\boldmath Measurements of $\jpsi$ Decays into $2(\pip\pin)\eta$ and $3(\pip\pin)\eta$
Based on a sample of $5.8\times 10^7$ $\jpsi$ events taken with the BESII detector, the branching fractions of $\jpsi\to 2(\pip\pin)\eta$ and $\jpsi\to 3(\pip\pin)\eta$ are measured for the first time to be $(2.26\pm0.08\pm 0.27)\times 10^{-3}$ and $(7.24\pm0.96\pm1.11)\times 10^{-4}$, respectively. \vspace{3\parskip} \noindent{PACS:} 13.25.Gv, 14.40.Gx, 13.40.Hq
jpsi_4pieta_6pieta.tex
\documentclass{elsart}
\usepackage{epsfig}


\newcommand{\BR}{{\cal B}_0}
\newcommand{\eff}{\varepsilon}
\newcommand{\psip}{\psi(2S)}
\newcommand{\psipp}{\psi(3770)}
\newcommand{\jpsi}{J/\psi}
\newcommand{\DDbar}{D\overline{D}}
\newcommand{\EE}{e^+e^-}
\newcommand{\MM}{\mu^+\mu^-}
\newcommand{\TT}{\tau^+\tau^-}
\newcommand{\GG}{\gamma\gamma}
\newcommand{\PP}{\pi^+\pi^-}
\newcommand{\PPJP}{\pi^+\pi^- J/\psi}
\newcommand{\KK}{K^+K^-}
\newcommand{\zz}{\bar{p} p}
\newcommand{\LL}{\ell^+\ell^-}
\newcommand{\OP}{\omega\pi^0}
\newcommand{\pip}{\pi^+}
\newcommand{\pin}{\pi^-}
\newcommand{\piz}{\pi^0}
%\newcommand{\pp}{\pi^+\pi^-}
\newcommand{\ppb}{p\bar{p}}
\newcommand{\jpsipp}{J/\psi \pi^+\pi^-}
\newcommand{\ppjpsi}{\pi^+\pi^- J/\psi}
\newcommand{\ra}{\rightarrow}
\newcommand{\jpsito}{J/\psi \rightarrow }
\newcommand{\pspto}{\psi(2S) \rightarrow }
\newcommand{\psppto}{\psi(3770) \rightarrow }
\newcommand{\rhopi}{\rho\pi}

%\newcommand{\omegapi}{\omega\pi^0}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\beqn}{\begin{eqnarray}}
\newcommand{\eeqn}{\end{eqnarray}}
\newcommand{\beqns}{\begin{eqnarray*}}
\newcommand{\eeqns}{\end{eqnarray*}}
\newcommand{\bfg}{\begin{figure}}
\newcommand{\efg}{\end{figure}}
\newcommand{\bitm}{\begin{itemize}}
\newcommand{\eitm}{\end{itemize}}
\newcommand{\bnum}{\begin{enumerate}}
\newcommand{\enum}{\end{enumerate}}
\newcommand{\btbl}{\begin{table}}
\newcommand{\etbl}{\end{table}}
\newcommand{\btbu}{\begin{tabular}}
\newcommand{\etbu}{\end{tabular}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\kp}{K^+}
\newcommand{\kn}{K^-}
\newcommand{\ks}{K^{0}_{S}}
\newcommand{\kstp}{K^{*+}}
\newcommand{\kstm}{K^{*-}}
\newcommand{\ksto}{K^{*0}}
\newcommand{\bksto}{\bar{K^{*0}}}
\newcommand{\etap}{\eta^{\prime}}
\newcommand{\rhoo}{\rho^0}
\newcommand{\g}{\gamma}
\newcommand{\be}{\begin{enumerate}}
\newcommand{\ee}{\end{enumerate}}
\newcommand{\bi}{\begin{itemize}}
\newcommand{\ei}{\end{itemize}}

\newcommand{\rar}{\rightarrow}
\newcommand{\ppp}{\pi^+\pi^-\pi^0}

%\newcommand{\pin}{\pi^-}
\newcommand{\pio}{\pi^0}
%\newcommand{\pip}{\pi^+}

\newcommand{\ar}{\rightarrow}
\newcommand{\uu}{\mu^+\mu^-}
\newcommand{\epen}{e^+e^-}
%\newcommand{\ppb}{p\bar{p}}
%\newcommand{\ppj}{\pi^+\pi^-J/\psi}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\renewcommand{\thefootnote}{\fnsymbol{footnote}}

\begin{document}

\begin{frontmatter}
\title{\boldmath  Measurements of  $\jpsi$ Decays into
$2(\pip\pin)\eta$ and $3(\pip\pin)\eta$
}

