Precision measurements, extra generations and heavy neutrino
V.A.~Ilyin
The existence of extra chiral generations with all fermions heavier than $M_Z$ is strongly disfavored by the precision electroweak data. The exclusion of one additional generation of heavy fermions in SUSY extension of Standard Model is less forbidden if chargino and neutralino have low degenerate masses with $\Delta m \simeq 1$ GeV. However the data are fitted nicely even by a few extra generations, if one allows neutral leptons to have masses close to $50$ GeV. Such heavy neutrino can be searched in the reaction $e^+ e^- \to N\bar{N}\gamma$ at LEP-200 with total final luminosity of $2600 pb^{-1}$.
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\begin{document}
\input def.tex

\title{Precision measurements, extra generations and heavy neutrino }

%\author{V.A.~Ilyin}
%\address{
%SINP Moscow State Univ., Moscow, Russia}
%\author{M.~Maltoni}
%\address{ Instituto de F\'{\i}sica Corpuscular~--~C.S.I.C.,
%Universitat de Val\`encia, Valencia, Spain} 
%\author{V.A.~Novikov, L.B.~Okun and M.I.~Vysotsky}
%\address{ITEP, Moscow, Russia}
%\author{A.N.~Rozanov}
%\address{ITEP and CPPM, IN2P3-CNRS, Univ. M\'editerran\'ee,
%Marseilles, France\\
%Presented by A.Rozanov, E-mail: rozanov@cppm.in2p3.fr}
\author{V.A.~Ilyin$^1$, M.~Maltoni$^2$, V.A.~Novikov$^3$, L.B.~Okun$^3$,
 A.N.~Rozanov$^{3,4}$  and M.I.~Vysotsky$^3$  }
\address{
$^1$  SINP Moscow State Univ., Moscow, Russia\\
$^2$  Instituto de F\'{\i}sica Corpuscular~--~C.S.I.C.,
Universitat de Val\`encia, Valencia, Spain\\ 
$^3$  ITEP, Moscow, Russia\\
$^4$  CPPM, IN2P3-CNRS, Univ. M\'editerran\'ee,
Marseilles, France\\
Presented by A.Rozanov, E-mail: rozanov@cppm.in2p3.fr 
%{\bf 11.09.2000 Version 2.1}
}


\twocolumn[\maketitle\abstract{
The existence of extra chiral generations with all 
fermions heavier than $M_Z$
is strongly disfavored by the precision
electroweak data.
The exclusion of
one additional generation of heavy fermions in SUSY extension of Standard
Model is less forbidden
if chargino and
neutralino have low degenerate  masses with  $\Delta m \simeq 1$ GeV.
 However the data are fitted nicely even by a few extra
generations, if one allows neutral leptons to have masses close
to $50$ GeV. Such heavy neutrino can be searched in the reaction
$e^+ e^- \to N\bar{N}\gamma$ at LEP-200 with total final luminosity
of $2600 pb^{-1}$.
}]


\section{Introduction}\label{sec:intr}%1


 The straightforward generalization of the
Standard Model (SM) through inclusion of extra chiral generation(s) of
heavy fermions, quarks ($q=U,D$)  and leptons ($l=N,E$), is an example of
New Physics at high  energies
which does not decouple at ``low"
($\sim m_{Z}$) energies.
New particles contribute to physical observables through
self-energies  of vector and axial currents.
This gives 
corrections \cite{fourgen}
$\delta V_i$
to the functions $V_i (i=A,R,m)$ which determine  \cite{2}
the values of physical
observables (axial coupling $g_A$, the ratio $R=g_V/g_A$, and the ratio
$m_W/m_Z$).

 We consider the case of several lepton and quarks $SU(2)_L$ doublets and their
right-handed singlet
companions: $(UD)_L$, $U_R$, $D_R$, $(NE)_L$, $N_R$, $E_R$.
In what follows we will assume that the mixing among new generations and
the three existing ones is small, hence new fermions contribute only to
oblique corrections (vector boson self energies).


