\quad\\[1cm] \Large Search for Charmless Two-body Baryonic Decays of $B$ Mesons
The Belle Collaboration
We report the results of a search for the rare baryonic decays $B^0 \to p\bar{p}$, $\Lambda\bar{\Lambda}$, %$B^0 \to\bar{\Lambda}p\pi^-$ and $B^+ \to p\bar{\Lambda}$. The analysis is based on a data set of $31.7\times 10^6 B\bar{B}$ events collected by the Belle detector at the KEKB $e^+e^-$ collider. %There is a $\sim$4$\sigma$ effect on the observation of %$B^0 \to\bar{\Lambda}p\pi^-$. No statistically significant signals are found, %for other modes, and we set branching fraction upper limits ${\mathcal B}(B^0 \to p\bar{p}) < 1.2 \times 10^{-6}$, ${\mathcal B}(B^0 \to \Lambda\bar{\Lambda}) < 1.0 \times 10^{-6}$, and ${\mathcal B}(B^+ \to p\bar{\Lambda}) < 2.2 \times 10^{-6}$ at the 90\% confidence level.
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\title{
 \quad\\[1cm] \Large
Search for Charmless Two-body Baryonic Decays of $B$ Mesons}

\author{The Belle Collaboration}




\maketitle

% This is the B --> 2-baryon paper's author list.
% Non-responding authors or those who said NO are commented out.
% ====================================================================
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\begin{center}
  K.~Abe$^{7}$,               % KEK
  K.~Abe$^{40}$,              % TohokuGakuin
% N.~Abe$^{43}$,              % TIT
% R.~Abe$^{29}$,              % Niigata
  T.~Abe$^{41}$,              % Tohoku
  I.~Adachi$^{7}$,            % KEK
  Byoung~Sup~Ahn$^{15}$,      % Korea
  H.~Aihara$^{42}$,           % Tokyo
  M.~Akatsu$^{22}$,           % Nagoya
% K.~Asai$^{23}$,             % Nara
% M.~Asai$^{8}$,             % Hiroshima
  Y.~Asano$^{47}$,            % Tsukuba
  T.~Aso$^{46}$,              % Toyama
  V.~Aulchenko$^{1}$,         % BINP
  T.~Aushev$^{12}$,           % ITEP
  A.~M.~Bakich$^{37}$,        % Sydney
  Y.~Ban$^{33}$,              % Peking
  E.~Banas$^{27}$,            % Krakow
% S.~Banerjee$^{38}$,         % Tata
% I.~Bedny$^{1}$,             % BINP
  S.~Behari$^{7}$,            % KEK
  P.~K.~Behera$^{48}$,        % Utkal
% D.~Beiline$^{1}$,           % BINP
  A.~Bondar$^{1}$,            % BINP
  A.~Bozek$^{27}$,            % Krakow
  M.~Bra\v cko$^{20,13}$,     % Ljubljana
  J.~Brodzicka$^{27}$,        % Krakow
  T.~E.~Browder$^{6}$,        % Hawaii
% B.~C.~K.~Casey$^{6}$,       % Hawaii
  P.~Chang$^{26}$,            % Taiwan
  Y.~Chao$^{26}$,             % Taiwan
  B.~G.~Cheon$^{36}$,         % Sungkyunkwan
  K.-F.~Chen$^{26}$,          % Taiwan
  R.~Chistov$^{12}$,          % ITEP
% S.-K.~Choi$^{7}$,           % Gyeongsang
  Y.~Choi$^{36}$,             % Sungkyunkwan
% M.~Danilov$^{12}$,          % ITEP
  L.~Y.~Dong$^{10}$,          % IHEP
% R.~Dowd$^{21}$,             % Melbourne
  J.~Dragic$^{21}$,           % Melbourne
  A.~Drutskoy$^{12}$,         % ITEP
  S.~Eidelman$^{1}$,          % BINP
  V.~Eiges$^{12}$,            % ITEP
  Y.~Enari$^{22}$,            % Nagoya
  C.~W.~Everton$^{21}$,       % Melbourne
  F.~Fang$^{6}$,              % Hawaii
  H.~Fujii$^{7}$,             % KEK
  C.~Fukunaga$^{44}$,         % TMU
  M.~Fukushima$^{9}$,        % ICRR
  N.~Gabyshev$^{7}$,          % KEK
  A.~Garmash$^{1,7}$,         % BINP+KEK
  T.~Gershon$^{7}$,           % KEK
% B.~Golob$^{19,13}$,         % Ljubljana
  A.~Gordon$^{21}$,           % Melbourne
% K.~Gotow$^{49}$,            % VPI
% H.~Guler$^{6}$,             % Hawaii
  R.~Guo$^{24}$,              % Kaohsiung
  J.~Haba$^{7}$,              % KEK
  H.~Hamasaki$^{7}$,          % KEK
% K.~Hanagaki$^{37}$,         % Princeton
  F.~Handa$^{41}$,            % Tohoku
  K.~Hara$^{31}$,             % Osaka
  T.~Hara$^{31}$,             % Osaka
  N.~C.~Hastings$^{21}$,      % Melbourne
  H.~Hayashii$^{23}$,         % Nara
  M.~Hazumi$^{7}$,            % KEK
  E.~M.~Heenan$^{21}$,        % Melbourne
% Y.~Higasino$^{22}$,         % Nagoya
% I.~Higuchi$^{41}$,          % Tohoku
  T.~Higuchi$^{42}$,          % Tokyo
% T.~Hirai$^{43}$,            % TIT
  T.~Hojo$^{31}$,             % Osaka
  T.~Hokuue$^{22}$,           % Nagoya
  Y.~Hoshi$^{40}$,            % TohokuGakuin
% K.~Hoshina$^{45}$,          % TUAT
  S.~R.~Hou$^{26}$,           % Taiwan
  W.-S.~Hou$^{26}$,           % Taiwan
  S.-C.~Hsu$^{26}$,           % Taiwan
  H.-C.~Huang$^{26}$,         % Taiwan
% T.~Igaki$^{22}$,            % Nagoya
  Y.~Igarashi$^{7}$,          % KEK
  T.~Iijima$^{7}$,            % KEK
  H.~Ikeda$^{7}$,             % KEK
% K.~Ikeda$^{23}$,            % Nara
  K.~Inami$^{22}$,            % Nagoya
  A.~Ishikawa$^{22}$,         % Nagoya
% H.~Ishino$^{43}$,           % TIT
  R.~Itoh$^{7}$,              % KEK
  H.~Iwasaki$^{7}$,           % KEK
  Y.~Iwasaki$^{7}$,           % KEK
% D.~J.~Jackson$^{31}$,       % Osaka
  P.~Jalocha$^{27}$,          % Krakow
  H.~K.~Jang$^{35}$,          % Seoul
% M.~Jones$^{6}$,             % Hawaii
% R.~Kagan$^{12}$,            % ITEP
% H.~Kakuno$^{43}$,           % TIT
% J.~Kaneko$^{43}$,           % TIT
  J.~H.~Kang$^{51}$,          % Yonsei
  J.~S.~Kang$^{15}$,          % Korea
% P.~Kapusta$^{27}$,          % Krakow
  N.~Katayama$^{7}$,          % KEK
  H.~Kawai$^{2}$,             % Chiba
  H.~Kawai$^{42}$,            % Tokyo
  Y.~Kawakami$^{22}$,         % Nagoya
% N.~Kawamura$^{1}$,          % Aomori
% T.~Kawasaki$^{29}$,         % Niigata
  H.~Kichimi$^{7}$,           % KEK
  D.~W.~Kim$^{36}$,           % Sungkyunkwan
  Heejong~Kim$^{51}$,         % Yonsei
  H.~J.~Kim$^{51}$,           % Yonsei
  H.~O.~Kim$^{36}$,           % Sungkyunkwan
  Hyunwoo~Kim$^{15}$,         % Korea
  S.~K.~Kim$^{35}$,           % Seoul
  T.~H.~Kim$^{51}$,           % Yonsei
  K.~Kinoshita$^{4}$,         % Cincinnati
% S.~Kobayashi$^{39}$,        % Saga
% S.~Koishi$^{43}$,           % TIT
% H.~Konishi$^{45}$,          % TUAT
% K.~Korotushenko$^{37}$,     % Princeton
  S.~Korpar$^{20,13}$,        % Ljubljana
  P.~Kri\v zan$^{19,13}$,     % Ljubljana
  P.~Krokovny$^{1}$,          % BINP
  R.~Kulasiri$^{4}$,          % Cincinnati
  S.~Kumar$^{32}$,            % Panjab