\date{15 Jan. 2004}

\maketitle



%\begin{center}
\begin{center}
M.~Ablikim$^{1}$,    J.~Z.~Bai$^{1}$,               Y.~Ban$^{11}$,
J.~G.~Bian$^{1}$,    X.~Cai$^{1}$,                  J.~F.~Chang$^{1}$,
H.~F.~Chen$^{17}$,   H.~S.~Chen$^{1}$,              H.~X.~Chen$^{1}$,
J.~C.~Chen$^{1}$,    Jin~Chen$^{1}$,                Jun~Chen$^{7}$,
M.~L.~Chen$^{1}$,    Y.~B.~Chen$^{1}$,              S.~P.~Chi$^{2}$,
Y.~P.~Chu$^{1}$,     X.~Z.~Cui$^{1}$,               H.~L.~Dai$^{1}$,
Y.~S.~Dai$^{19}$,    Z.~Y.~Deng$^{1}$,              L.~Y.~Dong$^{1}$$^a$,
Q.~F.~Dong$^{15}$,   S.~X.~Du$^{1}$,                Z.~Z.~Du$^{1}$,
J.~Fang$^{1}$,       S.~S.~Fang$^{2}$,              C.~D.~Fu$^{1}$,
H.~Y.~Fu$^{1}$,      C.~S.~Gao$^{1}$,               Y.~N.~Gao$^{15}$,
M.~Y.~Gong$^{1}$,    W.~X.~Gong$^{1}$,              S.~D.~Gu$^{1}$,
Y.~N.~Guo$^{1}$,     Y.~Q.~Guo$^{1}$,               Z.~J.~Guo$^{16}$,
F.~A.~Harris$^{16}$, K.~L.~He$^{1}$,                M.~He$^{12}$,
X.~He$^{1}$,         Y.~K.~Heng$^{1}$,              H.~M.~Hu$^{1}$,
T.~Hu$^{1}$,         G.~S.~Huang$^{1}$$^b$,         X.~P.~Huang$^{1}$,
X.~T.~Huang$^{12}$,  X.~B.~Ji$^{1}$,                C.~H.~Jiang$^{1}$,
X.~S.~Jiang$^{1}$,   D.~P.~Jin$^{1}$,               S.~Jin$^{1}$,
Y.~Jin$^{1}$,        Yi~Jin$^{1}$,                  Y.~F.~Lai$^{1}$,
F.~Li$^{1}$,         G.~Li$^{2}$,                   H.~H.~Li$^{1}$,
J.~Li$^{1}$,         J.~C.~Li$^{1}$,                Q.~J.~Li$^{1}$,
R.~Y.~Li$^{1}$,      S.~M.~Li$^{1}$,                W.~D.~Li$^{1}$,
W.~G.~Li$^{1}$,      X.~L.~Li$^{8}$,                X.~Q.~Li$^{10}$,
Y.~L.~Li$^{4}$,      Y.~F.~Liang$^{14}$,            H.~B.~Liao$^{6}$,
C.~X.~Liu$^{1}$,     F.~Liu$^{6}$,                  Fang~Liu$^{17}$,
H.~H.~Liu$^{1}$,     H.~M.~Liu$^{1}$,               J.~Liu$^{11}$,
J.~B.~Liu$^{1}$,     J.~P.~Liu$^{18}$,              R.~G.~Liu$^{1}$,
Z.~A.~Liu$^{1}$,     Z.~X.~Liu$^{1}$,               F.~Lu$^{1}$,
G.~R.~Lu$^{5}$,      H.~J.~Lu$^{17}$,               J.~G.~Lu$^{1}$,
C.~L.~Luo$^{9}$,     L.~X.~Luo$^{4}$,               X.~L.~Luo$^{1}$,
F.~C.~Ma$^{8}$,      H.~L.~Ma$^{1}$,                J.~M.~Ma$^{1}$,
L.~L.~Ma$^{1}$,      Q.~M.~Ma$^{1}$,                X.~B.~Ma$^{5}$,
X.~Y.~Ma$^{1}$,      Z.~P.~Mao$^{1}$,               X.~H.~Mo$^{1}$,
J.~Nie$^{1}$,        Z.~D.~Nie$^{1}$,               S.~L.~Olsen$^{16}$,
H.~P.~Peng$^{17}$,   N.~D.~Qi$^{1}$,                C.~D.~Qian$^{13}$,
H.~Qin$^{9}$,        J.~F.~Qiu$^{1}$,               Z.~Y.~Ren$^{1}$,
G.~Rong$^{1}$,       L.~Y.~Shan$^{1}$,              L.~Shang$^{1}$,
D.~L.~Shen$^{1}$,    X.~Y.~Shen$^{1}$,              H.~Y.~Sheng$^{1}$,
F.~Shi$^{1}$,        X.~Shi$^{11}$$^c$,                 H.~S.~Sun$^{1}$,
J.~F.~Sun$^{1}$,     S.~S.~Sun$^{1}$,               Y.~Z.~Sun$^{1}$,
Z.~J.~Sun$^{1}$,     X.~Tang$^{1}$,                 N.~Tao$^{17}$,
Y.~R.~Tian$^{15}$,   G.~L.~Tong$^{1}$,              G.~S.~Varner$^{16}$,
D.~Y.~Wang$^{1}$,    J.~Z.~Wang$^{1}$,              K.~Wang$^{17}$,
L.~Wang$^{1}$,       L.~S.~Wang$^{1}$,              M.~Wang$^{1}$,
P.~Wang$^{1}$,       P.~L.~Wang$^{1}$,              S.~Z.~Wang$^{1}$,
W.~F.~Wang$^{1}$$^d$     Y.~F.~Wang$^{1}$,              Z.~Wang$^{1}$,
Z.~Y.~Wang$^{1}$,    Zhe~Wang$^{1}$,                Zheng~Wang$^{2}$,
C.~L.~Wei$^{1}$,     D.~H.~Wei$^{1}$,               N.~Wu$^{1}$,
Y.~M.~Wu$^{1}$,      X.~M.~Xia$^{1}$,               X.~X.~Xie$^{1}$,
B.~Xin$^{8}$$^b$,        G.~F.~Xu$^{1}$,                H.~Xu$^{1}$,
S.~T.~Xue$^{1}$,     M.~L.~Yan$^{17}$,              F.~Yang$^{10}$,
H.~X.~Yang$^{1}$,    J.~Yang$^{17}$,                Y.~X.~Yang$^{3}$,
M.~Ye$^{1}$,         M.~H.~Ye$^{2}$,                Y.~X.~Ye$^{17}$,
L.~H.~Yi$^{7}$,      Z.~Y.~Yi$^{1}$,                C.~S.~Yu$^{1}$,
G.~W.~Yu$^{1}$,      C.~Z.~Yuan$^{1}$,              J.~M.~Yuan$^{1}$,
Y.~Yuan$^{1}$,       S.~L.~Zang$^{1}$,              Y.~Zeng$^{7}$,
Yu~Zeng$^{1}$,       B.~X.~Zhang$^{1}$,             B.~Y.~Zhang$^{1}$,
C.~C.~Zhang$^{1}$,   D.~H.~Zhang$^{1}$,             H.~Y.~Zhang$^{1}$,
J.~Zhang$^{1}$,      J.~W.~Zhang$^{1}$,             J.~Y.~Zhang$^{1}$,
Q.~J.~Zhang$^{1}$,   S.~Q.~Zhang$^{1}$,             X.~M.~Zhang$^{1}$,
X.~Y.~Zhang$^{12}$,  Y.~Y.~Zhang$^{1}$,             Yiyun~Zhang$^{14}$,
Z.~P.~Zhang$^{17}$,  Z.~Q.~Zhang$^{5}$,             D.~X.~Zhao$^{1}$,
J.~B.~Zhao$^{1}$,    J.~W.~Zhao$^{1}$,              M.~G.~Zhao$^{10}$,
P.~P.~Zhao$^{1}$,    W.~R.~Zhao$^{1}$,              X.~J.~Zhao$^{1}$,
Y.~B.~Zhao$^{1}$,    Z.~G.~Zhao$^{1}$$^e$,          H.~Q.~Zheng$^{11}$,
J.~P.~Zheng$^{1}$,   L.~S.~Zheng$^{1}$,             Z.~P.~Zheng$^{1}$,
X.~C.~Zhong$^{1}$,   B.~Q.~Zhou$^{1}$,              G.~M.~Zhou$^{1}$,
L.~Zhou$^{1}$,       N.~F.~Zhou$^{1}$,              K.~J.~Zhu$^{1}$,
Q.~M.~Zhu$^{1}$,     Y.~C.~Zhu$^{1}$,               Y.~S.~Zhu$^{1}$,
Yingchun~Zhu$^{1}$$^f$,            Z.~A.~Zhu$^{1}$,
B.~A.~Zhuang$^{1}$,
X.~A.~Zhuang$^{1}$,            B.~S.~Zou$^{1}$
\\(BES Collaboration)\\
\vspace{0.2cm}
%\label{att}
$^{1}${\it Institute of High Energy Physics, Beijing 100049, People's
Republic of
 China }\\
$^{2}${\it  China Center for Advanced Science and Technology,
Beijing 100080, People's Republic of China}\\
$^{3}${\it Guangxi Normal University, Guilin 541004, People's Republic of
China
}\\
$^{4}$ {\it Guangxi University, Nanning 530004, People's Republic of
China}\\
$^{5}$ {\it Henan Normal University, Xinxiang 453002, People's Republic of
China}\\
$^{6}${\it Huazhong Normal University, Wuhan 430079, People's Republic of
China}\\
$^{7}$ {\it Hunan University, Changsha 410082, People's Republic of China}\\
$^{8}${\it  Liaoning University, Shenyang 110036, People's Republic of
China}\\
$^{9}${\it Nanjing Normal University, Nanjing 210097, People's Republic of
China}\\
$^{10}$ {\it Nankai University, Tianjin 300071, People's Republic of
China}\\
$^{11}$ {\it Peking University, Beijing 100871, People's Republic of
China}\\
$^{12}$ {\it Shandong University, Jinan 250100, People's Republic of
China}\\
$^{13}$ {\it Shanghai Jiaotong University, Shanghai 200030, People's
Republic of
China} \\
$^{14}$ {\it Sichuan University, Chengdu 610064, People's Republic of
China}\\
$^{15}$ {\it Tsinghua University, Beijing 100084, People's Republic of
China}\\
$^{16}$ {\it University of Hawaii, Honolulu, Hawaii 96822, USA}\\
$^{17}$ {\it University of Science and Technology of China, Hefei 230026,
People's Republic of
China}\\
$^{18}$ {\it Wuhan University, Wuhan 430072, People's Republic of China}\\
$^{19}$ {\it Zhejiang University, Hangzhou 310028, People's Republic of
China}\\
\vspace{0.4cm}
$^{a}$ Current address: Iowa State University, Ames, Iowa 50011-3160, USA.\\
$^{b}$ Current address: Purdue University, West Lafayette, Indiana 47907,
USA.\\
$^{c}$ Current address: Cornell University, Ithaca, New York 14853, USA.\\
$^{d}$ Current address: Laboratoire de l'Acc{\'e}l{\'e}ratear Lin{\'e}aire,
F-91898 Orsay, France.\\
$^{e}$ Current address: University of Michigan, Ann Arbor, Michigan 48109,
USA.\\
$^{f}$ Current address: DESY, D-22607, Hamburg, Germany.\\