\section{LEPTOP fit to experimental data}\label{sec:LEPTOP}%2

We compare theoretical predictions for the case of
the presence of extra generations with
experimental data \cite{EWWG}
with the help of the code LEPTOP \cite{9XX}.
These experimental data are the latest updates presented at this conference
and they are well fitted by Standard Model.
We perform the four parameter ($m_t, m_H, \alpha_s, \bar{\alpha} $) fit
\footnote{The mass of Z-boson in the fit  was fixed to the latest experimental 
value $M_Z =  91.1875(21)$ GeV}
to
18 experimental observables.

\begin{table}[t]%1
\caption{LEPTOP fit of the precision observables.}\label{tab:observables}
\begin{tabular}{|l|l|l|r|}
\hline
Observ. & Exper.  & LEPTOP & Pull \\
           &  data   & fit    &      \\
\hline
%a) LEP-I & & & \\
%shape of $Z$-peak and & & & \\
%lepton asymmetries: & & & \\
%$M_Z$ {\tiny[GeV]} &   91.1875(21) &   &   \\
$\Gamma_Z$ {\tiny[GeV]} &    2.4952(23) &  2.4964(16)  & -0.5   \\
$\sigma_h$ [nb] &   41.541(37)& 41.479(15)  & 1.7    \\
$R_l$ &   20.767(25)& 20.739(18)  & 1.1   \\
$A_{FB}^l$ & 0.0171(10)  &  0.0164(3)  & 0.7   \\
%$\tau$-polarization: & & & \\
$A_{\tau}$ & 0.1439(42) &  0.1480(13)  & -1.0   \\
$A_e$ &  0.1498(48) &  0.1480(13) & 0.4  \\
%results for heavy quarks: & & & \\
$R_b$ &    0.2165(7) &   0.2157(1)  & 1.2   \\
$R_c$    &    0.1709(34)&   0.1723(1)  & -0.4   \\
$A_{FB}^b$  &    0.0990(20)&   0.1038(9)  & -2.4   \\
$A_{FB}^c$  &    0.0689(35)&   0.0742(7)  & -1.5   \\
%charge asymmetry for pairs of  & & & \\
%light quarks $q\bar{q}$: & & & \\
$s_l^2$ {\tiny $(Q_{FB})$}   &    0.2321(10)  &   0.2314(2)  & 0.7   \\
\hline
%b) SLC & & & \\
$s_l^2$ {\tiny ($A_{LR}$)} & {\it 0.2310(3)}&  {\it  0.2314(2)}  & -1.5   \\
%$A_{LR}$   & 0.1504(23)  &   0.1467(16)  & 1.6   \\
%$R_b$$^{**}$ &    0.2166(7)  &   0.2158(2)  & 0.9   \\
%$R_c$$^{**}$ &  0.1735(44) & 0.1723(1)  & 0.3 \\
$A_b$ &  0.911(25) &  0.9349(1)  & -1.0   \\
$A_c$ &  0.630(26)&   0.6683(6)  & -1.5   \\
\hline
%c) $p\bar{p} +$ LEP-II $+ \nu N$ & & & \\
$m_W$ {\tiny [GeV]} & 80.434(37) & 80.397(23)  & 1.0   \\
% & {\it 0.2228(13)}  &    &    \\
$s_W^2$ {\tiny  ($\nu N$)} & 0.2255(21)& 0.2231(2) & 1.1 \\
%  & {\it 80.255(109)} &   &  \\
\hline
$m_t$ {\tiny [GeV]}    & 174.3(5.1) &   { 174.0(4.2)} & 0.1\\
$m_H$ {\tiny [GeV]}    &   &  { $55^{+45}_{-26} $} &  \\
$\hat{\alpha}_s$ &           &  0.1183(27) &  \\
%$\bar{\alpha}^{-1}$ & 128.878(90)           & 128.849(85) & 0.3  \\
$\bar{\alpha}^{-1}$ & 128.88(9)           & 128.85(9) & 0.3  \\
{\small $\chi^2/n_{dof}$} & & 21.4/14 & \\
\hline
\end{tabular}
\end{table}
 
The fitted parameters
\footnote{ During this conference the new results on the electron-positron
  annihilation into hadrons in the range $\sqrt{s}=2-5$ GeV from BES \cite{BES}
  were released. With $\bar{\alpha}^{-1}=128.945(60)$ \cite{bolek}
  recalculated using these new BES results, we get from LEPTOP fit slighly
  higher prediction for the higgs mass
  $m_H =     78^{+53}_{-32}$ GeV,
  $m_t =     174.1(4.5)$ GeV,
  $\alpha_s =     0.1182(27)$,
  $\bar{\alpha}^{-1}=128.927(58)$ and 
  $\chi^2 / ndf =21.1/14 $.
}
together with the values of the predicted observables and their pulls
from the experimental data are given in the Table~\ref{tab:observables}.
Only the experimental value of the forward-backward assymetry in the 
Z decay into the pair of b-quarks $A_{FB}^b$ shows a hint for disagreement
with Standard Model.
 We take $m_D = 130$ GeV --
the lowest value allowed for the new quark mass from Tevatron search
\cite{13}  and take $m_U \ga m_D$.
As for the leptons from the extra generations, their masses are independent
parameters. To simplify the analyses we start with
 $m_N = m_U$, $m_E = m_D$.
Any value of higgs mass above $113.3$ GeV 
is allowed
\cite{higgs113} 
 in our fits, however
$\chi^2$ appears to be minimal for $m_H=113$ GeV.