% T.~Kuniya$^{39}$,           % Saga
% E.~Kurihara$^{2}$,          % Chiba
  A.~Kuzmin$^{1}$,            % BINP
  Y.-J.~Kwon$^{51}$,          % Yonsei
  J.~S.~Lange$^{5,34}$,       % Frankfurt
  G.~Leder$^{11}$,            % Vienna
  S.~H.~Lee$^{35}$,           % Seoul
% A.~Limosani$^{21}$,         % Melbourne
  D.~Liventsev$^{12}$,        % ITEP
  R.-S.~Lu$^{26}$,            % Taiwan
  J.~MacNaughton$^{11}$,      % Vienna
  G.~Majumder$^{38}$,         % Tata
  F.~Mandl$^{11}$,            % Vienna
% D.~Marlow$^{37}$,           % Princeton
% T.~Matsubara$^{42}$,        % Tokyo
% S.~Matsui$^{22}$,           % Nagoya
  T.~Matsuishi$^{22}$,        % Nagoya
  S.~Matsumoto$^{3}$,         % Chuo
% T.~Matsumoto$^{22}$,        % Nagoya
  Y.~Mikami$^{41}$,           % Tohoku
  W.~Mitaroff$^{11}$,         % Vienna
  K.~Miyabayashi$^{23}$,      % Nara
  Y.~Miyabayashi$^{22}$,      % Nagoya
  H.~Miyake$^{31}$,           % Osaka
  H.~Miyata$^{29}$,           % Niigata
% L.~C.~Moffitt$^{21}$,       % Melbourne
  G.~R.~Moloney$^{21}$,       % Melbourne
% G.~F.~Moorhead$^{21}$,      % Melbourne
  S.~Mori$^{47}$,             % Tsukuba
  T.~Mori$^{3}$,              % Chuo
% A.~Murakami$^{39}$,         % Saga
  T.~Nagamine$^{41}$,         % Tohoku
  Y.~Nagasaka$^{8}$,         % Hiroshima
  Y.~Nagashima$^{31}$,        % Osaka
  T.~Nakadaira$^{42}$,        % Tokyo
% T.~Nakamura$^{43}$,         % TIT
  E.~Nakano$^{30}$,           % OsakaCity
  M.~Nakao$^{7}$,             % KEK
% H.~Nakazawa$^{3}$,          % Chuo
  J.~W.~Nam$^{36}$,           % Sungkyunkwan
% S.~Narita$^{41}$,           % Tohoku
  Z.~Natkaniec$^{27}$,        % Krakow
  K.~Neichi$^{40}$,           % TohokuGakuin
  S.~Nishida$^{16}$,          % Kyoto
  O.~Nitoh$^{45}$,            % TUAT
  S.~Noguchi$^{23}$,          % Nara
  T.~Nozaki$^{7}$,            % KEK
  S.~Ogawa$^{39}$,            % Toho
  F.~Ohno$^{43}$,             % TIT
  T.~Ohshima$^{22}$,          % Nagoya
% Y.~Ohshima$^{43}$,          % TIT
  T.~Okabe$^{22}$,            % Nagoya
% T.~Okazaki$^{23}$,          % Nara
  S.~Okuno$^{14}$,            % Kanagawa
  S.~L.~Olsen$^{6}$,          % Hawaii
  W.~Ostrowicz$^{27}$,        % Krakow
  H.~Ozaki$^{7}$,             % KEK
  P.~Pakhlov$^{12}$,          % ITEP
  H.~Palka$^{27}$,            % Krakow
  C.~S.~Park$^{35}$,          % Seoul
  C.~W.~Park$^{15}$,          % Korea
  H.~Park$^{17}$,             % Kyungpook
% K.~S.~Park$^{36}$,          % Sungkyunkwan
  L.~S.~Peak$^{37}$,          % Sydney
  J.-P.~Perroud$^{18}$,       % Lausanne
  M.~Peters$^{6}$,            % Hawaii
  L.~E.~Piilonen$^{49}$,      % VPI
% E.~Prebys$^{37}$,           % Princeton
% J.~L.~Rodriguez$^{6}$,      % Hawaii
% F.~J.~Ronga$^{18}$,         % Lausanne
  N.~Root$^{1}$,              % BINP
  M.~Rozanska$^{27}$,         % Krakow
  K.~Rybicki$^{27}$,          % Krakow
% J.~Ryuko$^{31}$,            % Osaka
  H.~Sagawa$^{7}$,            % KEK
  Y.~Sakai$^{7}$,             % KEK
  H.~Sakamoto$^{16}$,         % Kyoto
% H.~Sakaue$^{30}$,           % OsakaCity
  M.~Satapathy$^{48}$,        % Utkal
  A.~Satpathy$^{7,4}$,        % KEK+Cincinnati
  O.~Schneider$^{18}$,        % Lausanne
  S.~Schrenk$^{4}$,           % Cincinnati
  C.~Schwanda$^{7,11}$,       % KEK+Vienna
  S.~Semenov$^{12}$,          % ITEP
  K.~Senyo$^{22}$,            % Nagoya
% Y.~Settai$^{3}$,            % Chuo
  M.~E.~Sevior$^{21}$,        % Melbourne
  H.~Shibuya$^{39}$,          % Toho
  B.~Shwartz$^{1}$,           % BINP
% A.~Sidorov$^{1}$,           % BINP
  V.~Sidorov$^{1}$,           % BINP
  J.~B.~Singh$^{32}$,         % Panjab
  S.~Stani\v c$^{47,\star}$,  % Tsukuba
  A.~Sugi$^{22}$,             % Nagoya
% A.~Sugiyama$^{22}$,         % Nagoya
  K.~Sumisawa$^{7}$,          % KEK
  T.~Sumiyoshi$^{7}$,         % KEK
% J.-I.~Suzuki$^{7}$,         % KEK
  K.~Suzuki$^{7}$,            % KEK
  S.~Suzuki$^{50}$,           % Yokkaichi
  S.~Y.~Suzuki$^{7}$,         % KEK
  S.~K.~Swain$^{6}$,          % Hawaii
% H.~Tajima$^{42}$,           % Tokyo
  T.~Takahashi$^{30}$,        % OsakaCity
  F.~Takasaki$^{7}$,          % KEK
  M.~Takita$^{31}$,           % Osaka
  K.~Tamai$^{7}$,             % KEK
  N.~Tamura$^{29}$,           % Niigata
  J.~Tanaka$^{42}$,           % Tokyo
  M.~Tanaka$^{7}$,            % KEK
% Y.~Tanaka$^{24}$,           % Nagasaki
  G.~N.~Taylor$^{21}$,        % Melbourne
  Y.~Teramoto$^{30}$,         % OsakaCity
  S.~Tokuda$^{22}$,           % Nagoya
  M.~Tomoto$^{7}$,            % KEK
  T.~Tomura$^{42}$,           % Tokyo
  S.~N.~Tovey$^{21}$,         % Melbourne
  K.~Trabelsi$^{6}$,          % Hawaii
% W.~Trischuk$^{37,\star}$,   % Princeton
% T.~Tsuboyama$^{7}$,         % KEK
  T.~Tsukamoto$^{7}$,         % KEK
  S.~Uehara$^{7}$,            % KEK
  K.~Ueno$^{26}$,             % Taiwan
  Y.~Unno$^{2}$,              % Chiba
  S.~Uno$^{7}$,               % KEK
% Y.~Ushiroda$^{7}$,          % KEK
% S.~E.~Vahsen$^{37}$,        % Princeton
  K.~E.~Varvell$^{37}$,       % Sydney
  C.~C.~Wang$^{26}$,          % Taiwan
  C.~H.~Wang$^{25}$,          % Lien-Ho
  J.~G.~Wang$^{49}$,          % VPI
  M.-Z.~Wang$^{26}$,          % Taiwan
  Y.~Watanabe$^{43}$,         % TIT
  E.~Won$^{35}$,              % Seoul
  B.~D.~Yabsley$^{7}$,        % KEK
  Y.~Yamada$^{7}$,            % KEK
  M.~Yamaga$^{41}$,           % Tohoku
  A.~Yamaguchi$^{41}$,        % Tohoku
  H.~Yamamoto$^{41}$,         % Tohoku
% T.~Yamanaka$^{31}$,         % Osaka
  Y.~Yamashita$^{28}$,        % NihonDental
  M.~Yamauchi$^{7}$,          % KEK
  S.~Yanaka$^{43}$,           % TIT
  J.~Yashima$^{7}$,           % KEK
  P.~Yeh$^{26}$,              % Taiwan
% M.~Yokoyama$^{42}$,         % Tokyo
  K.~Yoshida$^{22}$,          % Nagoya
  Y.~Yuan$^{10}$,             % IHEP
  Y.~Yusa$^{41}$,             % Tohoku
% H.~Yuta$^{1}$,              % Aomori
  C.~C.~Zhang$^{10}$,         % IHEP
  J.~Zhang$^{47}$,            % Tsukuba
% H.~W.~Zhao$^{7}$,           % KEK
  Y.~Zheng$^{6}$,             % Hawaii
  V.~Zhilich$^{1}$,           % BINP
and
  D.~\v Zontar$^{47}$         % Tsukuba
\end{center}