\end{center}
\vskip 0.3cm

%\end{center}
%\date{}
%\clearpapge
%\begin{document}

\begin{abstract}
Based on a sample of $5.8\times 10^7$ $\jpsi$ events taken with the
BESII detector, the branching fractions of $\jpsi\to 2(\pip\pin)\eta$
and $\jpsi\to 3(\pip\pin)\eta$ are measured for the first time to be
$(2.26\pm0.08\pm 0.27)\times 10^{-3}$ and $(7.24\pm0.96\pm1.11)\times
10^{-4}$, respectively.
\vspace{3\parskip}

\noindent{\it PACS:} 13.25.Gv, 14.40.Gx, 13.40.Hq

\end{abstract}
\end{frontmatter}
\clearpage


\section{Introduction}   \label{introd}
%  The $\jpsi$ decays provides a good laboratory to study  light hadron
%spectroscopy and search for glueballs, hybrids and exotic states.
More than one hundred exclusive decay modes of the 
$\jpsi$
have been reported  since its discovery
at Brookhaven~\cite{aube} and SLAC~\cite{augu} in 1974. According to
Ref.~\cite{physrep}, direct
hadronic, electromagnetic and radiative decays represent roughly
65\%, 14\%, and 7\% of the total $\jpsi$ decay rate, respectively. 
%It is
%important to estimate how much of this rate has been measured
%in exclusive studies of $\jpsi$ decays. In the discussion Ref.~\cite{physrep},
% calculated with a
%statistical model,
Up to now, only about half of all hadronic decays, 34.8\%, have been
measured in exclusive reactions.
The sample of 58 million $\jpsi$ events, taken at BESII, provides a chance to
measure some of the missing hadronic decays.
In this analysis, we report  the first measurements of
$\jpsi\ar 2(\pip\pin)\eta$ and $\jpsi\ar 3(\pip\pin)\eta$.


%Recently, $5.8\times 10^{7}$ $\jpsi$ events and
%$1.4\times 10^{7}$ $\psip$ events have been taken with the upgraded
%Beijing Spectrometer (BESII), which offers a unique opportunity
%to precisely measure the branching fractions of $\jpsi$ decays.

