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{\hfill {\rm International Workshop on Linear Colliders} \hfill}
{\hfill {\rm LCWS(2002), Jeju, Korea} \hfill}
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% Special definitions for this contribution

\def\gg{$\gamma \gamma$}
\def\wgg{$W_{\gamma \gamma}$}
\def\ggg{$\Gamma_{\gamma \gamma}$}
\def\gggsm{$\Gamma_{\gamma \gamma}^{SM}$}
\def\pgg{$\phi_{\gamma \gamma}$}
\def\pggsm{$\phi_{\gamma \gamma}^{SM}$}
\def\epem{$e^+ e^-$}

\def\z0{Z}

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\begin{document}
% \setcounter{page}{135}

\title{TWO-PHOTON WIDTH AND  PHASE MEASUREMENT FROM  
       THE SM HIGGS DECAYS INTO $WW$ AND $ZZ$   
            AT THE PHOTON COLLIDER} 

\author{P. NIE\.ZURAWSKI$^1$,
        A.F. \.ZARNECKI$^1$
        and  M. KRAWCZYK$^{2,3}$
\\
\\
    $^1$ {\it Institute of Experimental Physics, Warsaw University, Poland}
\\
    $^2$ {\it Theory Division, CERN, Switzerland}
\\
    $^3$ {\it Institute of Theoretical Physics, Warsaw University, Poland} 
}

\date{}

\maketitle

\begin{abstract}
Production of the Standard Model Higgs-boson at the photon collider at
TESLA is studied for the Higgs-boson masses above 170 GeV. 
By reconstructing $W^+ W^-$ and $\z0  \z0  $ final states,
not only the $h \rightarrow \gamma \gamma$ partial width 
but also the phase of the scattering amplitude can be measured.
 This opens a new window onto the precise
determination of the Higgs-boson couplings.
\end{abstract}

%***********************************************************************
% \section{Introduction}

A photon collider has been  proposed as a natural
extension of the \epem\ linear collider TESLA \cite{tdr_pc}.
%
It is the ideal place to study the properties of the Higgs-boson
and the electroweak symmetry breaking (EWSB).
%
This contribution summarizes results of \cite{wwzz_paper},
where the feasibility of measuring  Higgs-boson production
in $W^+ W^-$ and $\z0 \z0$ decay channels has been studied
for Higgs-boson mass above 170~GeV.

%***********************************************************************
% \section{Vector boson production}

We study the signal, ie. the Higgs-boson decays into vector bosons,
and the background from direct vector-bosons production.
%
For the $\z0  \z0 $ final state the direct, ie. non-resonant 
$\gamma \gamma \rightarrow \z0 \z0$ process is possible 
at the loop level only, while the non-resonant $W^+W^-$ pair 
production is a tree-level process, and is expected to be large.
%
Also an interference between the signal of $W^+W^-$ production 
via the Higgs resonance and the background from direct production
can be large.
%
The measurement of the interference contribution
allows us to access an information about the phase of
the $h \rightarrow \gamma \gamma $ amplitude, \pgg.
%
For the Higgs-boson masses around 350 GeV, we found that
the amplitude phase \pgg\ is more sensitive 
to the loop contributions of new,
heavy charged particles than  the \ggg\ itself.


%***********************************************************************
% \section{Analysis}

The analysis is based on the CompAZ parametrization \cite{compaz} of
the realistic photon collider luminosity spectra.
%
Presented results correspond to one year of TESLA photon collider
running at nominal luminosity.
%
The event generation 
according  to the cross-section formula 
% for vector-boson production including the Higgs  contribution 
\cite{cros_ww,cros_zz}
was done with PYTHIA~6.152.
%
The fast simulation program SIMDET version 3.01
was used to model the TESLA detector performance.