\small
\begin{center}
%%%$^{1}${Aomori University, Aomori}\\
$^{1}${Budker Institute of Nuclear Physics, Novosibirsk}\\
$^{2}${Chiba University, Chiba}\\
$^{3}${Chuo University, Tokyo}\\
$^{4}${University of Cincinnati, Cincinnati OH}\\
$^{5}${University of Frankfurt, Frankfurt}\\
%%%$^{7}${Gyeongsang National University, Chinju}\\
$^{6}${University of Hawaii, Honolulu HI}\\
$^{7}${High Energy Accelerator Research Organization (KEK), Tsukuba}\\
$^{8}${Hiroshima Institute of Technology, Hiroshima}\\
$^{9}${Institute for Cosmic Ray Research, University of Tokyo, Tokyo}\\
$^{10}${Institute of High Energy Physics, Chinese Academy of Sciences,
Beijing}\\
$^{11}${Institute of High Energy Physics, Vienna}\\
$^{12}${Institute for Theoretical and Experimental Physics, Moscow}\\
$^{13}${J. Stefan Institute, Ljubljana}\\
$^{14}${Kanagawa University, Yokohama}\\
$^{15}${Korea University, Seoul}\\
$^{16}${Kyoto University, Kyoto}\\
$^{17}${Kyungpook National University, Taegu}\\
$^{18}${IPHE, University of Lausanne, Lausanne}\\
$^{19}${University of Ljubljana, Ljubljana}\\
$^{20}${University of Maribor, Maribor}\\
$^{21}${University of Melbourne, Victoria}\\
%%%$^{24}${Nagasaki Institute of Applied Science, Nagasaki}\\
$^{22}${Nagoya University, Nagoya}\\
$^{23}${Nara Women's University, Nara}\\
$^{24}${National Kaohsiung Normal University, Kaohsiung}\\
$^{25}${National Lien-Ho Institute of Technology, Miao Li}\\
$^{26}${National Taiwan University, Taipei}\\
$^{27}${H. Niewodniczanski Institute of Nuclear Physics, Krakow}\\
$^{28}${Nihon Dental College, Niigata}\\
$^{29}${Niigata University, Niigata}\\
$^{30}${Osaka City University, Osaka}\\
$^{31}${Osaka University, Osaka}\\
$^{32}${Panjab University, Chandigarh}\\
$^{33}${Peking University, Beijing}\\
%%%$^{37}${Princeton University, Princeton NJ}\\
$^{34}${RIKEN BNL Research Center, Brookhaven NY}\\
%%%$^{39}${Saga University, Saga}\\
$^{35}${Seoul National University, Seoul}\\
$^{36}${Sungkyunkwan University, Suwon}\\
$^{37}${University of Sydney, Sydney NSW}\\
$^{38}${Tata Institute of Fundamental Research, Bombay}\\
$^{39}${Toho University, Funabashi}\\
$^{40}${Tohoku Gakuin University, Tagajo}\\
$^{41}${Tohoku University, Sendai}\\
$^{42}${University of Tokyo, Tokyo}\\
$^{43}${Tokyo Institute of Technology, Tokyo}\\
$^{44}${Tokyo Metropolitan University, Tokyo}\\
$^{45}${Tokyo University of Agriculture and Technology, Tokyo}\\
$^{46}${Toyama National College of Maritime Technology, Toyama}\\
$^{47}${University of Tsukuba, Tsukuba}\\
$^{48}${Utkal University, Bhubaneswer}\\
$^{49}${Virginia Polytechnic Institute and State University, Blacksburg VA}\\
$^{50}${Yokkaichi University, Yokkaichi}\\
$^{51}${Yonsei University, Seoul}\\
%%%$^{\star}${on leave from University of Toronto, Toronto ON}
$^{\star}${on leave from Nova Gorica Polytechnic, Slovenia}
\end{center}