%In this analysis, we reported  the first measurement of
%$\jpsi\ar 2(\pip\pin)\eta$,
%and $\jpsi\ar 3(\pip\pin)\eta$.
%\section{The BES Detector}  \label{BESD}

The upgraded Beijing Spectrometer (BESII) detector located
at the Beijing Electron-Positron Collider (BEPC)
is a large solid-angle
magnetic spectrometer which is described in detail in Ref.~\cite{besii}.
The momentum of the charged particle is determined by a
40-layer cylindrical main drift chamber (MDC) which has a momentum
resolution of
 $\sigma_{p}$/p=$1.78\%\sqrt{1+p^2}$ ($p$ in GeV/c).
Particle identification is accomplished by specific ionization ($dE/dx$)
measurements in the drift chamber and time-of-flight (TOF) information in
a barrel-like array of 48 scintillation counters. The $dE/dx$ resolution
is $\sigma_{dE/dx}=8.0\%$; the TOF resolution for Bhabha events is
$\sigma_{TOF}=180$ ps.
Radially outside of the time-of-flight counters is a 12-radiation-length
barrel shower counter (BSC) comprised of gas
tubes interleaved with lead sheets. The BSC measures
the energy and direction of photons with resolutions
of $\sigma_{E}/E\simeq21\%\sqrt{E}$ ($E$ in GeV), $\sigma_{\phi}=7.9$ mrad, and
$\sigma_{z}=2.3$ cm. The iron flux return of the magnet is instrumentd
with three double layers of counters that are used to identify muons.

A GEANT3 based Monte Carlo package (SIMBES) with detailed
consideration of the detector performance
is used. The consistency between data and Monte Carlo has been carefully
checked in many high purity physics channels, and the agreement is
reasonable.


% Since the decay $J/\psi\rightarrow\pi^+\pi^-\pi^0$ has been measured to be
% consistent with proceeding almost entirely through the $\rho\pi$
% intermediate state\cite{markii}, the final state angular distributions is specified completely by
% $\jpsi\to \rho\pi$.

%\section{General Criteria}  \label{gen_sel}
%\label{method}
%Each charged track reconstructed by MDC hits is required to satisfy
%following criteria:
%(1)have a good helix fit  in order to ensure a correct error matrix in the
%kinematic fit;
%(2)originated from the IP region, $\sqrt{V_x^2+V_y^2}<2$ cm
%and $|V_z|<20$ cm. Here $V_x$, $V_y$,
%and $V_z$ are the x, y, and z coordinates of the point of closest
%approach to the beam axis;
%(3)the transverse momentum is greater than 60MeV/c;
%(4)$|\cos\theta|\leq 0.8$ with $\theta$ is the polar angle of the track.


%A neutral cluster is assumed to be a photon candidate if the following
%requirements are satisfied:
%(1) the energy deposited in BSC is greater than 0.06~GeV/$c^2$;
%(2) the
%total hit layers should be greater than 1;
%(3)the angle between
%the direction of photon emission and the direction of shower development
%should be less than $30^{\circ}$;
%(4)the angle between photon and its nearset
%charged track is required to be greater than $10^{\circ}$.
%(5)if the angle
%between two neutral clusters is less than $10^{\circ}$ and the $2\gamma$
%invariant mass is less than 0.05~GeV/$c^2$, they are regarded as one neutral cluster.
%The direction and deposited energy of the neutral cluster
%for kinematic fit are from
%the one with larger energy.


\section{\boldmath Analysis of  $\jpsi\rar 2(\pip\pin)\eta$}
\label{4pieta}
%\subsection{Event Selection}
This decay is observed in the topology $\pip\pin\pin\pin\g\g$.
Events with four charged tracks and at least two isolated photons
are selected. The  selection criteria for charged tracks and photons
are described in detail in Ref.~\cite{rhopi}. Each charged track must be
well fitted to a helix, originating from the interaction region of R$_{xy}$
$<$ 0.02 m and $|z|~<$ 0.2m, and have a polar angle, $\theta$, in the range
$|\cos\theta|$ $<$ 0.8. 
%The TOF and dE/dx information are used to identify
%particles. At least one charged track must be identified as a pion. 

Isolated photons
are those that have energy deposited in the BSC greater than 60 MeV, the
angle between the direction at the first layer of the BSC and the developing
direction of the cluster less than 30$^{\circ}$, and the angle between
photons and any charged tracks larger than $10^{\circ}$.
 To eliminate tracks from $\gamma$ conversions,
%$\jpsi\ar\g\etap
%(\ar\eta\pi\pi)$,
the minimum angle between any two oppositely-charged tracks is
required to be
greater than $10^{\circ}$.

A 4C kinematic fit is  performed under the hypothesis
$\pip\pin\pip\pin\g\g$,
and the chi-squared, $\chi^{2}_{\pip\pin\pip\pin\g\g}$, is required to be less than 15. 
$\chi^{2}_{\pip\pin\pip\pin\g\g}$ is also required to be less than the
chi-squares for the
$\kp\kn\pip\pin\g\g$ and $\pip\pin\pip\pin\g\g\g$
hypotheses.
%Most of background events are eliminated if $\chi^{2}<15$ for 4C kinematic
%fit in  $\pip\pin\pin\pin\g\g$ hypothesis.
\begin{figure}[htpb]
\centerline{\includegraphics[width=0.5\textwidth,height=0.38\textheight]
        {4pieta_fit.eps}}
\caption{The distribution of $m_{\g\g}$ for candidate $J/\psi \ar
  \eta 2(\pi^+ \pi^-)$ events. Dots with error bars
are data, the histogram is the  shape of the $\eta$ from Monte Carlo
simulation, 
and the curve is background.}
\label{4pietafit}
\end{figure}

 After the above selection, the $m_{\g\g}$ distribution is shown in 
Fig.~\ref{4pietafit}, where a clear $\eta$ signal is observed.
Monte Carlo simulation is used to estimate the background,
%The main decay modes of $\jpsi$ involving $\eta$, which have 
%been observed,
%are $\jpsi\ar\phi\eta$, $\rho\eta$, $\omega\eta$, $\g\eta\pi\pi$, 
%$\omega\etap(\ar\eta\pip\pin)$ and $\phi\etap(\etap\ar\eta\pi\pi)$.
% $\rho\etap(\etap\ar\eta\pi\pi)$.
and backgrounds from simulated channels are listed in Table~\ref{bkg},
where $N^{MC}_{sel}$ is the number of events after event selection and
$N^{norm}$ is the background normalized to 58 million $\jpsi$ events.
The sum of background events is 18 events, which can be ignored.
%compared to about 5000
%signals.
Another possible background channel is from $\jpsi\ar\g\eta 2(\pip\pin)$.
No obvious $\eta$ signal is seen in the $m_{\g\g}$ distribution from 
$\jpsi\ar\g\eta 2(\pip\pin)$, as shown
in
Fig.~\ref{metapipi}(a). Therefore the background from this channel 
can also be ignored.

