation which imply
\begin{itemize}
\item[-] $\overline{D}$ and $D$ are diquark and anti diquark, i.e.
\[
B_{\overline{D}}=2/3\,,\qquad B_{D}=-2/3\,;
\]
\item[-] exotic quarks are leptoquarks, i.e.
\[
\begin{array}{c}
B_{D}=1/3\,,\qquad L_D=1\,,\\[2mm]
B_{\overline{D}}=-1/3\,,\qquad L_{\overline{D}}=-1\,.
\end{array}
\]
\end{itemize}
\end{itemize}
\end{slide}


%page-6

\begin{slide}
\begin{itemize}
\item Different generalizations of R--parity result in different ESSM superpotentials
\[
\begin{array}{rcl}
i)\qquad W_{ESSMI}&=& \frac{1}{2}M_{ij} N_i^c
N_j^c+W_0+W_1\,,\\[4mm] ii)\quad W_{ESSMII}&=&\frac{1}{2}M_{ij}
N_i^c N_j^c+W_0+W_2.
\end{array}
\]
where {\small
\[
\begin{array}{rcl}
W_0&=&\lambda_{ijk}S_i(H_{1j}H_{2k})+\kappa_{ijk}S_i(D_j\overline{D}_k)+h^N_{ijk}
N_i^c (H_{2j} L_k)+\\[3mm]
   &+& h^U_{ijk} u^c_{i} (H_{2j} Q_k)+h^D_{ijk} d^c_i (H_{1j} Q_k) + h^E_{ijk} e^c_{i} (H_{1j} L_k) \,,\\[3mm]
W_1&=& g^Q_{ijk}D_{i} (Q_j Q_k)+g^{q}_{ijk}\overline{D}_i d^c_j
u^c_k\,,\\[3mm] W_2&=& g^N_{ijk}N_i^c D_j d^c_k+g^E_{ijk} e^c_i
D_j u^c_k+g^D_{ijk} (Q_i L_j) \overline{D}_k\,.
\end{array}
\]
}
\item The ESSM superpotentials involve a lot of new Yukawa interactions that contribute to the amplitude of 
$K^0-\overline{K}^0$ oscillations and give rise to $\mu\to e^{-}e^{+}e^{-}$.
\item To suppress flavour changing processes one can postulate $Z^{H}_2$ symmetry under which all superfields 
except $H_d\equiv H_{13}$, $H_u\equiv H_{23}$ and $S\equiv S_3$ are odd.
\item The $Z^{H}_2$ symmetry simplifies the structure of interactions in the ESSM superpotentials 
{\small
\[
\begin{array}{rcl}
\lambda_{ijk}S_i(H_{1j}H_{2k})+\kappa_{ijk}S_i(D_j\overline{D}_k)
\longrightarrow  \lambda_i S(H_{1i}H_{2i})+\\[2mm]
+\kappa_i S(D_i\overline{D}_i)+f_{\alpha\beta}S_{\alpha}(H_d H_{2\beta})+
\tilde{f}_{\alpha\beta}S_{\alpha}(H_{1\beta}H_u)\,,
\end{array}
\]
where $\alpha,\beta=1,2$ and $i=1,2,3$\,.
}
\end{itemize}
\end{slide}


%page-7

\begin{slide}
\begin{itemize}
\item But $Z^{H}_2$ symmetry can only be approximate since it forbids all terms in $W_1$ and $W_2$ that
would allow the exotic quarks to decay.
\item In order to provide the correct breakdown of gauge symmetry and to suppress FCNC processes
we assume that
\begin{itemize}
{
\item[-] only one field $S=S_3$ may have appreciable couplings to the exotic quarks and $SU(2)$ doublets
$H_{1i}$ and $H_{2i}$ and the structure of the corresponding
Yukawa interactions is flavor diagonal\,;
\item[-] only one pair of $SU(2)$ doublets $H_{d}$ and $H_{u}$ is allowed to have Yukawa
couplings of the order of unity\,;
\item[-] the Yukawa couplings of exotic particles to the quarks and leptons of the first two generations are less
than $10^{-4}$ and $10^{-3}$ respectively\,;
\item[-] the Yukawa couplings of exotic particles to the quarks and leptons of the third generation as well as
to the fields $S_1$ and $S_2$ are smaller than 0.1\,. }
\end{itemize}
\end{itemize}
\end{slide}


