\quad\\[0.5cm] Measurements of Branching Fractions and $CP$ Asymmetries in $B\to \eta h$ Decays
P.~Chang
We report measurements of $B$ to pseudoscalar-pseudoscalar decays with at least one $\eta$ meson in the final state using $140 \mathrm{~fb}^{-1}$ of data collected by the Belle detector at KEKB $e^+ e^-$ collider. We observe the decay $\btoetapi$ and find evidence of $\btoetak$; the measured branching fractions are $\br(\btoetapi) = ( 4.8^{+0.8}_{-0.7} \mathrm{(stat)} \pm 0.3 \mathrm{(sys)}) \times 10^{-6}$ and $\br(\btoetak) = ( 2.1\pm 0.6 \mathrm{(stat)} \pm 0.2 \mathrm{(sys)}) \times 10^{-6}$. Their corresponding $CP$ violating asymmetries are measured to be $0.07\pm 0.15 \mathrm{(stat)} \pm 0.03 \mathrm{(sys)}$ for $\eta \pi^\pm$ and $-0.49\pm 0.31 \mathrm{(stat)} \pm 0.07 \mathrm{(sys)}$ for $\eta K^\pm$. No significant signals are found for neutral $B\to \eta h$ decays. We report the following upper limits on branching fractions at the 90\% confidence level: $\br(\btoetakz)< 2.0\times 10^{-6}, \; \br(\btoetapiz)<2.5 \times 10^{-6}$ and $\br (\btoetaeta) <2.0 \times 10^{-6}$.
etah_pr.tex
%\documentclass[aps,prl,preprint,tightenlines,superscriptaddress,showpacs,byrevtex]{revtex4}
%
%%% Use this for PRL submission 
%%% You also need to do the following:
%%%   * Comment out widetext, use eqnarray and \nonumber 
%%%     (for the first line) for eq:likelihood
%%%   * Change the figure size to 0.6
%%%   * Comment out preprint numbers and the Belle logo
%\documentclass[aps,prl,preprint,superscriptaddress,showpacs,byrevtex]{revtex4}
%
%%% Double-column style
%%% You also need to do the following:
%%%   * Use widetext for eq:likelihood, comment out \nonumber
%%%   * Change the figure size appropriately (should be less than 0.5)
%%%   * Comment out preprint numbers and the Belle logo
%\documentclass[aps,prl,twocolumn,superscriptaddress,showpacs,preprintnumbers,amsmath,amssymb]{revtex4}
\documentclass[aps,prl,superscriptaddress,showpacs,preprintnumbers,amsmath,amssymb]{revtex4}
%


% Some other (several out of many) possibilities
%\documentclass[preprint,aps]{revtex4}
%\documentclass[preprint,aps,draft]{revtex4}

\usepackage{graphicx} % Include figure files
\usepackage{dcolumn}  % Align table columns on decimal point
\usepackage{xspace}
\usepackage{color}
\graphicspath{{ps}}

\renewcommand{\arraystretch}{1.1}
\newcommand{\ud}{\ensuremath{\mathrm{d}}\xspace}
\newcommand{\cosq}{\ensuremath{\cos\theta^*}\xspace}
\newcommand{\bb}{\ensuremath{B \overline{B}}\xspace}
\newcommand{\btoetah}{\ensuremath{B^+ \to \eta h^+}\xspace}
\newcommand{\btoetapi}{\ensuremath{B^+ \to \eta \pi^+}\xspace}
%\newcommand{\bptoetapi}{\ensuremath{B^+ \to \eta \pi^{+}}\xspace}
%\newcommand{\bmtoetapi}{\ensuremath{B^- \to \eta \pi^{-}}\xspace}
\newcommand{\btoetak}{\ensuremath{B^+ \to \eta K^+}\xspace}
\newcommand{\btoetaks}{\ensuremath{B^0 \to \eta K^{0}_S}\xspace}
\newcommand{\btoetakz}{\ensuremath{B^0 \to \eta K^0}\xspace}    
\newcommand{\btoetapiz}{\ensuremath{B^0 \to \eta \pi^{0}}\xspace}
\newcommand{\btoetaeta}{\ensuremath{B^0 \to \eta \eta}\xspace}
\newcommand{\etatogg}{\ensuremath{\eta \to \gamma \gamma}\xspace}
\newcommand{\etatopi}{\ensuremath{\eta \to \pi^+ \pi^- \pi^0}\xspace}
\newcommand{\etagg}{\ensuremath{\eta_{\gamma \gamma}}\xspace}
\newcommand{\etapi}{\ensuremath{\eta_{3\pi}}\xspace}
%\newcommand{\etapi}{\ensuremath{\eta_{\pi^+ \pi^- \pi^0}}\xspace}
\newcommand{\qq}{\ensuremath{q \overline{q}}\xspace}
\newcommand{\cosg}{\ensuremath{\cos \theta^*_{\gamma}}\xspace}
\newcommand{\de}{\ensuremath{\Delta E}\xspace}
\newcommand{\br}{\ensuremath{\mathcal{B}}\xspace}
\newcommand{\acp}{\ensuremath{\mathcal{A}_{CP}}\xspace}
\newcommand{\thr}{\ensuremath{\theta_{\mathrm{thr}}}\xspace}
\newcommand{\blue}{\color{blue}}
\newcommand{\magenta}{\color{magenta}}