\begin{figure}%1
\epsfxsize190pt
\figurebox{120pt}{190pt}{n4m4c_mh-113md4130.eps}
\caption{
 Constraints on the number of extra generations $N_g$ and the mass
   difference in the extra generations $\Delta m$.
   The lowest allowed value  $m_D=130$ GeV from Tevatron search
% \cite{13}
   was used and $m_E=m_D$, $m_N=m_U$ was assumed.
%   All electroweak precision data and $m_H > 113.3$ GeV
%   at 95 \% C.L.
% \cite{higgs113}
%  were used in the fit.
% The cross corresponds to
%   $\chi^2$ minimum; regions show  $< 1\sigma$,
% $< 2\sigma$, etc. allowed domains.
}
\label{fig:mEmD}
\end{figure}

  In Figure \ref{fig:mEmD} the excluded
domains in coordinates ($N_g$, $\Delta m$) are shown 
(here $\Delta m = (m_U^2 - m_D^2)^{1/2}$).  Minimum
  of $\chi^2$ corresponds to $N_g =0.1$.  We see that one extra generation
corresponds to $2\sigma$ approximately.

% The behavior of division lines in
%Fig.~\ref{fig:mEmD} can be understood qualitatively.
%  For degenerate extra generations the
%corrections $\Delta V_i$ are negative.  They become positive and large when
%$\Delta m$ increases. That is why at large $\Delta m$ division lines approach
%$N_g=0$ value. In the intermediate region ($\Delta m \approx 125$ GeV)
%$\Delta V_i$ cross zero and this explains the turn to the right of the
%division lines. However, for different $i$ zero is reached for different
%$\Delta m$ values, that is why extra generations are excluded even for
%$\Delta m \approx 125$ GeV.
%% (see \cite{3}).


We checked that similar bounds are valid for the general choice of heavy
masses of leptons and quarks. In particular we found that for 
 $m_N = m_D = 130$ GeV and $m_E = m_U$ one extra generation is excluded
at 1.5 $\sigma$ level, while for  $m_E = m_U = 130$ GeV and $m_N = m_D$
the limits are even stronger than in Fig.~\ref{fig:mEmD}.
So the extra generations are excluded by 
the electroweak precision data, if all
extra fermions are heavy: $m \ga m_Z$. 


%The interesting question is:''Could we find the extensions of the
%Standard Model, which will hide the corrections induced by extra
% generations ?'' In the following we will consider two such cases:
% SUSY extensions  and 50 GeV heavy neutrino. 


\section{Extra generations in case of SUSY}\label{sec:SUSY}%3

%We investigated bounds on extra generations which occur in SUSY
%extensions.
 When SUSY particles are heavy they decouple
% (i.e.  their
%contributions to electroweak observables become power suppressed)
 and the
same standard model exclusion plots shown in Fig.~\ref{fig:mEmD}  are valid.
One possible exception is a contribution of the third
generation squark doublet, enhanced by large stop-sbottom splitting. In this
way we get noticeable positive contributions to functions $V_i$  \cite{36,5},
which may help to compensate negative contributions of degenerate extra
generations.
\begin{figure}%2
\epsfxsize190pt
\figurebox{120pt}{190pt}{n4msbc_mh120md4130.eps}
\caption{
The 2-dimensional exclusion plot for the $N_g$
degenerate extra generations and the mass of sbottom $m_{\tilde{b}}$
in SUSY models and for the choice
  $m_D = m_U = m_E = m_N = 130$ GeV,
using $m_h =120 $ GeV, $m_{\tilde{g}} = 200$ GeV and assuming the absence
of $\tilde {t}_L - \tilde {t}_R$ mixing.
% Little cross corresponds to $\chi^2$ minimum; regions show  $< 1\sigma$,
% $< 2\sigma$, etc. allowed domains.
}
\label{fig:msb}
\end{figure}
 We analyze the simplest case of the absence of $\tilde {t}_L
-\tilde {t}_R $ mixing in Fig.~\ref{fig:msb}.  In this figure the case of degenerate extra
generations with common mass $130$ GeV is considered (contributions of
superpartners of new generations to $V_i$ are negligible since new up- and
down- particles are degenerate).  Exclusion plot is presented in coordinates
$(N_{g}, m_{sbottom})$.  We see that with inclusion of SUSY new
heavy generations are also disfavoured.