\normalsize



% to make it single spaced
\tighten

\begin{abstract}



We report the results of a search for the rare baryonic decays 
$B^0 \to p\bar{p}$, $\Lambda\bar{\Lambda}$, 
%$B^0 \to\bar{\Lambda}p\pi^-$
and $B^+ \to p\bar{\Lambda}$.
The analysis is based on a
data set of $31.7\times 10^6 B\bar{B}$ events collected by the 
Belle detector at the KEKB $e^+e^-$
collider.  
%There is a $\sim$4$\sigma$ effect on the observation of
%$B^0 \to\bar{\Lambda}p\pi^-$.  
No statistically significant signals are
found, 
%for other modes, 
and we set branching fraction upper limits
${\mathcal B}(B^0 \to p\bar{p}) < 1.2 \times 10^{-6}$, 
${\mathcal B}(B^0 \to \Lambda\bar{\Lambda}) < 1.0 \times 10^{-6}$, and 
${\mathcal B}(B^+ \to p\bar{\Lambda}) < 2.2 \times 10^{-6}$ 
at the 90\% confidence level.



\end{abstract}
%
%
%
\pacs{PACS numbers: 13.20.H }  



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\pagestyle{plain}      

%CLEO at CESR and experiments at the two B-factories, BABAR
%at PEPII and Belle\cite{Belle} at KEKB\cite{KEKB}, have observed many 
%charmless decays of $B$ mesons into final states with mesons.
%Theoretical models also predict charmless decays with baryons
%in the final state\cite{Theory}, but these have not yet been observed.
%The CLEO experiment has published\cite{CLEO} a search
%for exclusive rare baryonic decays with an accumulated luminosity of
%5.41 fb$^{-1}$ on the $\Upsilon(4S)$ resonance.
%We perform the same search with about six times more 
%integrated luminosity,
%$31.7 \times 10^6 B\bar{B}$ pairs, for the rare baryonic decays   
%$B^0 \to p\bar{p}$, $B^0 \to \Lambda\bar{\Lambda}$, 
%$B^0 \to\bar{\Lambda}p\pi^-$
% and $B^+ \to p\bar{\Lambda}$.\footnote{The charge conjugate states are also
% included unless specifically mentioned.}  

  The Belle collaboration recently reported the observation of the
  decay process $B^+ \to p\bar{p}K^+$\cite{ppk}, which is the first known
  example of a $B$ meson decay to a charmless final state
  containing baryons. In this paper we report the results of
  a search for the related two-body modes $B^0\to
  p\bar{p}$, $\Lambda\bar{\Lambda}$  and 
 $B^+\to p\bar{\Lambda}$\cite{foot}.  In the
  Standard Model, these decays are expected to proceed via
  color-suppressed  $b\to u$ tree diagrams (Figs.~1(a) and (c)) and
  $b\to s,~d$ penguin diagrams (Figs.~1(b) and (d)).  The search is based
  on a 29.4 fb$^{-1}$  sample of $e^+e^-$ data accumulated at the
  $\Upsilon(4S)$ resonance, which contains 31.7 million $B\bar{B}$
  pairs.   A previous search for these decays by the
  CLEO collaboration using a 5.41~fb$^{-1}$ sample of
  $\Upsilon(4S)$ data yielded 90\% confidence-level (C.L.) 
  upper limits\cite{CLEO}.   




%The CLEO Collaboration, and more recently the Belle and BaBar Collaborations, 
%have observed many $B$ decay modes to charmless mesonic final states such as
%$B \to K\pi, \pi\pi$ [1-3].
%%$\cite{Meson1}\cite{Meson2}\cite{Meson3}. 
%In contrast, the most recent search for
%exclusive charmless baryonic final states\cite{CLEO} is based on 
%only 5.41 fb$^{-1}$ of data on 
%the $\Upsilon(4S)$
%resonance. 
%Such $B$ decay processes, though more complicated,  
%are expected to exist\cite{Theory}; we illustrate in Fig.~1 with 
%simple decay diagrams. In this paper, we report on our
%search for two-body charmless modes $B^0 \to p\bar{p}$,  
%$\Lambda\bar{\Lambda}$, and $B^+ \to p\bar{\Lambda}$\cite{foot}, 
%based on 29.4 
%fb$^{-1}$ of $\Upsilon(4S)$ data, or 31.7 million $B\bar{B}$ pairs.
%This offers a unique  opportunity to study weak decays of $B$ mesons into
%baryon anti-baryon pairs which is not possible for $D$ mesons.

\begin{figure}[t]
\centering
\vspace{-1pc}
\epsfig{figure=feyn.eps,width=3.5in}
\centering
\caption{
Illustrative diagrams for $B$ decays to charmless baryon pairs.}
\label{Feyn}
\end{figure} 

Belle\cite{Belle} is a general purpose detector 
operating at the KEKB asymmetric $e^+e^-$ collider\cite{KEKB}. 
Tracking information is provided by a
silicon vertex detector  and a central drift chamber (CDC) in
a 1.5 Tesla magnetic field.
Hadron identification (PID) for $\pi/K/p$ 
discrimination is obtained from
CDC $dE/dx$ measurements, aerogel
${\check{\rm C}}$erenkov counter pulse heights, 
and timing information from the time-of-flight  system.
Electron identification is based mainly on CsI(Tl) electromagnetic
calorimeter and CDC $dE/dx$ information. $K_L$ and muons are 
identified by a 
system of resistive plate counters interleaved with 
the iron plates of the flux-return iron yoke.
 
The event selection criteria are based on tracking and PID
requirements, and are optimized using Monte Carlo (MC)
simulated event samples.