\def\calL{{\mathcal L}}
\def\calH{{\mathcal H}}
\def\calF{{\mathcal F}}
\def\BR{{\mathcal B}}
\def\Mbc{M_{\rm bc}}
\def\LR{{\mathcal R}}

\begin{document}

%\vspace*{-3\baselineskip}
%\resizebox{!}{3cm}{\includegraphics{belle.eps}}


\preprint{\vbox{ %\hbox{   }
                 \hbox{Belle-Preprint 2004-38}
                 \hbox{KEK-Preprint 2004-79} 
                 %\hbox{hep-ex nnnn, if available}
}}

\title{ \quad\\[0.5cm] Measurements of Branching Fractions and $CP$ Asymmetries 
in $B\to \eta h$ Decays}

%%%% >>>>> insert the authorlist here. BEFORE the abstract !!!!! <<<<<
%\input{author}
%\collaboration{Belle Collaboration}
%\noaffiliation
%%% Paper:    B -> eta h
%%% Journal:  Physical Review D (Rapid Communication)
%%% Contacts: P. Chang (pchang@phys.ntu.edu.tw)
%%% Non-responding authors or those who said NO are commented out.
%%% ====================================================================
%%% Click the RELOAD button on your web browser to see the updated file.
%%% ====================================================================
%%% Use \input{author} to insert this material into your latex file.
%%%%% Force institutions to appear in alphabetical order when typeset.
%%%\affiliation{Aomori University, Aomori}
\affiliation{Budker Institute of Nuclear Physics, Novosibirsk}
\affiliation{Chiba University, Chiba}
\affiliation{Chonnam National University, Kwangju}
%%%\affiliation{Chuo University, Tokyo}
\affiliation{University of Cincinnati, Cincinnati, Ohio 45221}
%%%\affiliation{University of Frankfurt, Frankfurt}
\affiliation{Gyeongsang National University, Chinju}
\affiliation{University of Hawaii, Honolulu, Hawaii 96822}
\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba}
\affiliation{Hiroshima Institute of Technology, Hiroshima}
%%%\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing}
\affiliation{Institute of High Energy Physics, Vienna}
\affiliation{Institute for Theoretical and Experimental Physics, Moscow}
\affiliation{J. Stefan Institute, Ljubljana}
\affiliation{Kanagawa University, Yokohama}
\affiliation{Korea University, Seoul}
%%%\affiliation{Kyoto University, Kyoto}
\affiliation{Kyungpook National University, Taegu}
\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne}
\affiliation{University of Ljubljana, Ljubljana}
\affiliation{University of Maribor, Maribor}
\affiliation{University of Melbourne, Victoria}
\affiliation{Nagoya University, Nagoya}
\affiliation{Nara Women's University, Nara}
\affiliation{National Central University, Chung-li}
\affiliation{National Kaohsiung Normal University, Kaohsiung}
\affiliation{National United University, Miao Li}
\affiliation{Department of Physics, National Taiwan University, Taipei}
\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow}
\affiliation{Nihon Dental College, Niigata}
\affiliation{Niigata University, Niigata}
\affiliation{Osaka City University, Osaka}
\affiliation{Osaka University, Osaka}
\affiliation{Panjab University, Chandigarh}
\affiliation{Peking University, Beijing}
\affiliation{Princeton University, Princeton, New Jersey 08545}
%%%\affiliation{RIKEN BNL Research Center, Upton, New York 11973}
%%%\affiliation{Saga University, Saga}
\affiliation{University of Science and Technology of China, Hefei}
\affiliation{Seoul National University, Seoul}
\affiliation{Sungkyunkwan University, Suwon}
\affiliation{University of Sydney, Sydney NSW}
\affiliation{Tata Institute of Fundamental Research, Bombay}
\affiliation{Toho University, Funabashi}
\affiliation{Tohoku Gakuin University, Tagajo}
\affiliation{Tohoku University, Sendai}
\affiliation{Department of Physics, University of Tokyo, Tokyo}
\affiliation{Tokyo Institute of Technology, Tokyo}
\affiliation{Tokyo Metropolitan University, Tokyo}
%%%\affiliation{Tokyo University of Agriculture and Technology, Tokyo}
%%%\affiliation{Toyama National College of Maritime Technology, Toyama}
\affiliation{University of Tsukuba, Tsukuba}
%%%\affiliation{Utkal University, Bhubaneswer}
\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061}
\affiliation{Yonsei University, Seoul}
 \author{P.~Chang}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{K.~Abe}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{K.~Abe}\affiliation{Tohoku Gakuin University, Tagajo} % TohokuGakuin
% \author{N.~Abe}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