 Situation changes in case of light chargino and
neutralino. The latter are still not excluded - dedicated search at LEP II
still allows the existence of such  particles with masses as
low as 68 GeV 
(gaugino region with light sneutrino) \cite{charginoL3}
or 77 GeV 
(higgsino case) \cite{charginoDELPHI}
 if their mass difference is $\approx 1$ GeV.
Analytical formulas for corrections to the functions $V_i$ from
quasi degenerate chargino and neutralino were derived and analyzed in
\cite{14XX}. Corrections are big and this allows one to get lower bounds on
masses of chargino and neutralino:  $m_{\chi}>54$ GeV for the case of higgsino
domination and $m_{\chi}>61$ GeV for the case of wino domination at $95\%$
CL.

\begin{figure}%3
\epsfxsize190pt
\figurebox{120pt}{190pt}{n4c_higgsino_chargino80_small.eps}
\caption{
 Constraints on the number of extra generations $N_g$ and the mass
   difference in the extra generations $\Delta m$
in case of $80$ GeV
higgsino-dominated  quasi degenerate chargino and neutralino.
   The lowest allowed value  $m_D=130$ GeV from Tevatron search
% \cite{13}
   was used and $m_E=m_D$, $m_N=m_U$ was assumed.
%   All electroweak precision data and $m_h > 113.3$ GeV
%   at 95 \% C.L.
% \cite{higgs113}
%  were used in the fit.
%    The cross corresponds to $\chi^2$ minimum; regions show  $< 1\sigma$,
% $< 2\sigma$, etc. allowed domains.
}
\label{fig:degenerate}
\end{figure}

 Fig.~\ref{fig:degenerate} demonstrates how presence of chargino-neutralino pair (dominated
by higgsino) with mass $80$ GeV slightly relaxes the bounds shown on Fig.~\ref{fig:mEmD}. 
 We see that one
extra generation of heavy fermions is allowed within $1.5 \sigma$ domain
in case of the light chargino.


\section{Heavy neutrino with $m_N < m_Z$}\label{sec:heavy}%4

For particles with masses of the order of $m_Z/2$ oblique corrections
drastically differ from what we have for masses $\ga m_Z$. In particular,
renormalization of $Z$-boson wave function produces large negative
contribution to $V_A$.
 Quasi-stable neutral lepton $N$ should have the mass slightly above
 $m_Z/2$ to avoid increasing the invisible $Z$-width and it
should have the mixing angle with three known generations smaller
than $10^{-6}$ to avoid desintegration in the detector.
We consider new heavy neutrino  with Dirac mass and
we suppose that the Majorana mass of $N_R$ is negligible.
% closing eyes
%on the emerging (un)naturalness problem. Thus, our neutral lepton $N$
%is a heavy Dirac particle.
 From the analysis of the initial set of precision data
in papers \cite{2X,3X} it was found that
the existence of additional light fermions with masses $\approx 50$ GeV is
allowed.  Now analyzing all precision data
and using bounds from direct searches we conclude, that the only  presently
allowed light fermion is neutral lepton $N$.

\begin{figure}%4
\epsfxsize190pt
\figurebox{120pt}{190pt}{n4mn4c_mh0md4200.eps}
\caption{
Constraints on the number of extra generations $N_g$ and the mass
   of the neutral heavy lepton $m_N$.
   The values  $m_U=220$ GeV, $m_D=200$ GeV, $M_E=100$ GeV
   were used.
% All electroweak precision data and $m_H > 113.3$ GeV
%   at 95 \% C.L. from LEP II 
%  \cite{higgs113}
% were used in the fit.
%    The cross corresponds to $\chi^2$ minimum; regions show  $< 1\sigma$,
%$< 2\sigma$, etc. allowed domains.
%The lower bound on $m_N$ from LEP I data ($m_N=45GeV$)
% \cite{1X}
%corresponds to the lowest point on the y axis $m_Z/2$.
}
\label{fig:mN}
\end{figure}

  As an example we take $m_U =
220$ GeV, $m_D = 200$ GeV, $m_E = 100$ GeV and draw exclusion plot in
coordinates ($m_N, N_g$), see Fig.~\ref{fig:mN}.
  From this  plot it is clear that for the case of fourth
generation with $m_N \approx 50$ GeV description of the data is not worse
than for the Standard Model and that even two new generations with $m_{N_1}
\approx m_{N_2} \approx 50$ GeV are allowed within $1.5 \sigma$.