All primary charged tracks 
are required to satisfy the following track quality 
criteria based on
the track impact parameters relative to the   
interaction point (IP), which is determined run-by-run.
The $z$ axis is defined by the positron beam line.
The deviations from the IP position are required to be within
$\pm$0.05 cm in the transverse ($x$-$y$) plane, and within $\pm$2 cm
in the $z$ direction.
%Tracks with hits in the KLM system and muon likelihood ratio greater
%than 0.95, or tracks with showers in ECL 
%and electron likelihood ratio greater than 0.95, are rejected. 
Tracks that satisfy the muon or electron identification
requirements are rejected.

Primary proton candidates are selected based
on $p/K/\pi$ likelihood functions
obtained from the hadron identification system. 
The selection criteria are
${L_p \over {L_p+L_K}}> 0.6 $ and  ${L_p \over {L_p+L_{\pi}}}> 0.6$,
where $L_{p/K/\pi}$ stands for the proton/kaon/pion likelihood. 

$\Lambda$ candidates are reconstructed via the $p\pi^-$ decay channel and
are selected using cuts on four parameters:
% by four parameters which are tabulated 
%according to three different momentum ranges. Parameters used are
the angular difference between the $\Lambda$ flight direction
and the direction pointing from IP to the decay vertex in the
transverse plane; the distance between each track and the
IP in the transverse plane; the distance between the decay vertex and
the IP in the transverse plane; 
and the displacement in $z$ of the closest approach points of
the two tracks to the beam axis. The secondary protons are required
to have ${L_p \over {L_p+L_{\pi}}}> 0.6$. 
The $p\pi^-$ mass spectrum after the application of
the above selection criteria is shown
in Fig.~2 for a typical run period. 
%fitted with a Gaussian and a $2^{nd}$ order polynomial gives a mass 
The peak position is consistent with the nominal $\Lambda$ mass
\cite{pdg} and the mass resolution is about 0.9 MeV/$c^2$. 
Finally, we require the invariant mass of the $\Lambda$ candidate 
%formed by these two tracks 
%with the appropriate proton and pion mass assignments
to be within $\pm$5 MeV/$c^2$ of the nominal
$\Lambda$ mass.

%Since the background
%levels for decay modes containing $\Lambda$'s are very low, 
%there is  
%few $B$ candidates were 
%found in the 
%no requirement on the PID likelihoods for the secondary proton
%from the $\Lambda$ decay was applied.


\begin{figure}[t]
\centering
\vspace{-1.5pc}
\epsfig{figure=lam.eps,width=2.4in}
\label{Lam}
\centering
\caption{
The mass distribution of the selected $\Lambda \to p \pi^-$ 
candidates for 
a typical run period. The MC distribution is shown as a dashed
histogram.
The $\pm 5$ MeV mass window is indicated by the vertical arrows.}
\end{figure}


%Due to very few  $\Lambda$ candidates and  
Due to the high momentum of the primary particles 
from these two-body decay modes,
the background from generic $B$ decays is negligible.
%contribute 
%negligibly in the candidate region. 
%in the searched final states, 
This is checked with  MC samples of $B^+B^-$ and  
$B^0\bar{B^0}$ pairs where the $B$-mesons decay dominantly via 
$b \to c$ processes. We also checked 
backgrounds using MC samples of charmless $B$ meson decays 
that include low multiplicity $B$ decays into 
final states with $\pi$,
$K$, $K^*$, $\rho$, $\omega$, $\phi$, $\eta$, and $\eta^\prime$ mesons.
%The data size  corresponds to
%150 million $B^0\bar{B^0}$ and 190 million $B^+B^-$ pairs.
Only the $p\bar{p}$ mode is found to have any background
contamination. However, the level of this contamination is negligible,
corresponding to less than one event for the current data set.

The main background is from continuum $q\bar{q}$ processes. 
This is confirmed using
an off-resonance data set (2.3 fb$^{-1}$ taken 60 MeV 
below the $\Upsilon(4S)$) and a MC sample of 
65 million continuum events.
%running 5 million `uds' MC samples and 3 million `charm' MC samples.
%We also took `continuum' data outside $\Upsilon(4S)$ resonance region
%to background control.
These continuum events have a jet-like topology while
$B\bar{B}$ events are more spherical in the $\Upsilon(4S)$ center 
of mass (CM) frame. 
For continuum event rejection we use 
$\cos\theta_T$, the cosine of the angle between 
the direction of one primary decay particle and the 
thrust axis\cite{thrust} of the non-candidate tracks and showers.
%two `thrust' axes. 
%The first axis
%is taken as the
%direction of one primary  $B$ decay daughter. 
%The second axis is determined by 
%final-state particles excluding the ones which reconstruct candidate $B$.
% such that it has the
%minimum transverse
%momentum sum. For signal, 
This distribution is nearly flat for signal events and is strongly
peaked at $\pm$1 for continuum background.
We also use $\cos\theta_B$, the cosine of the angle between
the  $B$ candidate flight direction and
the positron beam direction. 
%Due to the angular momentum
%consideration, 
The signal has a $\sin^2\theta_B$ distribution
while the background is uniformly distributed.
We require the absolute values of $\cos\theta_T$ and $\cos\theta_B$ to be
less than 0.9 for $\Lambda\bar{\Lambda}$ decays and less than 0.8 for 
the other modes. For the latter case, the background reduction 
factor is more than five, while $\sim$70\% of the signal is retained.           




%% Typical table
%h:here t:top b:bottom
\begin{table}[t]
\twocolumn[\hsize\textwidth\columnwidth\hsize\csname
@twocolumnfalse\endcsname    

\caption{Results of search for the exclusive baryon modes. 
The signal yields,
{\it Y}, and errors are determined from
maximum likelihood fits. The 90\% C.L. upper limits from the fits
and from the counting method are listed together. We quote the higher
values as our conservative estimates for upper limits. 
The efficiencies, $\varepsilon$, are obtained from MC.
The 90\% C.L. upper limits for the
 branching fractions, {$\mathcal B$},
determined by this experiment
are shown along with previous CLEO results.}
%and the
%systematic errors are the errors related to two different methods to
%determine {$\mathcal B$}'s.
%For a comparison,
\medskip
\label{xsyield}
\begin{tabular}{cccccc}
{Mode} &
{\it Y} &
UL (fitting/counting) &              
{$\varepsilon$ (\%)} &
{$\mathcal B$}$(10^{-6})$ &
{CLEO $\mathcal B$}$(10^{-6})$
\\
\hline
$p\bar{p}$ &
$0.6^{+2.7}_{-0.6}$ &
7.0/9.7 &
$27.5 \pm 2.0$ &
$< 1.2$ &
$< 7.0$
\\
$\Lambda\bar{\Lambda}$ &
$0.0^{+0.5}_{-0.0}$ &
3.0/3.2 &
$10.8 \pm 1.1$ &
$< 1.0$ &
$< 3.9$
\\
$p\bar{\Lambda}$ &     
$1.0^{+2.5}_{-1.0}$ &
7.0/10.4 &
$16.2 \pm 1.4$ &
$< 2.2$ &
$< 2.6$ 
\end{tabular}
\vskip1pc
]       
\end{table}