% The invariant-mass resolution obtained from a  full simulation of $W^+ W^-$  
% and $\z0 \z0$ events based on the PYTHIA and SIMDET programs, 
% has been parametrized as a function of the \gg\ center-of-mass energy \wgg .
%
The distribution 
of the reconstructed invariant mass for 
$\gamma \gamma \rightarrow W^+ W^-$ 
 and $\gamma \gamma \rightarrow \z0  \z0 $ events
is shown in  Fig.~\ref{fig:convol}.
% 
 Results coming from the full event simulation  based  on PYTHIA
 and SIMDET  are  compared with the distribution
 obtained  by the numerical convolution of the cross-section 
 formula with the CompAZ spectra and parametrized detector resolution.
%
%
%***********************************************************************
% \section{Results}
%
Based on the parametric description of the expected mass distributions, 
a number of  experiments were simulated, each corresponding to one year
of TESLA photon collider running at the nominal luminosity.
%
The ``theoretical'' distributions were then fitted, simultaneously to
the observed $W^+ W^-$ and $\z0 \z0$ mass spectra, with the 
width \ggg\ and phase \pgg\ considered as the only free parameters.
%
Results of the fits performed for different Higgs-boson masses
and at different electron-beam energies are shown in Fig.~\ref{fig:final_5}.
%
They indicate that with a proper choice of the beam energy, the $\gamma \gamma$
partial width can be measured with an accuracy of 3 to 8\%, while
the  phase of the amplitude with an accuracy between 30 and 100~mrad,
see Fig. \ref{fig:final_5}.
%
The \pgg\ measurement opens a new window to  the precise
determination of the Higgs-boson couplings
and to  searches of ``new physics''.


\begin{thebibliography}{99}

\bibitem{tdr_pc}   
 B. Badelek et al., TESLA TDR, Part~6, Chapter~1, .

\bibitem{wwzz_paper}
   P.Nie\.zurawski, A.F.\.Zarnecki, M.Krawczyk, .

\bibitem{compaz}
   A.F.\.Zarnecki, .

\bibitem{cros_ww} 
G.Belanger, F.Boudjema,   Phys. Lett. B288 (1992) 210;
D.A.Morris, et al.,  Phys. Lett. B323 (1994) 421; 
I.F.Ginzburg, I.P.Ivanov,  Phys. Lett. B408 (1997) 325.

\bibitem{cros_zz} 
  G.J.Gounaris  et al.,  Eur. Phys. J. C13 (2000) 79. 

\bibitem{2HDM}
I.F.Ginzburg, M.Krawczyk, P.Osland,
Nucl. Instrum. Meth. A472 (2001) 149.

\end{thebibliography}

%***********************************************************************
%
% 2 plots on the last page
% 
%  convol_wwzz.eps 
\begin{figure}[p]
  \begin{center}
  \epsfig{figure=e3_zarnecki_fig1.eps,height=6cm,clip=}
  \end{center}
  \vspace{-0.5cm}
  \caption{Distribution of the reconstructed invariant mass
        for $\gamma \gamma \rightarrow W^+ W^-$ events with a 
        SM Higgs-boson mass of 180 GeV and an 
        electron-beam energy of 152.5 GeV (left plot) 
        and
        for $\gamma \gamma \rightarrow \z0  \z0 $ events, with a 
        SM Higgs-boson mass of 300 GeV and an 
        electron-beam energy of 250 GeV (right plot). 
        The distribution expected without the Higgs contribution is
        also shown (dashed line).
          }
  \label{fig:convol}
\end{figure}
%

%
%  final_gam_5.eps  + final_phi_5.eps
%
\begin{figure}[p]
  \begin{center}
  \epsfig{figure=e3_zarnecki_fig2a.eps,width=6.7cm,clip=}
  \epsfig{figure=e3_zarnecki_fig2b.eps,width=6.7cm,clip=}
  \vspace{-0.5cm}
  \end{center}
  \caption{Average statistical error in the 
           determination of the  Higgs-boson width \ggg\ (left plot)
           and phase  \pgg\ (right plot), expected
           after one year of photon collider running, from the simultaneous 
          fit to the observed $W^+ W^-$ and $ZZ$ mass spectra,
          as a function  of the Higgs-boson mass $M_h$.
          The yellow (tick light) band shows the size of 
          the deviations expected in the SM-like  2HDM~(II)~\cite{2HDM}
          with an additional contribution due to the charged
          Higgs-boson of  mass $M_{H^+}=800$ GeV. 
          }
  \label{fig:final_5}
\end{figure}
%

\end{document}