%page-8

\begin{slide}
{\large\bfseries III. The analysis of RG flow}
\begin{itemize}
\item According to our assumptions the superpotential of the ESSM can be written as
{\small
\[
\begin{array}{rcl}
W_{ESSM}&\simeq& \lambda S(H_{d} H_{u})+\kappa_i S(D_i\overline{D}_i)+h_t(H_{u}Q)t^c+\\[2mm]
&&+h_b(H_{d}Q)b^c+h_{\tau}(H_{d}L)\tau^c+...\,,
\end{array}
\]
}
\item We assume that this superpotential is formed near the Planck scale and RG equations
should be used to compute the gauge and Yukawa couplings at $Q\simeq M_Z$.
\item The inclusion of loop effects induces mixing between $U(1)_{N}$ and $U(1)_Y$
in the gauge kinetic part of the Lagrangian
{\small
\[
\mathcal{L}_{kin}=-\frac{1}{4}\left(F^Y_{\mu\nu}\right)^2-
\frac{1}{4}\left(F^{N}_{\mu\nu}\right)^2-\frac{\sin\chi}{2}F^{Y}_{\mu\nu}F^{N}_{\mu\nu}-...\,.
\]
}
\item It can be eliminated by a non--unitary transformation
{\small
\[
B^Y_{\mu}=B_{1\mu}-B_{2\mu}\tan\chi\,,\qquad B^{N}_{\mu}=B_{2\mu}/\cos\chi\,.
\]
}
which changes the interaction between the $U(1)_{N}$ gauge field and matter fields so that
{\small
\[
D_{\mu}=\partial_{\mu}-ig_1 Q^{Y}_iB_{1\mu}-i(g'_1Q^{N}_i+g_{11}Q^Y_i)B_{2\mu}-...,
\]
}
where
{\small
\[
g_1=g_Y\,,\quad g'_1=g_{N}/\cos\chi\,,\quad g_{11}=-g_Y\tan\chi\,.
\]
}
\end{itemize}
\end{slide}


%page-9

\begin{slide}
\begin{itemize}
{\small
\item The RG flow of the gauge couplings is affected by the kinetic term mixing
{\small
\[
\frac{d g_2}{dt}=\frac{\beta_2 g_2^3}{(4\pi)^2}\,,\qquad\qquad \frac{d g_3}{dt}=\frac{\beta_3 g_3^3}{(4\pi)^2}\,,
\]
\[
\begin{array}{rcl}
\displaystyle\frac{d G}{d t}&=&G\times B\,,\qquad
G=\left(
\begin{array}{cc}
g_1 & g_{11}\\[2mm]
0   & g'_1
\end{array}
\right)\,,\\[6mm]
B&=&\displaystyle\frac{1}{(4\pi)^2}
\left(
\begin{array}{cc}
\beta_1 g_1^2 & 2g_1g'_1\beta_{11}+2g_1g_{11}\beta_1\\[2mm]
0 & g^{'2}_1\beta'_1+2g'_1 g_{11}\beta_{11}+g_{11}^2\beta_1
\end{array}
\right)\,,
\end{array}
\]
\[
\beta_3=0\,,\quad\beta_2=4\,,\quad \beta_1=\frac{48}{5}\,,\quad \beta'_1=\frac{47}{5}\,,\quad \beta_{11}=-\frac{\sqrt{6}}{5}\,.
\]
}
\vspace{-1.5cm}
\item In the $E_6$ inspired models one can expect that
{\small
\[
\begin{array}{c}
g_3(M_X)=g_2(M_X)=g_1(M_X)=g'_1(M_X)=g_0\,,\\[4mm]
g_{11}(M_X)=0\,.
\end{array}
\]
}
\vspace{-1.2cm}
\item The hypothesis of the gauge coupling unification permits to evaluate
{\small
\[
\begin{array}{rclcc}
g_0&\simeq &1.21\,,&\quad & M_X \simeq 2\cdot 10^{16}\,\mbox{GeV}\,,\\[2mm]
\displaystyle\frac{g_1(M_Z)}{g'_1(M_Z)}&\simeq& 0.99\,,&\quad& g_{11}(M_Z)\simeq 0.020\,.
\end{array}
\]
}
\vspace{-1.2cm}
\item The running of the Yukawa couplings obeys the RG equations
{\small
\[
\begin{array}{rcl}
\displaystyle\frac{dh_t}{dt}&=&\displaystyle
\frac{h_t}{(4\pi)^2}\biggl[\lambda^2+6h_t^2-\frac{16}{3}g_3^2-3g_2^2-\frac{13}{15}g_1^2-
\frac{3}{10}g^{'2}_1\biggr]\,,\\[5mm]
\displaystyle\frac{d\lambda}{dt}&=&\displaystyle
\frac{\lambda}{(4\pi)^2}\biggl[4\lambda_i^2+3\Sigma_{\kappa}+3h_t^2-3g_2^2-\frac{3}{5}g_1^2-
\frac{19}{10}g^{'2}_1\biggr]\,,\\[5mm]
\displaystyle\frac{d\kappa_i}{dt}&=&\displaystyle
\frac{\kappa_i}{(4\pi)^2}\biggl[2\kappa^2_i+2\lambda^2+3\Sigma_{\kappa}-\frac{16}{3}g_3^2-
\frac{4}{15}g_1^2-\frac{19}{10}g^{'2}_1
\biggr]\,,
\end{array}
\]
\[
\Sigma_{\kappa}=\kappa_1^2+\kappa_2^2+\kappa_3^2\,,\qquad i=1,\,2,\,3\,.
\]
}}
\end{itemize}
\end{slide}