%The distribution of $m_{\g\g}$ shown in Fig.~\ref{g4pi} shows that no obvious $\eta$ signals are observed
%and only contributes the continuum background.

%To estimate its contribution, 100,000 events are generated with HOWL
%generator. No obvious $\eta$ signals are observed and only
%contributes the continuum background.

%After above selection, the distribution of $m_{\g\g}$ is shown in
%Fig.\ref{g4pi}. No obvious $\eta$ signals are observed and only
%contributes the continuum background.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=0.7\textwidth,height=0.26 \textheight]
        {ks_4pieta.eps}
\caption{(a) Distribution of $m_{\g\g}$ from Monte Carlo simulation of
$\jpsi\ar\g 2(\pip\pin)\eta$. (b) Distribution of $m_{\pip\pin}$ from
the $\eta$ signal region (blank histogram) and $\eta$ sidebands
(shaded histogram) for $J/\psi \ar \gamma\gamma 2(\pi^+ \pi^-)$
events.}
\label{metapipi}
\end{center}

\end{figure}

\begin{table}[htpb]
\caption{Background estimates for the $J/\psi \ar \eta 2(\pi^+ \pi^-)$
  case. $N^{MC}_{sel}$ are the number of events
passing selection criteria; $N^{norm}$ is the background normalized to
58 million  $J/\psi$ events.}
\begin{center}
\begin{tabular}{c|c|c|c}
\hline
Channel & MC sample &$N^{MC}_{sel}$ & $N^{norm}$\\
\hline
$\jpsi\ar\phi\eta$ & 40,000 &0 & 0\\
$\jpsi\ar\rho\eta$ & 40,000 & 0 & 0\\
$\jpsi\ar\g\eta\pip\pin$ & 70,000 & 2 & 3\\
$\jpsi\ar\omega\eta(\eta\ar\g\g)$ & 40,000 & 11 & 8\\
$\jpsi\ar\omega\etap(\etap\ar\pip\pin\eta)$ &100,000 & 135& 2\\
$\jpsi\ar\phi\etap(\etap\ar\pip\pin\eta)$ & 40,000 & 2 & 0\\
$\jpsi\ar\g\etap(\etap\ar\pip\pin\eta)$ & 50,000 & 6 & 5 \\
\hline
\end{tabular}
\end{center}
\label{bkg}
\end{table}


Background from events with a $\ks$ in the final state are estimated
 from $\eta$ sidebands.  Fig.~\ref{metapipi}(b) shows the mass
 distribution of all $\pip\pin$ pairs for events with
 $m_{\gamma\gamma}$ in the $\eta$ region
 ($|m_{\g\g}-0.55|<0.05$~GeV/$c^2$), and the shaded histogram is for
 $\eta$ sidebands ($0.45$~GeV/$c^2$ $<m_{\g\g}<0.50$ GeV/$c^2$ and
 0.60 GeV/$c^2$ $<m_{\g\g}<$0.65 GeV/$c^2$).  From
 Fig.~\ref{metapipi}, we conclude that the $\ks$ signals are consistent
with coming from background, as estimated 
from $\eta$ sideband events. 
%Therefore the background events with $\ks$
% events are ignored.
 


%\subsection{Branching Fraction}
The  $m_{\g\g}$ distribution, shown in Fig.~\ref{4pietafit}, is fitted
with a Monte Carlo determined  shape for the $\eta$ and a second
order polynomial and yields
4839$\pm$158  $J/\psi \ar 2(\pi^+ \pi^-) \eta$, $\eta \ar \gamma
\gamma$ events.
%After considering the detection
%efficiency, $(9.43\pm0.10)\%$, the branching fraction is given



\section{\boldmath Analysis of $\jpsi\ar 3(\pip\pin)\eta$}
\label{6pieta}
%\subsection{Event Selection}
Events with six good charged tracks and at least two isolated photons
 are selected. The angle between two oppositely charged tracks is required to
 be greater than $10^{\circ}$ to remove $\gamma$ conversions.  A four
 constraint kinematic fit is made to the hypothesis $J/\psi \ar
 3(\pip\pin)\g\g$, and $\chi^{2}_{\pip\pin\pip\pin\pip\pin\g\g}$ is
 required to be less than 15.

After the above selection, the two photon invariant mass distribution
is shown in Fig. \ref{eta7pi}; an $\eta$ signal is evident.
\begin{figure}[htpb]
\centerline{\includegraphics[width=0.5\textwidth,height=0.38\textheight]
        {6pieta_fit.eps}}
\caption{Distribution of $m_{\g\g}$ for  $J/\psi \ar
 3(\pip\pin)\g\g$ candidate events. Dots with error bars
are data, the histogram is the $\eta$ shape determined by Monte Carlo
 simulation, 
and the curve is background.}
\label{eta7pi}
\end{figure}


%\begin{figure}[htpb]
%\centerline{\includegraphics[width=0.5\textwidth,height=0.45\textheight]
%        {6pieta/ppall.eps}}
%\caption{The distribution of $m_{\g\g}$ and the curves are the results of
%the fit described in the text.}
%\label{pi07pi}