We use the following two kinematic variables to identify the reconstructed
$B$ meson candidates: 
the beam constrained mass, $m_{\rm bc} =
\sqrt{E^2_{\rm beam}-p^2_B}$, and the energy difference, $\Delta{E} =
E_B - E_{\rm beam}$, where $E_{\rm beam}$, $p_B$ and $E_B$ are 
the beam energy, the
momentum and energy of the reconstructed $B$ meson in the $\Upsilon(4S)$
CM frame, respectively. 
%The signal is peaked at 5.28 GeV
%in $ m_{\rm bc}$ and at zero in $\Delta{E}$.
%We also use the side-band region 5.20
%GeV $< m_{\rm bc} <$ 5.26 GeV and 
%0.1 GeV $< |\Delta{E}| <$ 0.2 GeV to study the
%background shapes of $m_{\rm bc}$ and $\Delta{E}$.
We retain events with   5.20
GeV/$c^2$ $< m_{\rm bc} <$ 5.29 GeV/$c^2$ and 
$-0.2$ GeV $< \Delta{E} <$ 0.2 GeV.
The signal yield is extracted 
%within 5.20
%GeV/$c^2$ $< m_{\rm bc} <$ 5.29 GeV/$c^2$ and $-0.20$ GeV $< \Delta{E} <$ 0.20 GeV
by maximizing the likelihood function 
%$$ L = \prod_{i=1}^{N} [f_sP_s(m_{{\rm bc}_i},\Delta{E}_i)+
%(1-f_s)P_b(m_{{\rm bc}_i},\Delta{E}_i)],$$
%where $P_{s(b)}$ denotes the signal (background) pdf and $f_s$ is 
%the fitting parameter which represents  the signal
%fraction of the total $N$ candidates.  
$$ L = e^{-(s+b)}\prod_{i=1}^{N} [sP_s(m_{{\rm bc}_i},\Delta{E}_i)+
bP_b(m_{{\rm bc}_i},\Delta{E}_i)],$$
where $N$ is the total number of candidate events, $s(b)$ denotes 
the signal (background)
yield and $P_{s(b)}$ denotes the signal (background) probability
density function (pdf).    
                                                                   

%After the final selection, the effective efficiencies (i.e. the branching
%fraction 64\% of $\Lambda$ decaying into $p\pi$ is included)
%of these three modes are shown in Table~1. 
%CLEO's numbers are also shown. 
%Note their selection cuts are less stringent than ours.  

The $m_{\rm bc}$ and $\Delta{E}$ signal pdf's are determined by MC.
%We use Gaussian distributions to model the signal
%pdf's for both $m_{\rm bc}$ and $\Delta{E}$. 
We use a Gaussian function as the signal
pdf for the $m_{\rm bc}$ distribution and a sum of two Gaussians 
%as the signal pdf 
for the  $\Delta{E}$ distribution.  The
Gaussian parameters (mean and $\sigma$) are
determined separately for each mode. 
Background shapes are determined from
events in sideband regions of $\Delta{E}$ and $m_{\rm bc}$ separately.
We adopt an empirical function\cite{Argus} to model 
the $m_{\rm bc}$ background shape 
(for events with  0.1 GeV $< |\Delta{E}| <$ 0.2 GeV)
and a first-order polynomial for the
$\Delta{E}$ background shape (for events with 5.20
GeV/$c^2$ $< m_{\rm bc} <$ 5.26 GeV/$c^2$).   


Table~1 summarizes the results. The efficiencies for the
$\Lambda\bar{\Lambda}$ and $p\bar{\Lambda}$ modes include
the $\Lambda \to p\pi^-$ branching fraction (64\%). The efficiencies
are determined from signal MC 
%(added with $\sim$ 60 million continuum background) 
with the identical event selection and fitting procedure as
for the data.
Figures~3 and 4 show the 
%projected distributions of
$m_{\rm bc}$ (with $|\Delta{E}| < 0.05$ GeV)  and $\Delta{E}$ (with
5.27 GeV/$c^2$ $< m_{\rm bc} < $ 5.29 GeV/$c^2$) projections for these 
three modes, respectively.
%Fit projections with the
%nominal fit shown as a smooth curve are shown.
Projections of the fits are shown as smooth curves.
%There are some enhancement in the $\bar{\Lambda}p\pi^-$ mode.
%About 15 signal events are obtained with statistical
%fluctuation of 5 events. The significance from the fit is 3.7 $\sigma$
%away from zero event.
No statistically significant signals are found and we determine 
90\% C.L. upper
limits on the signal yields 
by integrating the likelihood function.
%requiring $$ {{\int_0^{UL} L df_s}
%\over {\int_0^1 L df_s}} = 0.90.$$ 
%We also compute limits using a counting method\cite{Gary}.
%The nominal signal region 
%is defined as 5.27 GeV/$c^2$ $< m_{\rm bc} <$ 5.29 GeV/$c^2$ and $-0.05$ 
%GeV $< \Delta{E} <$ 0.05 GeV. 
%From the number of expected background events predicted by the fit and
%observed events in the signal region, we calculate
%the upper limit for the signal yield at 90\% C.L.
We also compute limits using a counting method\cite{Gary}. We define
a signal region by 5.27 GeV/$c^2$ $< m_{\rm bc} <$ 5.29 GeV/$c^2$ and
                $|\Delta{E}| < 0.05$ GeV, and treat the number of
background events from the maximum likelihood fit as a
                prediction for the background in this region. We then
                count the number of events actually observed, and apply
                the method of \cite{Gary} to obtain 90\% C.L. 
                intervals.     

To estimate the possible influence of fluctuations on the
determination of the upper limits,
we vary the parameters of the pdf's by one standard deviation and
change the form of the $\Delta{E}$ signal pdf to a single Gaussian.
%change the form of signal pdf's to double Gaussians. 
%We also use $\Delta{E}$ only to determine
%the signal yields. 
The relative change of the upper limit is 25\%, which
is mainly due to the changes in the background shape. 
The upper limit determination  by the counting method is checked by
redefining the signal region (varying the $\Delta{E}$ range from 2$\sigma$ to 
4$\sigma$) and comparing the outcomes.  The
upper limits from both methods listed in column 3 of Table~1
include these fluctuations.
%take these fluctuations into account. 
We quote the values from the counting method as the most conservative
upper limits.
Fit projections  with the signal yield fixed at the upper limit 
for each mode
are shown as the superimposed dashed curves in 
Figs.~3 and 4 for comparison.