\section{Possibility for the direct search of the 50 GeV heavy neutrino}\label{sec:search}%5


The direct search of the heavy neutrino is possible in
$e^+e^-$-annihilation into a pair of heavy neutrinos with the emission
of initial state bremsstrahlung photon
\begin{equation}
e^+ e^- \to \gamma + \; \mbox{\rm N} \bar{\mbox{\rm N}}
\label{eq:1}
\end{equation}
The main background is the production of the pairs of conventional
neutrinos with initial state bremsstrahlung photon
\begin{equation}
e^+ e^- \to \gamma + \; \nu_i \bar\nu_i
\label{eq:2}
\end{equation}
where $i = e, \mu, \tau$. These background neutrinos are produced
in decays of real and virtual $Z$. In case of  $\nu_e
\bar\nu_e$, two mechanisms contribute, through $s$-channel $Z$ boson
and from $t$-channel exchange of $W$ boson.
We calculated the signal and background distributions
and rates \cite{mn50} using CompHEP \cite{comphep} computer code.

\begin{figure}%5
\epsfxsize210pt
\figurebox{120pt}{210pt}{minv200.eps}
\caption{
$d\sigma/d M_{inv}$ (in pb) for 
Standard Model and for the different values of $m_N$.
%Cuts applied: $|\cos\vartheta_\gamma|<0.95$ and $p_T^\gamma>0.0375\sqrt{s}$. 
%The photon detection efficiency 74\% is assumed.
}
\label{fig:minv200}
\end{figure}

In Fig.~\ref{fig:minv200} the distribution on
``invisible" mass $M_{inv}$ (invariant mass of the neutrino 
pair)
%\footnote{$M_{inv}$ is directly connected with another variable
%frequently used, $x_\gamma\equiv E_\gamma/E_{beam}=1-M_{inv}^2/s$.}
is represented for SM background and the $N\bar N$ signal for $\sqrt{s}=200$
GeV and different values of $N$ masses, $M_N=46-100$ GeV. Here we applied
kinematical cuts on the photon polar angle and transverse momentum,
$|\cos\vartheta_\gamma|<0.95$ and $p_T^\gamma>0.0375\sqrt{s}$, being the
ALEPH selection criteria \cite{ALEPH}.
The photon detection efficiency 74\% is assumed.
For highest significance of the $N\bar N$ signal, evaluated as
$N_S/\sqrt{N_B}$, one should include whole interval on $M_{inv}$ allowed
kinematically, so we applied  $M_{inv}>2m_N$ cut.

\begin{figure}%6
\epsfxsize210pt
\figurebox{120pt}{210pt}{sign-mn200.eps}
\caption{
$N\bar N$ signal significances at LEP-2 at different statistics
as function of the neutrino mass. 
%Cuts applied: $M_{inv}>2m_N$, $|\cos\vartheta_\gamma|<0.95$ and
%$p_T^\gamma>0.0375\sqrt{s}$.
%For the significance the photon detection efficiency 74\% is assumed.
}
\label{fig:s-mN}
\end{figure}

On Fig.~\ref{fig:s-mN} the signal
significances
% (for different samples of data)
 are represented as a function
of $m_N$. One can derive that only the analysis based on combined data from
all four experiments both from 1997-1999 runs ($\sqrt{s}=182-202$ GeV) and
from the current run, in total $\sim 2600$ pb$^{-1}$, can exclude at 95\%
CL the interval of $N$ mass up to $\sim 50$ GeV.

Another possibility is to search for 50 GeV neutrino at the future
TESLA $e^+ - e^-$ electron-positron linear collider.
The increase in energy
leads to the decrease both of the signal and the background,
but it is 
compensated by the proposed increase of
luminosity
% of the future linear $e^+ e^-$-collider. Thus for TESLA the
%expected year luminosity at the first stage ($\sqrt{s}=360$ or 500 GeV) is
of 300 ${\rm fb}^{-1}$/year \cite{TESLA}.
Further advantage of the linear collider is the possibility to use
polarized beams.
 This is important in suppressing the cross section of $e^+ e^-
\to \nu_e\bar{\nu}_e\gamma$ as this reaction goes mainly through the
$t$-channel exchange of the $W$ boson.
% and gives substantial contribution to
%the background\footnote{For ``light" neutrinos $45 \; {\rm GeV} < M_N < 50$
%GeV the ratio of $s$ channel to $t$ channel contributions is enhanced at
%the shoulder of $Z$-peak.}.
 However, even without exploiting the beam
polarization the advantage of TESLA in the total number of events is
extremely important. Thus, Standard Model is expected to give approximately
0.3 million single photon events for $M_{inv}>100$ GeV while the number of
50 GeV neutrino pairs would be about 4000. 
%\begin{figure}%7
%\epsfxsize190pt
%\figurebox{120pt}{190pt}{sign-mn360.eps}
%\caption{
%$N\bar N$ signal significances at TESLA at different statistics
%as function of the neutrino mass. 
%}
%\label{fig:s-mN360}
%\end{figure}
%
% On Fig.~\ref{fig:s-mN360}
% the significance of TESLA experiment
%is represented as a function of $N$ mass. Here we applied cuts
%$|\cos\vartheta_\gamma|<0.95$, $p_T^\gamma>0.0375\sqrt{s}$ and
%$M_{inv}>2m_N$, and assumed photon detection efficiency to be 74\%,
%similarly to the LEP II case.
Although the signal over background ratio is still small
(2.3-0.5\% for $m_N=45-100$ GeV correspondingly) the significance of the
signal is excellent, higher than 5 standard deviations for $m_N<60$ GeV.