%\end{figure}
%\subsection{Background Analysis}

Monte Carlo simulation indicates that background from the decay modes
 listed in Table~\ref{bkg} can be ignored.  Other possible backgrounds
 are from $\jpsi\ar\g 2(\pip\pin)\eta$ and $\jpsi\ar\g
 3(\pip\pin)\eta$ events. As described in Section~\ref{4pieta}, the
 $m_{\g\g}$ distribution from $\jpsi\ar\g 2(\pip\pin)\eta$ shows no
 clear $\eta$ peak.
%Fig.\ref{mcxg4pieta} shows the distribution of $m_{\g\g}$ from Monte Carlo
%simulation of $\jpsi\ar\g 2(\pip\pin)\eta$.
%No clear $\eta$ peak is observed  at 0.55 GeV/$c^2$.
%\begin{figure}
%\centerline{\includegraphics[width=0.5\textwidth,height=0.33\textheight]
%        {6pieta/xg4pieta.eps}}
%\caption{The distribution of $m_{\g\g}$ from $\jpsi\ar\g 2(\pip\pin)\eta$
%Monte Carlo simulation.}
%\label{mcxg4pieta}
%\end{figure}
% So the background events from this decay
%modes also can be ignored.
For $\jpsi\ar\g 3(\pip\pin)\eta$,
the  $m_{\g\g}$ distribution from Monte Carlo simulation, shown in  
Fig.~\ref{m6etapipi}(a), 
also does not show a peak in the $\eta$ region, so its contribution can
also be ignored.

%So the background events from this decay mode also can be ignored.
The background with $\ks$ final states can also be estimated, as was
done previously, using the $\eta$
sidebands. Fig.~\ref{m6etapipi}(b) shows the $\pip\pin$ mass
distribution. The full histogram is the $m_{\pip\pin}$ distribution
for events in the $\eta$ signal region ($|m_{\g\g}-0.55|<$0.05
GeV/$c^2$), and the shaded histogram is for events from the $\eta$
sidebands (0.45 GeV/$c^2 <m_{\g\g}<$ 0.50 GeV/$c^2$ and 0.60
GeV$/c^2<m_{\g\g}<$ 0.65 GeV/$c^2$).  As in Section~\ref{4pieta}, we
can conclude from Fig.~\ref{m6etapipi}(b) that most events with $\ks$
are associated with backgrounds which are measured by $\eta$
sidebands.
%Thus the background events with $\ks$ signals
%are ignored.



\begin{figure}[htpb]

\begin{center}
\includegraphics[width=0.7\textwidth,height=0.26\textheight]
        {ks_6pieta.eps}
\caption{(a) The $m_{\g\g}$ distribution from Monte Carlo simulation
of $\jpsi\ar\g 3(\pip\pin)\eta$; (b) The distribution of
$m_{\pip\pin}$ from $\eta$ signal events (histogram) and $\eta$
sidebands (shaded histogram) for $J/\psi \ar \gamma \gamma 3(\pi^+
\pi^-)$ events.}
\label{m6etapipi}
\end{center}

\end{figure}




%\subsection{Branching Fraction}

Fitting the $\g\g$ mass distribution in Fig.~\ref{eta7pi}  with the
Monte Carlo shape for $\eta$
and a second order polynomial, as described in Section~\ref{4pieta}, yields
616$\pm$ 82 events.

\section{Detection efficiency}
%The detection efficiency of a decay mode is usually obtained
%from Monte Carlo simulation with corresponding generator.
%For the two decay modes analyzed in this paper, there is no 
%specific generator for them.
Initially events were generated according to uniform phase space. 
%The uniform phase space events are generated
%to get their efficiencies.
However, the $\cos\theta$ distribution of charged tracks in $\jpsi\ar
2(\pip\pin)\eta$ was inconsistent with that from Monte Carlo
simulation. Much better agreement is obtained when the angular
distribution is generated according to $1+\alpha\cos^2\theta$, where
$\alpha=0.65\pm 0.03$ is obtained by fitting the $\cos\theta$
distribution of charged tracks.  Fig.~\ref{4picos}(a) and
Fig.~\ref{4picos}(b) show the comparison of the $\cos\theta$ distributions for charged
tracks and $\eta$, respectively, with Monte Carlo simulated events
with the charged tracks generated according to this distribution. 
Including the contribution
from $\eta$ sidebands, the angular distributions are
consistent.



For $\jpsi\ar 3(\pip\pin)\eta$, the 
detection efficiency is obtained from phase 
space events since  the $\cos\theta$ distributions
of charged tracks and $\eta$ are consistent with those from Monte
Carlo simulation,  as shown in Fig.~\ref{6picos}(a) and
Fig.~\ref{6picos}(b), respectively.
For the above two decay
modes, the detection efficiencies are listed in Table~\ref{result}.



\begin{figure}[htpb]
\begin{minipage}[t]{6.5cm}
\begin{center}

\centerline{\includegraphics[width=0.8\textwidth,height=0.3\textheight]
        {4pieta_angle.eps} }
\caption{The $\cos\theta$ distribution of (a) charged tracks and (b)
$\eta$ particles, where the crosses are data, the shaded histogram is from Monte
Carlo simulation of $\jpsi\ar 2(\pip\pin)\eta$, and the full histogram
is the sum of sideband background and Monte Carlo simulation.}
\label{4picos}
\end{center}
\end{minipage}
\hfill
\begin{minipage}[t]{6.5cm}
\begin{center}
\includegraphics[width=0.8\textwidth,height=0.3\textheight]
        {6pieta_angle.eps} 
\caption{The $\cos\theta$ distribution of (a) charged tracks and (b)
  $\eta$ particles, where the crosses are data, the shaded histogram is from Monte
  Carlo simulation of $\jpsi\ar 3(\pip\pin)\eta$, and the full
  histogram is the sum of sideband background and Monte Carlo simulation.}
\label{6picos}
\end{center}
\end{minipage}
\end{figure}



\section{Systematic errors }
\label{syserreta}
The systematic errors mainly come from the following sources:


%\subsection{MDC tracking}
~~(1) The MDC tracking efficiency has been measured using channels like
$\jpsi\ar\Lambda \bar{\Lambda}$ and
$\psi(2S)\ar\pip\pin\jpsi, \jpsi\ar\mu^+\mu^-$. It is found that the Monte
Carlo simulation agrees with data within 1-2\% for each charged track.
Therefore,
8\% and 12\% are taken as the systematic errors in the tracking
efficiencies for the
4-prong and 6-prong final states analyzed here.

