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{\hfill {\rm International Workshop on Linear Colliders} \hfill}
{\hfill {\rm LCWS(2002), Jeju, Korea} \hfill}
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\title{ THE SM HIGGS-BOSON PRODUCTION IN~\( \gamma \gamma \rightarrow h\rightarrow b\overline{b} \) AT THE PHOTON COLLIDER AT~TESLA  
%\thanks{This work is supported in part by the BMBF--KBN collaboration program TESLA} 
} 
\author{P.\ NIE\.ZURAWSKI$^1$,
%\thanks{e-mail address: pniez@fuw.edu.pl}$\;$, 
	A.\ F.\ \.ZARNECKI$^1$
	and M.\ KRAWCZYK$^{2,3}$
\\
\\
$^1$ {\it  Institute of Experimental Physics, Warsaw University, Poland}
%                  ul. Ho\.za 69, 00-681 Warsaw, Poland}
\\
$^2$ {\it Theory Division, CERN, Switzerland }\\
%CH-1211 Geneva 23, Switzerland \\
%                                {\it and} \\
$^3$ {\it Institute of Theoretical Physics, Warsaw University, Poland }
%         ul. Ho\.za 69, 00-681 Warsaw, Poland }
}
\date{}
\maketitle
\begin{abstract}
 Measuring the \( \Gamma (h\rightarrow \gamma \gamma ){\rm {Br}}
(h\rightarrow b\overline{b}) \) decay
at the photon collider at TESLA is studied for a Standard Model 
Higgs boson of mass \( m_{h}=120 \) GeV. The main background due to the 
process \( \gamma \gamma \rightarrow Q\overline{Q}(g) \), where \( Q=b,\, c \),
is estimated  using the NLO QCD program (G.~Jikia); the results obtained 
are compared with 
the
%  corresponding 
LO estimate. Using a realistic luminosity spectrum and 
performing a detector simulation, 
%with the SIMDET program,
 we find that 
%the 
\( \Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b}) \)
%decay 
can be measured with an accuracy better than 2\%
after one year of photon collider running.
\end{abstract}