%page-10

\begin{slide}
\begin{itemize}
\item The requirement of validity of perturbation theory up to $Q\simeq M_X$ restricts 
the interval of variations of Yukawa couplings at $Q\simeq M_t$.
\item Whereas the restrictions on $\kappa_i$ do not change much when $\tan\beta$ varies 
the upper limit on $\lambda$ depends rather strongly on $\tan\beta$.
\end{itemize}
\vspace{-1cm}
\hspace{0cm}{\small $\lambda_{max}$}\\
\vspace{-1.5cm}
\begin{center}
{\hspace*{-10mm}\includegraphics[height=100mm,keepaspectratio=true]{l-tanb.eps}}\\
{\small $\tan\beta$}\\[2mm]
\vspace{10cm}
\end{center}
\end{slide}


%page-11

\begin{slide}
{\large\bfseries IV. Spectrum of the Higgs bosons}
\begin{itemize}
\item The Higgs boson potential of the ESSM is given by
{\small
\[
\begin{array}{rcl}
V&=&V_F+V_D+V_{soft}+\Delta V\, ,\\[7mm]
V_F&=&\lambda^2|S|^2(|H_d|^2+|H_u|^2)+\lambda^2|(H_d H_u)|^2\,,\\[3mm]
V_D&=&\displaystyle\frac{g_2^2}{8}\biggl(H_d^+\sigma_a H_d+H_u^+\sigma_a H_u\biggr)^2+
\frac{{g'}^2}{8}\biggl(|H_d|^2-|H_u|^2\biggr)^2\\[3mm]
&&+\displaystyle\frac{g^{'2}_1}{2}\biggl(\tilde{Q}_1|H_d|^2+\tilde{Q}_2|H_u|^2+\tilde{Q}_S|S|^2\biggr)^2\,,\\[5mm]
V_{soft}&=&m_{S}^2|S|^2+m_1^2|H_d|^2+m_2^2|H_u|^2+\\[3mm]
&&\qquad\qquad\qquad\qquad+\biggl[\lambda A_{\lambda}S(H_u H_d)+h.c.\biggr]\,,
\end{array}
\]
}
where $g'=\sqrt{3/5}\cdot g_1(M_Z)$\,.
\vspace{-1.3cm}
\item At the tree level it contains five fundamental parameters
\[
\lambda\,,\quad m_1^2\,,\quad m_2^2\,,\quad m_S^2\,,\quad A_{\lambda}\,.
\]
\vspace{-1.5cm}
\item At the physical vacuum
{\small
\begin{gather*}
H_1=\frac{1}{\sqrt{2}}\left(
\begin{array}{c}
v_1\\ 0
\end{array}
\right) , \quad H_2=\dfrac{1}{\sqrt{2}}\left(
\begin{array}{c}
0\\ v_2
\end{array}
\right) ,\quad S=\frac{s}{\sqrt{2}},\\[2mm]
v^2=v_1^2+v_2^2=(246\, GeV)^2\, ,\quad
\tan\beta=v_2/v_1\, .
\end{gather*}
}
\vspace{-2cm}
\item From the conditions for the extrema
{\small
\[
\frac{\partial V}{\partial v_1}=\frac{\partial V}{\partial
v_2}=\frac{\partial V}{\partial s}=0
\]
}
one can express soft masses $m_1^2$, $m_2^2$, $m_s^2$ via \\
$\tan\beta$, $s$ and $v$.
\end{itemize}
\end{slide}