% the whole interval of N neutrino
%mass under discussion. It means that fourth generation Dirac neutrino will
%be excluded at the 95\% CL in TESLA experiment. However, if such a neutrino
%exists this new particle will be discovered with $5\sigma$ significance
%after one year of the TESLA operation at first stage if $m_N<60$ GeV.

%\section*{Acknowledgments}
%This is where one places acknowledgments for funding bodies etc.
%Note that there are no section numbers for the Acknowledgments and
%Appendix. The style file will automatically generate the heading 
%for references.
%\begin{appendix}
%\section*{Appendix}
%We can insert an appendix here and place equations so that they are
%given numbers such as Eq.~(\ref{eq:app}). 
%\begin{equation}
%x = y.
%\label{eq:app}
%\end{equation}
%\end{appendix}

\begin{thebibliography}{99}

\bibitem{fourgen}
M.~Maltoni, V.~Novikov, L.~Okun et al., {\it Phys. Lett.}
B {\bf 476}, 107 (2000).

\bibitem{2}
V.A.Novikov, L.B.Okun, A.N.Rozanov et al., {\it Rep. Prog. Phys.} {\bf 62},
1275 (1999).

% \bibitem{1X}
% L3, M.Acciarri et al., {\it Phys. Lett.} B {\bf 431}, 199 (1998); \\
% DELPHI, P.Abreu et al.,{\it Phys. Lett.} B {\bf 274}, 230 (1992);
%                       {\it Z.Phys.} C {\bf 74}, 577 (1997); \\
% OPAL, R.Akers et al., {\it Z. Phys.} {\bf C65}, 47 (1995); \\
% ALEPH, D.Buskulic et al., {\it Phys. Lett.} B {\bf 313}, 520 (1993).
% 
%
%\bibitem{34}
%T.Inami et al., {\it Mod. Phys. Lett.} A {\bf 10}, 1471 (1995).
%
%\bibitem{35}
%A. Masiero et al., {\it Phys. Lett.} B {\bf 355}, 329 (1995).
%
%\bibitem{3}
%V.A.Novikov, L.B.Okun, A.N.Rozanov et al.,
%{\it Mod. Phys. Lett.} A {\bf 10},  1915 (1995); 
%Erratum - ibid. A {\bf 11}, 687 (1996).
%
%\bibitem{33}
%J.Erler and P.Langacker, Review of Particle Physics,
% {\it The European Physical Journal} C {\bf 3}, 91, Chapter 10.6 (1998.
%
%\bibitem{111}
%M.Peskin and T.Takeuchi, {\it Phys. Rev. Lett.} {\bf 65}, 964 (1990);
%{\it  Phys. Rev.} D {\bf 46}, 381 (1992).%
%
%\bibitem{EWWG}
%LEP EWWG and SLD HFEWG, CERN-EP/99-15, 8 Febr. 1999.

\bibitem{EWWG}
\noindent{\sf EWWG, lepewwg.web.cern.ch/LEPEWW G/plots/summer2000;
A.Straessner, Moriond-2000.}

\bibitem{9XX}
V.Novikov et al., Preprint ITEP 19-95; Preprint CPPM -1-95;
\noindent {\sf cppm.in2p3.fr./leptop/intro$\_$leptop.html}

\bibitem{BES} Zhengguo Zhao, these proceedings

\bibitem{bolek}
Bolek Pietrzyk, these proceedings.

\bibitem{13} From charged current decays $m_D > 128$ GeV,  
PDG, D.E. Groom et al 
 {\it The European Physical Journal} C {\bf 15}, (2000).