\begin{figure}[t]
\centering
\vspace{-1.5pc}
\epsfig{figure=mergemb.eps,width=3.3in}
\label{mergemb}
\centering
\caption{
The distributions of $m_{\rm bc}$ for (a) $B^0\to p\bar{p}$, (b)
$B^0\to \Lambda\bar{\Lambda}$ and (c) $B^+\to p\bar{\Lambda}$ candidates.
         The solid curve is the projection of the maximum likelihood fit. 
The dashed curve shows the fit with the signal yield
fixed at the 90\% C.L. upper limit.
}
\end{figure}

\begin{figure}[t]
\centering
\vspace{-1.5pc}
\epsfig{figure=mergede.eps,width=3.3in}
\label{mergede}
\centering
\caption{
The distributions of $\Delta{E}$ for (a) $B^0\to p\bar{p}$, (b)
$B^0\to \Lambda\bar{\Lambda}$ and (c) $B^+\to p\bar{\Lambda}$ candidates.
         The solid curve is the projection of the maximum likelihood fit.
The dashed curve shows the fit with the signal yield
fixed at the 90\% C.L. upper limit. 
}
\end{figure}



      
The systematic error due to the efficiency of the
proton identification ($p$-$K$ and $p$-$\pi$) criteria
is studied using $\Lambda$ samples. 
We vary the likelihood ratio requirement for protons and compare the
ratio of reconstructed $\Lambda$ yields in data and MC. The overall error 
is about 3\%. 
We include a 2\% error per track to account 
for the uncertainty in tracking efficiency. 
%It is about 1.5\% discrepancy for protons with momenta 
%less than 1.5 GeV and 3.5\% for high momentum protons. 
The $\Lambda$ reconstruction efficiency is checked by comparing the
flight distance distributions of data and MC. They agree very well 
and no additional error is assigned. 
%We assign 10\% error 
%for each $\Lambda$ due to the uncertainty of the decay angular distributions
%of secondary  protons. 
%polarization effect which can not be
%determined with such low statistics.   
%The systematic error on the efficiency determination is studied by the
%tracking group and the PID group via calibration modes to compare
%data with MC, we quote 3\% error per track. The proton likelihood
%ratios against kaon and the  transverse flight distance
%of $\Lambda decays$ for data and MC are shown in
%Fig.~\ref{hi} and Fig.~\ref{low}, for two different $\Lambda$ momentum
%ranges. The error of $\Lambda$ identification is at 10\% level.
The correlated parts of the errors are added
linearly to obtain
the overall uncertainty in the tracking efficiency and the uncertainty 
in the PID efficiencies (for $p$ and $\bar{p}$), then the
resulting errors are combined in quadrature. 
When determining the upper limit for the
branching fraction, the efficiency was reduced by one standard deviation.
The efficiencies and upper limits for all three decay modes
are listed in Table 1. 




%Tighter selection criteria can be imposed to
%reduce background. The surviving events are assumed to be background
%and the numbers are between 1 to 4. Due to the change in the
%efficiency and yields in the signal region, 
%the upper limits for the branching fractions increase by 90\%, 15\%, 
%and 40\% for $p\bar{p}$,
%$\Lambda\bar{\Lambda}$, and $p\bar{\Lambda}$, 
%respectively. We quote the larger error from the two different approaches
%as a systematic error. The results are given in Table~1. 


In summary, we have performed a search for 
the rare baryonic decays $B^0 \to p\bar{p}$, 
$\Lambda\bar{\Lambda}$, %$B^0 \to\bar{\Lambda}p\pi^-$
and $B^+ \to p\bar{\Lambda}$ with 
31.7 million $B\bar{B}$ events collected by the Belle detector 
at the KEKB $e^+e^-$
collider.  
%There is a 3.7 $\sigma$ effect on the observation of
%$B^0 \to\bar{\Lambda}p\pi^-$. The branching fraction is determined
%to be: $9.5^{+3.6}_{-3.2}\pm2.2 \times 10^{-6}$.
No statistically significant signals are found for these modes, and we set
upper limits on their branching fractions at 
the 90\% C.L.. The upper limits are:
\begin{eqnarray*}
{\mathcal B}(B^0 &\to p\bar{p}&) < 1.2 \times 10^{-6};     \\
{\mathcal B}(B^0 &\to \Lambda\bar{\Lambda}&) < 1.0 \times 10^{-6}; \\
{\mathcal B}(B^+ &\to p\bar{\Lambda}&) <  2.2 \times 10^{-6}.
\end{eqnarray*} 


These are currently the most stringent limits for these
decays. The limit 
on $B^0 \to p\bar{p}$ has been improved by a factor of six 
compared to the existing bound\cite{CLEO}. 
These limits are considerably below corresponding 
charmless mesonic branching fractions which are typically at the level
of $10^{-5}$.  
In contrast, the recent Belle  measurement of 
$B^+ \to p\bar{p}K^+$\cite{ppk} 
indicates a relatively large
branching fraction of $4.3 \times 10^{-6}$. 
The underlying physics\cite{Theory} is now being probed
with  rapidly accumulating data and new experimental results.  

   

%The more stringent limits in two-body decays indicate that we need much
%more data to positively identify these exclusive rare baryonic decays. 


%% Please paste this acknowledgement into your latex file.

We wish to thank the KEKB accelerator group for the excellent
operation of the KEKB accelerator.
We acknowledge support from the Ministry of Education,
Culture, Sports, Science, and Technology of Japan
and the Japan Society for the Promotion of Science;
the Australian Research Council
and the Australian Department of Industry, Science and Resources;
the National Science Foundation of China under contract No.~10175071;
the Department of Science and Technology of India;
the BK21 program of the Ministry of Education of Korea
and the CHEP SRC program of the Korea Science and Engineering Foundation;
the Polish State Committee for Scientific Research
under contract No.~2P03B 17017;
the Ministry of Science and Technology of the Russian Federation;
the Ministry of Education, Science and Sport of Slovenia;
the National Science Council and the Ministry of Education of Taiwan;
and the U.S.\ Department of Energy. 

\begin{thebibliography}{99}
%\bibitem{Meson1}
%CLEO Collaboration, R. Godang {\it et al.}, Phys. Rev. Lett. {\bf 80}, 
%3456 (1998). 
%\bibitem{Meson2}
%Belle Collaboration, K. Abe {\it et al.}, Phys. Rev. Lett. {\bf 87}, 
%101801  (2001). 
%\bibitem{Meson3}
%BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. Lett. {\bf 87}, 
%151802 (2001)  

\bibitem{ppk}
Belle Collaboration, K. Abe {\it et al.}, hep-ex/0202017. 


%\bibitem{Rare}Belle Collaboration, P. Chang, Proc. XXXth Int. Conf. on High
%              Energy Phys. (ICHEP00), World Scientific, Singapore, 2001, to
%              be published.
%              BABAR Collaboration, T. Champion, Proc. ICHEP00,
%              World Scientific, Singapore, 2001, to be published.