%\subsection{Photon detection efficiency}


~~(2) The photon detection efficiency has been studied with different 
methods using $\jpsi\ar\rhoo\pio$ events~\cite{pheff}; the difference
between data and Monte Carlo simulation is about 2\% for each photon. In
this analysis, 4\% is taken as the systematic error for the $\eta$
decaying into  two photons.


%\subsection{Kinematic fit}
~~(3) The kinematic fit is useful to reduce background.  The
systematic error from the kinematic fit is studied using the clean
channel $\jpsi\ar\pip\pin\pio$, as described in Ref.~\cite{rhopi}. The
efficiency difference of the kinematic fit between data and Monte
Carlo simulation is about 4\%. With the same method, the decay modes
$\jpsi\ar 2(\pip\pin)\pio$ and $\jpsi\ar 3(\pip\pin)\pio$ are also
analyzed. The efficiency difference of kinematic fit between data and
Monte Carlo are 4.3\% and 5.5\% respectively. Since $\jpsi\ar
2(\pip\pin)\pio$ and $\jpsi\ar 3(\pip\pin)\pio$ are similar to the two
channels analyzed in this paper, 4.3\% and 5.5\% are taken as the
systematic error of the kinematic fit.

%an important method for selecting events. To estimate the
%systematic error from this source, we should select a clean sample without
%kinematic firstly. In the analysis of $\jpsi\ar\pip\pin\pio$\cite{rhopi},

%It is difficult for us to find a decay mode to select a
%clean sample. In this analysis, the channel $\jpsi\ar 2(\pip\pin)\pio$
%and  $\jpsi\ar 3(\pip\pin)\pio$ are analyzed to estimate the systematic
%error from kinematic fit. The method is described in detail as following:


%\subsection{Particle identification}
%~~(4) The particle identification efficiency of pions is studied
%with the channel $\jpsi\ar 2(\pip\pin)\pio$. The result indicates that the 
%identification efficiency obtained
%from  data is in good agreement with that from Monte Carlo simulation
%(shown
%in Fig. \ref{pid5pi}).
%Therefore the systematic errors from
%particle identification for the two decay modes analyzed in this paper are
%considered to be negligible.

%\begin{figure}[htpb]

%\begin{center}
%\includegraphics[width=0.4\textwidth,height=0.26\textheight]
%        {pipeff1.eps}
%\caption{The $\pip$ particle identification efficiency versus momentum 
%from a study of $\jpsi\ar
%\pip\pin\pip\pin\pio$ events. The dots represent Monte Carlo simulation, and the
%circles are data.  }
%\label{pid5pi}
%\end{center}

%\end{figure}



%Events with four charged tracks and two photons are selected.
%A 4C kinematic fit is performed and the $\chi^2$ is required to be less than
%15. The invariant mass of two photon is required to be in the region
%$|m_{\g\g}-0.135|<0.04$ GeV/$c^2$. To study one charged tracks, the other three
%charged tracks are identified as pions by TOF\& $dE/dx$.





%Fig.\ref{fpid5pi} shows the identified efficiencies of one of charged tracks,
%the dots represent for Monte Carlo simulation and the circles are for
%data.
%The above analysis shows that the identified efficiency obtained
%from  data is consistent with that from Monte Carlo simulation.
%For the decay modes of $\jpsi\ar 2(\pip\pin)\eta$ and  $\jpsi\ar
%3(\pip\pin)\eta$, the systematic error from
%Particle ID can be ignored.


%\subsection{Monte Carlo Model}
%Different models for simulating hadronic interaction also possibly give
%different efficiencies. In the measurement of branching fractions, it will
%lead to the change of results. Take SIMBES for example, FLUKA is set to be
%default for simulating hadronic interaction, but GCALOR also can be used to
%simulate hadronic interaction. In this analysis, the difference between
%the detection efficiencies obtained from Monte Carlo models is less than 5\%
%which is regarded as the systematic error listed in Table~\ref{syserr}.

%\subsection{Monte Carlo statistics}
%\item Background uncertainty

%\subsection{Background uncertainty}
~~(4) Other possible $\jpsi$ decay modes which may contribute to $\eta$ signals have
been studied, and the background from them can be ignored. The error
from the background under the $\eta$ peak is included in the fitting
error.  The uncertainties of the background shape in the two
channels are estimated to be about 3.4\% by changing the order
of the polynomial. Possible background
from the continuum events~\cite{yuancz}
is estimated using data at $\sqrt{s}=3.07$ GeV/c. 
After applying the same selection criteria as above, no significant 
$\eta$ signal is observed. Therefore, the background from this source
is also negligible. From the above analysis, the background uncertainty
for
the two decay modes is less than 5\%, which is taken as the background
systematic error.



%\item Branching fraction of $\eta\ar\g\g$
%\subsection{Branching fraction of $\eta\ar\g\g$}

~~(5) The branching fraction of $\eta\ar\g\g$ is $(39.43\pm0.26)\%$ \cite{pdg2004}. The error is also taken as a
systematic error.

%\item Flux of $\jpsi$ total number

%\subsection{Flux of $\jpsi$ total number}
~~(6) The number of $\jpsi$ events is $(57.70\pm 2.72)\times 10^6$, determined  from
inclusive 4-prong hadrons~\cite{fangss}. The uncertainty,
4.7\%, is
also a systematic error. Table \ref{syserr}
lists
the systematic errors from all sources.

\begin{table}[h] \centering
\caption{\label{toterr}Summary of systematic errors (\%)}
%\mbox{} \hskip -1cm

\begin{tabular}{l|c|c}
\hline
\hline
Source &   $2(\pip\pin)\eta~$ & $3(\pip\pin)\eta~$   \\\hline

MDC Tracking &   8 &12  \\

Photon effieciency &4 & 4 \\
Kinematic fit &4.3 & 5.5  \\

%Particle ID   & ignored & ignored \\

Background & 5 &  5 \\

%MC statistics & 0.99 & 1.73 \\
$B(\eta\ar\g\g)$ & 0.7 & 0.7\\
Number of  $\jpsi$ evetns  & 4.7&4.7\\
\hline
Total  & 12.1 &15.4 \\
 \hline
\hline
\end{tabular}
\label{syserr}\end{table}

%%%%%%%%fah 

\section{Results}

The branching fractions are calculated with the following relation:
\begin{equation}
B(\jpsi\ar n(\pip\pin)\eta)={\frac{N_{obs}}{\eff\cdot B(\eta\ar\g\g)\cdot
N_{\jpsi}}},
\end{equation}

where n is 2 or 3, $N_{obs}$ is the observed events, $\eff$ is the detection
efficiency, $B(\eta\ar\g\g)$ is the branching fraction of  $\eta\ar\g\g$,
and $N_{\jpsi}$ the total number of $\jpsi$ events.