%page-12

\begin{slide}
\begin{itemize}
\item Then tree level masses of the Higgs bosons depend on four variables:
\[
\lambda\,,\qquad \tan\beta\,,\qquad s\,,\qquad A_{\lambda}\; (\mbox{or}\; m_A^2)\,.
\]
\vspace{-1.5cm}
\item After the gauge symmetry breaking four goldstone modes are absorbed by $W$, $Z$ and $Z'$.
\vspace{-2cm}
\item Thus the Higgs sector of the ESSM involves
\begin{itemize}
\item[--] one pseudoscalar $\qquad m_A^2\simeq \displaystyle \frac{\sqrt{2}\lambda A_{\lambda}}{\sin 2\beta}\,s$\,,
\item[--] two charged states $\qquad m_{H^{\pm}}^2\simeq m_A^2$\,,
\item[--] three scalars
{\small
\[
\begin{array}{rcl}
m_{h_1}^2 &\approx & g^{'2}_1\tilde{Q}_S^2s^2\simeq M^2_{Z'}\,,\\[3mm]
m_{h_2}^2 &\approx & m_A^2\,,\\[3mm]
m_{h_3}^2 &\le     &\displaystyle \frac{\lambda^2}{2}v^2\sin^22\beta+M_Z^2\cos^22\beta+\\[0mm]
                  &&\qquad\qquad+g^{'2}_1v^2\biggl(\tilde{Q}_1\cos^2\beta+\tilde{Q}_2\sin^2\beta\biggr)^2\,.
\end{array}
\]
}
\end{itemize}
\vspace{-1.7cm}
\item One CP--even Higgs boson is always heavy because it has almost the same mass as $Z'$.
From the direct searches at the Tevatron
\[
M_{Z'}>500-600\,\mbox{GeV}\,.
\]
\vspace{-2.5cm}
\item Masses of another CP--even, CP--odd and charged Higgs bosons are very close to $m_A$.
\end{itemize}
\end{slide}



%page-13

\begin{slide}
\begin{itemize}
{\small
\item When $\lambda>g^{'}_1$ the parameter of $m_A$ is limited from below and above so that the Higgs spectrum has
a hierarchical structure. For $\lambda=0.79$, $\tan\beta=2$, $X_t=\sqrt{6} M_S$ and $M_{Z'}=M_S=700\,\mbox{GeV}$ we get}
\end{itemize}
\vspace{-0.5cm}
\begin{center}
{\small One--loop Higgs boson spectrum}\\
{\hspace*{-10mm}\includegraphics[height=90mm,keepaspectratio=true]{one-loop-spectr1.eps}}\\
{\small $m_A$}\\[2mm]
\end{center}
\vspace{1cm}
\begin{center}
{\small One--loop mass of the lightest Higgs boson}\\
{\hspace*{-10mm}\includegraphics[height=90mm,keepaspectratio=true]{mh-ma1.eps}}\\
{\small $m_A$}\\[2mm]
\end{center}
\end{slide}