%\bibitem{foot} {The charge conjugate states are also
%included unless specifically mentioned.}  
\bibitem{foot} {
Charge-conjugate processes are included throughout the
                analysis.}


\bibitem{CLEO}CLEO Collaboration, T.E. Coan {\it et al.}, Phys.
Rev. {\bf D 59}, 111101 (1999).
 
\bibitem{Belle}{
  	Belle Collaboration, A. Abashian {\it et al.},
	KEK Progress Report 2000-4 (2000),
	to be published in Nucl. Inst. and Meth. A.
}

\bibitem{KEKB}{
	E. Kikutani ed., KEKB Accelerator, KEK Preprint 2001-157 (2001), 
        to be published in Nucl. Inst. and Meth. A.
%        KEKB B Factory Design Report, KEK Report 95-7 (1995),
%	unpublished; Y. Funakoshi {\it et al.}, Proc. 2000
%        European Particle Accelerator Conference, Vienna (2000).
}


\bibitem{pdg}{
  	Particle Data Group, D.E. Groom {\it et al.},
	Eur. Phys. J. C {\bf 15}, 1 (2000).
} 


\bibitem{thrust} E. Farhi, Phys. Rev. Lett. {\bf 39}, 1587 (1977).  

\bibitem{Argus}H. Albrecht {\it et al.}, Phys. Lett. B {\bf 241}, 278 (1990);
H. Albrecht {\it et al.}, {\it ibid}. {\bf 254}, 288 (1991). 

\bibitem{Gary} G.J. Feldman and R.D. Cousins, Phys. Rev. D {\bf 57}, 
               3873 (1998).

%\bibitem{geant}{ 
%	R. Brun {\it et al.}, GEANT 3.21, CERN Report No. DD/EE/84-1 (1987).
%}


\bibitem{Theory}{
    N. Deshpande, J. Trampetic, and A. Soni, Mod. Phys. Lett. A {\bf 3},
     749 (1988);
    V. Chernyak and I. Zhitnitsky, Nucl. Phys. B {\bf 345}, 137 (1990);
     M. Jarfi, {\it et al.}, Phys. Lett. B {\bf 237}, 513 (1990);
          M. Jarfi {\it et al.}, Phys. Rev. D {\bf 43}, 1599 (1991);
      S.M. Sheikholeslami and
     M.P. Khanna, Phys. Rev. D {\bf 44}, 770 (1991);
     Y. Kohara, Nuovo Cim. A {\bf 104}, 555 (1991);
     T. Mannel, W. Roberts, and Z. Ryzak, Phys. Rev. D {\bf 45}, 875 (1992);  
     G. Kaur and \break\hfil 
     M.P. Khanna, Phys. Rev. D {\bf 46}, 466 (1992);
     W.S. Hou and A. Soni, Phys. Rev. Lett. {\bf 86}, 4247 (2001);
     C.K. Chua, W.S. Hou and S.Y. Tsai, hep-ph/0108068;
     H.Y. Cheng and K.C. Yang, hep-ph/0112245.     }


\end{thebibliography}

\end{document}







hep-ex0203027.extracted_bib
\begin{thebibliography}{99}
%\bibitem{Meson1}
%CLEO Collaboration, R. Godang {\it et al.}, Phys. Rev. Lett. {\bf 80}, 
%3456 (1998). 
%\bibitem{Meson2}
%Belle Collaboration, K. Abe {\it et al.}, Phys. Rev. Lett. {\bf 87}, 
%101801  (2001). 
%\bibitem{Meson3}
%BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. Lett. {\bf 87}, 
%151802 (2001)  

\bibitem{ppk}
Belle Collaboration, K. Abe {\it et al.}, hep-ex/0202017. 


%\bibitem{Rare}Belle Collaboration, P. Chang, Proc. XXXth Int. Conf. on High
%              Energy Phys. (ICHEP00), World Scientific, Singapore, 2001, to
%              be published.
%              BABAR Collaboration, T. Champion, Proc. ICHEP00,
%              World Scientific, Singapore, 2001, to be published.


%\bibitem{foot} {The charge conjugate states are also
%included unless specifically mentioned.}  
\bibitem{foot} {
Charge-conjugate processes are included throughout the
                analysis.}


\bibitem{CLEO}CLEO Collaboration, T.E. Coan {\it et al.}, Phys.
Rev. {\bf D 59}, 111101 (1999).
 
\bibitem{Belle}{
  	Belle Collaboration, A. Abashian {\it et al.},
	KEK Progress Report 2000-4 (2000),
	to be published in Nucl. Inst. and Meth. A.
}

\bibitem{KEKB}{
	E. Kikutani ed., KEKB Accelerator, KEK Preprint 2001-157 (2001), 
        to be published in Nucl. Inst. and Meth. A.
%        KEKB B Factory Design Report, KEK Report 95-7 (1995),
%	unpublished; Y. Funakoshi {\it et al.}, Proc. 2000
%        European Particle Accelerator Conference, Vienna (2000).
}


\bibitem{pdg}{
  	Particle Data Group, D.E. Groom {\it et al.},
	Eur. Phys. J. C {\bf 15}, 1 (2000).
} 


\bibitem{thrust} E. Farhi, Phys. Rev. Lett. {\bf 39}, 1587 (1977).  

\bibitem{Argus}H. Albrecht {\it et al.}, Phys. Lett. B {\bf 241}, 278 (1990);
H. Albrecht {\it et al.}, {\it ibid}. {\bf 254}, 288 (1991). 

\bibitem{Gary} G.J. Feldman and R.D. Cousins, Phys. Rev. D {\bf 57}, 
               3873 (1998).

%\bibitem{geant}{ 
%	R. Brun {\it et al.}, GEANT 3.21, CERN Report No. DD/EE/84-1 (1987).
%}


\bibitem{Theory}{
    N. Deshpande, J. Trampetic, and A. Soni, Mod. Phys. Lett. A {\bf 3},
     749 (1988);
    V. Chernyak and I. Zhitnitsky, Nucl. Phys. B {\bf 345}, 137 (1990);
     M. Jarfi, {\it et al.}, Phys. Lett. B {\bf 237}, 513 (1990);
          M. Jarfi {\it et al.}, Phys. Rev. D {\bf 43}, 1599 (1991);
      S.M. Sheikholeslami and
     M.P. Khanna, Phys. Rev. D {\bf 44}, 770 (1991);
     Y. Kohara, Nuovo Cim. A {\bf 104}, 555 (1991);
     T. Mannel, W. Roberts, and Z. Ryzak, Phys. Rev. D {\bf 45}, 875 (1992);  
     G. Kaur and \break\hfil 
     M.P. Khanna, Phys. Rev. D {\bf 46}, 466 (1992);
     W.S. Hou and A. Soni, Phys. Rev. Lett. {\bf 86}, 4247 (2001);
     C.K. Chua, W.S. Hou and S.Y. Tsai, hep-ph/0108068;
     H.Y. Cheng and K.C. Yang, hep-ph/0112245.     }


\end{thebibliography}