\bibitem{higgs113} Kara Hoffman,, these proceedings

%\bibitem{6X} K.Ackerstaff et al., (OPAL),{\it Europ. Phys. J.}
%C {\bf 1}, 45 (1998).
%
%\bibitem{11X} A.Dolgov, L.Okun and V.Zakharov, {\it Nucl. Phys.}
%B {\bf 41}, 197 (1972).
%
%\bibitem{10X} 
%a) DELPHI Collaboration, Photon Events with Missing Energy at LEP-2,
%HEP99-6-141, contribution to HEP-99 Conference, Tampere, Finland; \\
%
%b) ALEPH collaboration, Single and multi-photon production in 
%$e^+e^-$ collisions at a centre-of-mass energy of 188.6 GeV,
%HEP99-6-429, contribution to HEP-99 Conference, Tampere, Finland.

\bibitem{36}
I.V.Gaidaenko et al., {\it JETP Lett.}  {\bf 67}, 761 (1998).

\bibitem{5}
I.V.Gaidaenko et al., {\it Phys. Rep.} {\bf 320}, 119 (1999.

\bibitem{charginoL3} L3 note 2583, paper contributed to this conference.

\bibitem{charginoDELPHI} DELPHI 2000-081, CONF 380, paper contributed to
    this conference.

%\bibitem{14X} P.Abreu et al., (DELPHI), CERN - EP/99 - 037 (1999).

\bibitem{14XX} M.Maltoni and M.I.Vysotsky, {\it Phys. Lett.}
 B {\bf 463}, 230 (1999).

%\bibitem{lep2}
%Limits on Higgs boson masses from combining the data of the four LEP
%experiments at $\sqrt{s} < 183$ GeV,
%ALEPH, DELPHI, L3 and OPAL Collaborations,
%Preprint CERN-EP-99-060 (1999)

\bibitem{2X}
 N.Evans, {\it Phys. Lett.} B {\bf 340}, 81 (1994).

\bibitem{3X}
P.Bamert and C.P.Burgess, {\it Z. Phys.} C {\bf 66}, 495 (1995).%%%%

\bibitem{mn50}
V.~Ilyin, M.~Maltoni, V.~Novikov et al., hep-ph/0006324.

\bibitem{comphep}
A.Pukhov et al, CompHEP user's manual v.3.3, Preprint INP MSU
98-41/542 (1998); hep-ph/9908288.

\bibitem{ALEPH}
%  "ALEPH Collaboration, Single- and Multi-Photon Production in $e^+e^-$
%  Collisions at Centre-of-Mass Energies between 188.6 and 201.6 GeV,
%  ALEPH 2000-008, CONF 2000-005, contribution
%  to Moriond Conference, March 2000, France".
%
%  "ALEPH Collaboration, Single- and Multi-Photon Production in $e^+e^-$
%  Collisions at a Centre-of-Mass Energy of 183 GeV",
ALEPH Coll.,  Phys. Lett. {\bf B429} (1998) 201.


\bibitem{TESLA}
\noindent {\sf www.desy.de/njwalker/ecfa-desy-wg4/ parameter\_list.html}

\end{thebibliography}

 
\end{document}


%%%%%%%%%%%%%% End of osaka.tex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%















hep-ph0009167.extracted_bib
\begin{thebibliography}{99}

\bibitem{fourgen}
M.~Maltoni, V.~Novikov, L.~Okun et al., {\it Phys. Lett.}
B {\bf 476}, 107 (2000).

\bibitem{2}
V.A.Novikov, L.B.Okun, A.N.Rozanov et al., {\it Rep. Prog. Phys.} {\bf 62},
1275 (1999).

% \bibitem{1X}
% L3, M.Acciarri et al., {\it Phys. Lett.} B {\bf 431}, 199 (1998); \\
% DELPHI, P.Abreu et al.,{\it Phys. Lett.} B {\bf 274}, 230 (1992);
%                       {\it Z.Phys.} C {\bf 74}, 577 (1997); \\
% OPAL, R.Akers et al., {\it Z. Phys.} {\bf C65}, 47 (1995); \\
% ALEPH, D.Buskulic et al., {\it Phys. Lett.} B {\bf 313}, 520 (1993).
% 
%
%\bibitem{34}
%T.Inami et al., {\it Mod. Phys. Lett.} A {\bf 10}, 1471 (1995).
%
%\bibitem{35}
%A. Masiero et al., {\it Phys. Lett.} B {\bf 355}, 329 (1995).
%
%\bibitem{3}
%V.A.Novikov, L.B.Okun, A.N.Rozanov et al.,
%{\it Mod. Phys. Lett.} A {\bf 10},  1915 (1995); 
%Erratum - ibid. A {\bf 11}, 687 (1996).
%
%\bibitem{33}
%J.Erler and P.Langacker, Review of Particle Physics,
% {\it The European Physical Journal} C {\bf 3}, 91, Chapter 10.6 (1998.
%
%\bibitem{111}
%M.Peskin and T.Takeuchi, {\it Phys. Rev. Lett.} {\bf 65}, 964 (1990);
%{\it  Phys. Rev.} D {\bf 46}, 381 (1992).%
%
%\bibitem{EWWG}
%LEP EWWG and SLD HFEWG, CERN-EP/99-15, 8 Febr. 1999.