%page-14

\begin{slide}
\begin{itemize}
{\small
\item For small values of $\lambda$  ($\lambda<g^{'}_1$) $m_A$ is bounded from above only
so that some of the Higgs states may gain masses below $1\,\mbox{TeV}$. If $\lambda=0.3$, 
$\tan\beta=2$, $X_t=\sqrt{6} M_S$ and $M_{Z'}=M_S=700\,\mbox{GeV}$ we have}
\end{itemize}
\vspace{-0.5cm}
\begin{center}
{\small One--loop Higgs boson spectrum}\\
{\hspace*{-10mm}\includegraphics[height=90mm,keepaspectratio=true]{one-loop-spectr8.eps}}\\
{\small $m_A$}\\[2mm]
\end{center}
\vspace{1cm}
\begin{center}
{\small One--loop mass of the lightest Higgs boson}\\
{\hspace*{-10mm}\includegraphics[height=90mm,keepaspectratio=true]{mh-ma8.eps}}\\
{\small $m_A$}\\[2mm]
\end{center}
\end{slide}



%page-15

\begin{slide}
\begin{itemize}
{\item Even at the tree level the lightest Higgs scalar in the ESSM can be
heavier $120\,\mbox{GeV}$.}
\end{itemize}
\vspace{-0.6cm}
\begin{center}
{\small Tree level upper bound on $m_{h_1}$}\\
{\hspace*{-10mm}\includegraphics[height=90mm,keepaspectratio=true]{mh8-tanb.eps}}\\
{\small $\tan\beta$}\\[2mm]
\end{center}
\begin{itemize}
{%\small
\item Two--loop theoretical restriction on $m_{h_1}$ in the ESSM does not exceed
$150-155\,\mbox{GeV}$.}
\end{itemize}
\vspace{-0.6cm}
\begin{center}
{\small  Two--loop upper bound on $m_{h_1}$}\\
{\hspace*{-10mm}\includegraphics[height=90mm,keepaspectratio=true]{mh9-tanb.eps}}\\
{\small $\tan\beta$}\\[2mm]
\end{center}
\end{slide}



%page-16

\begin{slide}
{\large\bfseries V. Collider phenomenology}
\begin{itemize}
\item $Z'$, exotic quarks and leptons may be produced at
future colliders.
\item At the LHC the $Z'$ boson can be discovered if it has a mass below
$4-4.5\,\mbox{TeV}$.\\[2mm]
\hspace{-1cm}\fbox{\parbox{140mm}{\tiny
A.Leike, Phys.Rept. 317 (1999) 143;\\
J.Kang, P.Langacker, Phys.Rev.D 71 (2005) 035014.}}
\item Its diagnostic via asymmetries should be possible up to
$M_{Z'}\simeq 2-2.5\,\mbox{TeV}$.\\[2mm]
\hspace{-1cm}\fbox{\parbox{140mm}{\tiny
M.Dittmar, A.Nicollerat, A-S.Djouadi, Phys.Lett.B 583 (2004)
111.}}\\[2mm]
\end{itemize}
\begin{center}
{\small\qquad Cross section for Drell-Yan production at the LHC}\\
\epsfig{file=phenofig1.ps,height=14cm,angle=90}
\end{center}
\end{slide}