Table~\ref{result} 
summarizes the quantities used in the calculation  of the two
branching fractions and the final results, including systematic errors.
\begin{table}[htpb]
\caption{Numbers used and branching fractions measured.}
\begin{center}
\begin{tabular}{c|c|c|c}
\hline
Decay Modes   & $N_{obs}$ & $\eff$(\%)  & Branching Fraction \\
\hline
$\jpsi\ar 2(\pip\pin)\eta$ & 4839$\pm$158  & 9.43$\pm$0.10  &
$(2.26\pm 0.08 \pm 0.27)\times 10^{-3}$   \\

$\jpsi\ar 3(\pip\pin)\eta$ & 616$\pm$82  & 3.74$\pm$0.06    &
$(7.24\pm 0.96 \pm 1.11)\times 10^{-4}$   \\
\hline
\end{tabular}
\end{center}
\label{result}
\end{table}

\section{Summary}

In this paper, the decays of $\jpsi\ar 2(\pip\pin)\eta$ and $\jpsi\ar
2(\pip\pin)\eta$ are studied with the BESII $5.8\times 10^7$ $J/\psi$
event sample and their branching fractions are 
measured for the first time to be:

\begin{center}
$B(\jpsi\ar 2(\pip\pin)\eta)= (2.26\pm0.08\pm0.27)\times 10^{-3}$
\end{center}
\begin{center}
$B(\jpsi\ar 3(\pip\pin)\eta)= (7.24\pm0.96\pm1.11)\times 10^{-4}$
\end{center}

Comparing with other branching fractions of $\jpsi$ decaying into stable
hadrons, the branching fractions of $\jpsi\ar 2(\pip\pin)\eta$ and 
$\jpsi\ar 3(\pip\pin)\eta$ are not large. 

%Since about half of
%$\jpsi$ decays have not been measured, great efforts are needed  
%to search for the other $\jpsi$ decay modes with $5.8\times 10^7$ 
%$\jpsi$ samples.

%\acknowledgments

   The BES collaboration thanks the staff of BEPC and the computing 
center for their hard efforts.
This work is supported in part by the National Natural Science Foundation
of China under contracts Nos. 19991480, 10225524, 10225525, the Chinese Academy
of Sciences under contract No. KJ 95T-03, the 100 Talents Program of CAS
under Contract Nos. U-11, U-24, U-25, and the Knowledge Innovation Project
of CAS under Contract Nos. U-602, U-34 (IHEP); and by the
National Natural Science Foundation of China under Contract
No.10175060 (USTC), and No. 10225522 (Tsinghua University); and by the
U. S. Department of Energy under Contract N0. DE-FG02-04ER41291.



 \begin{thebibliography}{120}
\bibitem{aube} J. J. Aubert,  et al., Phys. Rev. Lett. 33 (1974) 1404.
\bibitem{augu} J. E. Augustin, et al., Phys. Rev. Lett. 33 (1974) 1406.
\bibitem{physrep} L. Kopke and A. Wermes, Phys. Rep. 174 (1989) 67.
\bibitem{besii} J. Z. Bai, et al., Nucl. Instrum. Methods,
 A458 (2001) 627.
\bibitem{rhopi} J. Z. Bai, et al., Phys. Rev. D70 (2004) 012005.

\bibitem{pdg2004}S. Eidenlman, et al.,(Particle
Data Group), Phys. Lett. B592 (2004) 1, and references therein.

\bibitem{pheff} S. M. Li, et al., High Energy Phys. and Nucl. Phys. 28
(2004) 859 (in Chinese).
%\bibitem{rhopi} J. Z. Bai, {\it et al.}, hep-ex/0402013 
%(submitted to Phys. Rev. D)
\bibitem{yuancz} P. Wang, X. H. Mo, C. Z. Yuan, Phys. Lett.  B557 (2003)
192 

\bibitem{fangss} S. S. Fang,  et al., High Energy Phys. and Nucl. Phys. 27,(2003)
277 (in Chinese).


\end{thebibliography}


\end{document}

hep-ex0411073.extracted_bib
\begin{thebibliography}{120}
\bibitem{aube} J. J. Aubert,  et al., Phys. Rev. Lett. 33 (1974) 1404.
\bibitem{augu} J. E. Augustin, et al., Phys. Rev. Lett. 33 (1974) 1406.
\bibitem{physrep} L. Kopke and A. Wermes, Phys. Rep. 174 (1989) 67.
\bibitem{besii} J. Z. Bai, et al., Nucl. Instrum. Methods,
 A458 (2001) 627.
\bibitem{rhopi} J. Z. Bai, et al., Phys. Rev. D70 (2004) 012005.

\bibitem{pdg2004}S. Eidenlman, et al.,(Particle
Data Group), Phys. Lett. B592 (2004) 1, and references therein.

\bibitem{pheff} S. M. Li, et al., High Energy Phys. and Nucl. Phys. 28
(2004) 859 (in Chinese).
%\bibitem{rhopi} J. Z. Bai, {\it et al.}, hep-ex/0402013 
%(submitted to Phys. Rev. D)
\bibitem{yuancz} P. Wang, X. H. Mo, C. Z. Yuan, Phys. Lett.  B557 (2003)
192 

\bibitem{fangss} S. S. Fang,  et al., High Energy Phys. and Nucl. Phys. 27,(2003)
277 (in Chinese).


\end{thebibliography}