\bibitem{EWWG}
\noindent{\sf EWWG, lepewwg.web.cern.ch/LEPEWW G/plots/summer2000;
A.Straessner, Moriond-2000.}

\bibitem{9XX}
V.Novikov et al., Preprint ITEP 19-95; Preprint CPPM -1-95;
\noindent {\sf cppm.in2p3.fr./leptop/intro$\_$leptop.html}

\bibitem{BES} Zhengguo Zhao, these proceedings

\bibitem{bolek}
Bolek Pietrzyk, these proceedings.

\bibitem{13} From charged current decays $m_D > 128$ GeV,  
PDG, D.E. Groom et al 
 {\it The European Physical Journal} C {\bf 15}, (2000).

\bibitem{higgs113} Kara Hoffman,, these proceedings

%\bibitem{6X} K.Ackerstaff et al., (OPAL),{\it Europ. Phys. J.}
%C {\bf 1}, 45 (1998).
%
%\bibitem{11X} A.Dolgov, L.Okun and V.Zakharov, {\it Nucl. Phys.}
%B {\bf 41}, 197 (1972).
%
%\bibitem{10X} 
%a) DELPHI Collaboration, Photon Events with Missing Energy at LEP-2,
%HEP99-6-141, contribution to HEP-99 Conference, Tampere, Finland; \\
%
%b) ALEPH collaboration, Single and multi-photon production in 
%$e^+e^-$ collisions at a centre-of-mass energy of 188.6 GeV,
%HEP99-6-429, contribution to HEP-99 Conference, Tampere, Finland.

\bibitem{36}
I.V.Gaidaenko et al., {\it JETP Lett.}  {\bf 67}, 761 (1998).

\bibitem{5}
I.V.Gaidaenko et al., {\it Phys. Rep.} {\bf 320}, 119 (1999.

\bibitem{charginoL3} L3 note 2583, paper contributed to this conference.

\bibitem{charginoDELPHI} DELPHI 2000-081, CONF 380, paper contributed to
    this conference.

%\bibitem{14X} P.Abreu et al., (DELPHI), CERN - EP/99 - 037 (1999).

\bibitem{14XX} M.Maltoni and M.I.Vysotsky, {\it Phys. Lett.}
 B {\bf 463}, 230 (1999).

%\bibitem{lep2}
%Limits on Higgs boson masses from combining the data of the four LEP
%experiments at $\sqrt{s} < 183$ GeV,
%ALEPH, DELPHI, L3 and OPAL Collaborations,
%Preprint CERN-EP-99-060 (1999)

\bibitem{2X}
 N.Evans, {\it Phys. Lett.} B {\bf 340}, 81 (1994).

\bibitem{3X}
P.Bamert and C.P.Burgess, {\it Z. Phys.} C {\bf 66}, 495 (1995).%%%%

\bibitem{mn50}
V.~Ilyin, M.~Maltoni, V.~Novikov et al., hep-ph/0006324.

\bibitem{comphep}
A.Pukhov et al, CompHEP user's manual v.3.3, Preprint INP MSU
98-41/542 (1998); hep-ph/9908288.

\bibitem{ALEPH}
%  "ALEPH Collaboration, Single- and Multi-Photon Production in $e^+e^-$
%  Collisions at Centre-of-Mass Energies between 188.6 and 201.6 GeV,
%  ALEPH 2000-008, CONF 2000-005, contribution
%  to Moriond Conference, March 2000, France".
%
%  "ALEPH Collaboration, Single- and Multi-Photon Production in $e^+e^-$
%  Collisions at a Centre-of-Mass Energy of 183 GeV",
ALEPH Coll.,  Phys. Lett. {\bf B429} (1998) 201.


\bibitem{TESLA}
\noindent {\sf www.desy.de/njwalker/ecfa-desy-wg4/ parameter\_list.html}

\end{thebibliography}