%***********************************************************************
%\section{Introduction}
%***********************************************************************
%Besides the discovery of the Higgs boson, it will be crucial
%to determine its properties  with a high accuracy.  
%in order to confirm its origin. 
A photon collider option of the TESLA
$e^+e^-$ collider \cite{TDR} offers a  unique possibility to produce
the Higgs boson as an \( s \)-channel resonance and to determine its properties  
with a high accuracy.  The neutral Higgs boson
couples to the photons  through a loop 
with  the massive charged particles,
%This $h\gamma \gamma$ coupling
thus $h\gamma \gamma$ coupling
%As a result the Higgs cross section
is sensitive to contributions of new particles.
%, which appear in various extensions of  the SM. 
%
The SM Higgs boson with a  mass below \( \sim 140\) GeV is expected
to decay mainly into the \( b\bar{b} \) final state. 
Here we consider the process \( \gamma \gamma \rightarrow h\rightarrow 
b\overline{b} \) for a Higgs-boson mass of \( m_{h}=120 \) GeV
at a photon collider at TESLA \cite{NZKBB}.
Both the signal and  background
events are generated according to a  realistic photon--photon luminosity
spectrum.
% \cite{V.Telnov}, parametrized by a CompAZ model \cite{CompAZ}. 
%Our  analysis incorporates 
A  simulation
of the detector response is incorporated as well. \smallskip
%This contribution summarizes results of \cite{NZKBB}.
%according to the program SIMDET \cite{SIMDET}.
%
%
%\section{Results}
%
%
In  the analysis we use the CompAZ parametrization \cite{CompAZ} of 
the spectrum \cite{V.Telnov} to generate  energies of the colliding photons.
%
%
For the energy of primary electrons
 \( \sqrt{s_{ee}} =  2 E_{e} \) = 210 GeV,  we obtain a
 peak of the \( J_{z} \) = 0 component 
of the photon--photon luminosity spectrum 
at the invariant mass of the two colliding photons 
\( W_{\gamma \gamma } \) equal to 120 GeV.
%the considered mass of the Higgs boson.
%
%
We assume the integrated luminosity
of the primary $e^- e^-$ beams equal to \( L_{ee}^{geom} =502 \; \rm fb^{-1} \)
%, expected for one year of the photon collider running 
\cite{V.Telnov}. \smallskip %\\*[-1.2cm]
%
%
%\section{Details of a simulation and the first results }
%
%\vspace{-0.74cm}
A generation of signal events was done with
PYTHIA 6.205 \cite{PYTHIA}, with the parameters for a Higgs boson
as in  HDECAY \cite{HDECAY}. 
A parton shower algorithm, implemented in PYTHIA,
was used to generate the final-state particles. 
%
The background events due to processes 
\( \gamma \gamma \rightarrow b\bar{b}(g),\, \, c\bar{c}(g) \)
were  generated using the program written by G.~Jikia \cite{JikiaAndSoldner},
where a complete  NLO QCD  calculation for the production of  massive
quarks is performed within the massive-quark scheme.\footnote{%
Other background contributions, from the resolved photon(s)
 interactions and the overlaying events, were found to be negligible.} 
%
For a comparison we generated also the  LO background events
%,
%using the QED Born cross section for the processes
% \( \gamma \gamma \rightarrow b\bar{b} \) and \( \gamma \gamma \rightarrow c\bar{c} \), 
% including in addition a parton shower,
 as  implemented in  PYTHIA.
%
%
The fragmentation was performed using the PYTHIA program. A fast
simulation  for a TESLA detector (SIMDET 3.01 \cite{SIMDET})
was used  to model a detector performance. The jets were reconstructed with the Durham algorithm (\( y_{cut} = 0.02 \)).
% 
The double $b$-tag was required to select the signal
\( h\rightarrow b\bar{b} \) events 
%(
%a fixed efficiency for the $b\bar{b}$-tagging,
(\( \varepsilon _{bb}=70\% \)
%,
 and 
%a fixed 
% probability  for a mistagging of the 
%\( c\bar{c} \) events, 
\( \varepsilon _{cc}=3.5\% \) were assumed). 
%
The following cuts were used  to 
%suppress a background:
select reconstructed $b \bar{b}$ events:
%
(1) a total visible energy \( E_{vis} > 90 \) GeV;
%
(2) the ratio of the total longitudinal momentum of all 
 observed particles to the total visible energy 
%is taken to be 
\( |P_{z}|/E_{vis}<0.1 \);
%
(3) a number of jets \( N_{jets}=2,\, 3 \); 
%
(4) for each jet
%, $i=1, ..., N_{jets}$, 
we require 
%   \( |\cos \theta _{i}|<0.75 \).
   \( |\cos \theta _{jet}|<0.75 \).
%
The obtained
 distributions of the reconstructed \( \gamma \gamma  \) invariant
mass \( W_{rec} \) are shown in 
Fig. \ref{fig:ResultWithNLOBackgd} (left). 
%
%\section{Final results}
%
%We can calculate 
The expected relative statistical error of
\( \Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b}) \) is equal to
%
%\[
%\frac{\Delta \left[ 
%\Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b})\right] }
%{\left[ \Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b})
% \right] =}\frac{\sqrt{N_{obs}}}{N_{obs}-N_{bkgd}}\; .\]
%
\( \sqrt{N_{obs}}/(N_{obs}-N_{bkgd}) \).
%
%The accuracy,
If estimated from the  selected
mass region,
it is equal to 1.9\%. 
%
%
%
We introduce  the corrected, reconstructed invariant mass as: 
%
%\begin{equation}
%\label{eq:Wcorr2}
\(
W_{corr}\equiv \sqrt{W^{2}_{rec}+2P_{T}(E_{vis}+P_{T})}
\).
%\end{equation}
% 
%
The distributions of the \( W_{corr} \) 
%, obtained for the  signal and background events,
are shown in Fig.~\ref{fig:ResultWithNLOBackgd} (right). 
%
In the selected \( W_{corr} \) region one 
%expects:
achieves an relative accuracy
%
% Varmin=115. Varmax=128. Precision with LO= 1.5447 % with NLO=1.73505 %
%
\(
\Delta \left[ 
\Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b})\right] %
/\left[ \Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b})
         \right] =1.7\% \; . \) \smallskip
%
% This is the final result of our analysis.
%
%
%\pagebreak
%
%\section{Conclusions}
%
%We achieve a precision of the measurement of the 
%\( \Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow 
%b\overline{b}) \) equal to  1.7\%. 
%
Assuming \( {\rm Br}(h\rightarrow b\overline{b}) \) 
will be measured to 1.5\% \cite{Brient}, Higgs-boson partial width 
\( \Gamma (h\rightarrow \gamma \gamma ) \) can be extracted with accuracy of 2.3\%.
Using in addition the result from the $e^+ e^-$ Linear Collider for 
\( {\rm Br}(h\rightarrow \gamma \gamma) \) 
%to 10\% 
\cite{Boos}, one can extract 
\( \Gamma_{\rm tot} \) with a precision of 10\%.
%
%
%
%
%
%All have done, you may send the source TEX files to editor@lcws2002.korea.ac.kr. 
%
%
%
%
%
\vspace*{-0.9cm}
\begin{thebibliography}{1}
\vspace*{-0.5cm}
\bibitem{TDR}B.~Badelek \etal, {\it TESLA TDR}, DESY 2001-011, .