%page-17

\begin{slide}
\begin{itemize}
\item The hierarchical structure of the Yukawa interactions in the ESSM implies that
exotic particles decay predominantly into the quarks and leptons of the third generation. 
\item The exotic quarks decay either via
\[
\overline{D}\to t+\tilde{b}\,,\qquad \overline{D}\to b+\tilde{t}
\]
if exotic quarks $\overline{D}_i$ are diquarks or via
\[
\begin{array}{ll}
D\to t+\tilde{\tau}\,,\qquad & D\to \tau+\tilde{t}\,,\\
D\to b+\tilde{\nu}_{\tau}\,,\qquad & D\to \nu_{\tau}+\tilde{b}\,,
\end{array}
\]
if exotic quarks $D_i$ are leptoquarks. 
\item The non--Higgsino decay modes are
\[
\begin{array}{ll}
\tilde{H}^0\to t+\tilde{\overline{t}}\,,\qquad &\tilde{H}^0\to \overline{t}+\tilde{t}\,,\\
\tilde{H}^0\to b+\tilde{\overline{b}}\,,\qquad &\tilde{H}^0\to \overline{b}+\tilde{b}\,,\\
\tilde{H}^0\to \tau+\tilde{\overline{\tau}}\,,\qquad &\tilde{H}^0\to \overline{\tau}+\tilde{\tau}\,,\\
\tilde{H}^{-}\to b+\tilde{\overline{t}}\,,\qquad &\tilde{H}^{-}\to \overline{t}+\tilde{b}\,,\\
\tilde{H}^{-}\to \tau+\tilde{\overline{\nu}_{\tau}}\,,\qquad &\tilde{H}^{-}\to \overline{\nu}_{\tau}+\tilde{\tau}\,.
\end{array}
\]
\item Assuming that $\tilde{f}\to f+\chi^0$ the exotic quark will produce either
$t$-- and $b$--quarks or $t$--quark and $\tau$--lepton in the final state with rather high probability.
\end{itemize}
\end{slide}



%page-18

\begin{slide}
\begin{center}
{\small\qquad Cross section for pair production of $b$, $t$ and exotic particles at the LHC}\\
\epsfig{file=phenofig2.ps,height=16cm,angle=90}
\end{center}
\begin{itemize}
\item Since $\sigma(pp\to D\overline{D}+X)$ may be comparable with $\sigma(pp\to t\overline{t}+X)$ 
the presence of light exotic quark will result in appreciable enhancement of the cross section of 
either 
\[
pp\to t\overline{t}b\overline{b}+X\,,\qquad pp\to b\overline{b}b\overline{b}+X
\]
if exotic quarks are diquarks or 
\[
pp\to t\overline{t}l\overline{l}+X\,,\qquad pp\to b\overline{b}l\overline{l}+X
\]
if new quark states are leptoquarks.
\end{itemize}
\end{slide}



%page-19

\begin{slide}
\begin{center}
{\small\qquad Cross section for pair production of exotic particles at the LHC}\\
\epsfig{file=phenofig3.ps,height=11.5cm,angle=90}
\end{center}
\begin{itemize}
{\small
\item While at the LHC $\sigma(pp\to \tilde{H}\tilde{\overline{H}}+X)$ is expected to be 
considerably smaller than $\sigma(pp\to D\overline{D}+X)$ they become comparable at the ILC.}
\end{itemize}
\begin{center}
{\small\qquad Cross section for pair production of exotic quarks and leptons
at future ILC}\\
\epsfig{file=phenofig5a.ps,height=11.5cm,angle=90}
\end{center}
\end{slide}


%page-20

\begin{slide}
{\large\bfseries VI.Conclusions}
\begin{itemize}
{
\item We have presented a self--consistent supersymmetric model with
additional $U(1)_{N}$ factor which naturally arises after the
breakdown of $E_6$ symmetry. \vspace{-7mm}
\item The SM like Higgs boson in the ESSM is lighter
than $150-155\,\mbox{GeV}$ and can be considerably heavier than in 
the MSSM and NMSSM.
\item When the lightest Higgs scalar is relatively heavy the masses 
of the charged, CP--odd and heaviest CP--even Higgs states are almost 
degenerate and very large
\[
m_{H^{\pm}}\simeq m_A\simeq m_{H}\gtrsim 1\,\mbox{TeV}\,.
\]
\item The possible manifestations of the considered model at the LHC are
enhanced production of $l^{+}l^{-}$, $t\bar{t}$ or $b\bar{b}$ pairs coming from either
$Z'$ boson or exotic particle decays.
\item The discovery at future colliders of the exotic particles and extra $Z'$ boson 
predicted by the ESSM would provide circumstantial evidence for superstring theory.
%would provide circumstantial evidence for 
%$E_6$ gauge structure at high energies and superstring theory.
%represent a possible indirect signature of an underlying 
%$E_6$ gauge structure at high energies providing a window into string theory.
}
\end{itemize}
\end{slide}




\end{document}




