\bibitem{NZKBB}P. Nie\.zurawski, A.F. \.Zarnecki, M. Krawczyk,  accepted by Acta Phys.~Polon.~B.

\bibitem{CompAZ}A.F. \.Zarnecki, .
% {\it submitted to Acta Phys.~Polon.} {\bf B}; http://info.fuw.edu.pl/\textasciitilde{}zarnecki/compaz/compaz.html.

\bibitem{V.Telnov}V.~Telnov, \textit{Nucl.~Instrum.~Meth.} {\bf A355}, 3 (1995); 
V.~Telnov, 
talk at the 2nd Workshop of ECFA-DESY Study,
Saint~Malo, France, April 2002.

\bibitem{PYTHIA}T.~Sj\"ostrand \etal, {\it Comput. Phys. Commun.} {\bf 135}, 238 (2001).
%P.~Eden, C.~Friberg, L.~Lonnblad, G.~Miu, S.~Mrenna,
% E.~Norrbin, {\it Comput. Phys. Commun.} {\bf 135}, 238 (2001), .

\bibitem{HDECAY}A.~Djouadi, J.~Kalinowski, M.~Spira, {\it Comput. Phys. Commun.} {\bf 108}, 56 (1998).
%, \mbox.

\bibitem{JikiaAndSoldner}G.~Jikia, S.~S\"oldner-Rembold, {\it Nucl.~Instrum.~Meth.} {\bf A472}, 133 (2001), . 

\bibitem{SIMDET}M.~Pohl, H.~J.~Schreiber, DESY-99-030.

\bibitem{Brient}
J-C.~Brient,
\newblock  LC-PHSM-2002-003; 
M.~Battaglia, 
\newblock  .
%``Measuring Higgs branching ratios and telling the SM from a MSSM Higgs  boson at the e+ e- linear collider,''

%\cite{Boos}
\bibitem{Boos}
%E.~Boos, J.~C.~Brient, D.~W.~Reid, H.~J.~Schreiber, R.~Shanidze,
E.~Boos \etal, 
%``Measuring the Higgs branching fraction into two photons at future  linear e+ e- colliders,''
\textit{Eur.\ Phys.\ J.\ } {\bf C19}, 455 (2001), .
%%CITATION = ;%%


%\bibitem{wwzz}
%P. Nie\.zurawski, A.F. \.Zarnecki, M. Krawczyk,  
%\textit{Study of the Higgs-boson decays into 
%       $W^+W^-$ and $Z Z $ at the Photon Collider},
%   CERN-TH/2002-165, IFT-28/2002, \mbox.

\end{thebibliography}
%%% Figures 
%%%
\vspace*{-0.8cm}
\begin{figure}[h]
{\centering \resizebox*{!}{\figheight}%
            {\includegraphics{nloresult.eps} \includegraphics{wcorr.eps}}  \par}

\caption{\label{fig:ResultWithNLOBackgd}
Reconstructed invariant mass \protect\( W_{rec}\protect \) (left) and corrected invariant mass \protect\( W_{corr}\protect \) (right)
distributions for the selected $b\bar{b}$ events.
Contributions of the signal, due to the Higgs boson with a mass 
$m_h = 120$ GeV, and of the heavy-quark 
 background, calculated in the NLO QCD, are indicated. For
 comparison, the LO background estimate  is also plotted (dots). 
Arrows indicate the mass window optimized for the measurement of the 
\( \Gamma (h\rightarrow \gamma \gamma ){\rm Br}(h\rightarrow b\overline{b}) \).
}
\end{figure}
%%
%%%%
%\begin{figure}[t]
% \vspace{-1cm}
%{\centering \resizebox*{!}{\figheight}%
%               {\includegraphics{wcorr.eps}} \par}

%\caption{\label{fig:Wcorr}
%As in Fig. \ref{fig:ResultWithNLOBackgd}, for the corrected invariant mass \protect\( W_{corr}\protect \) distributions.
%}
%\end{figure}
%%%

\end{document}
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