% \author{I.~Adachi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{H.~Aihara}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
  \author{M.~Akatsu}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{Y.~Asano}\affiliation{University of Tsukuba, Tsukuba} % Tsukuba
% \author{T.~Aso}\affiliation{Toyama National College of Maritime Technology, Toyama} % Toyama
% \author{V.~Aulchenko}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{T.~Aushev}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
% \author{T.~Aziz}\affiliation{Tata Institute of Fundamental Research, Bombay} % Tata
% \author{S.~Bahinipati}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
  \author{A.~M.~Bakich}\affiliation{University of Sydney, Sydney NSW} % Sydney
  \author{V.~Balagura}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
  \author{Y.~Ban}\affiliation{Peking University, Beijing} % Peking
  \author{S.~Banerjee}\affiliation{Tata Institute of Fundamental Research, Bombay} % Tata
% \author{M.~Barbero}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
% \author{A.~Bay}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
  \author{I.~Bedny}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{U.~Bitenc}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
  \author{I.~Bizjak}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
  \author{S.~Blyth}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{A.~Bondar}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{A.~Bozek}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
  \author{M.~Bra\v cko}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba}\affiliation{University of Maribor, Maribor}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
  \author{J.~Brodzicka}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
  \author{T.~E.~Browder}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
% \author{M.-C.~Chang}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{Y.~Chao}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{A.~Chen}\affiliation{National Central University, Chung-li} % NCU
 \author{K.-F.~Chen}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
% \author{W.~T.~Chen}\affiliation{National Central University, Chung-li} % NCU
  \author{B.~G.~Cheon}\affiliation{Chonnam National University, Kwangju} % Chonnam
  \author{R.~Chistov}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
  \author{S.-K.~Choi}\affiliation{Gyeongsang National University, Chinju} % Gyeongsang
  \author{Y.~Choi}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
% \author{Y.~K.~Choi}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
  \author{A.~Chuvikov}\affiliation{Princeton University, Princeton, New Jersey 08545} % Princeton
  \author{S.~Cole}\affiliation{University of Sydney, Sydney NSW} % Sydney
  \author{J.~Dalseno}\affiliation{University of Melbourne, Victoria} % Melbourne
  \author{M.~Danilov}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
  \author{M.~Dash}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
% \author{L.~Y.~Dong}\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing} % IHEP
% \author{R.~Dowd}\affiliation{University of Melbourne, Victoria} % Melbourne
  \author{J.~Dragic}\affiliation{University of Melbourne, Victoria} % Melbourne
  \author{A.~Drutskoy}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
  \author{S.~Eidelman}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{V.~Eiges}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
% \author{Y.~Enari}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{D.~Epifanov}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
% \author{C.~W.~Everton}\affiliation{University of Melbourne, Victoria} % Melbourne
% \author{F.~Fang}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{S.~Fratina}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
% \author{H.~Fujii}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{N.~Gabyshev}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{A.~Garmash}\affiliation{Princeton University, Princeton, New Jersey 08545} % Princeton
  \author{T.~Gershon}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{A.~Go}\affiliation{National Central University, Chung-li} % NCU
  \author{G.~Gokhroo}\affiliation{Tata Institute of Fundamental Research, Bombay} % Tata
% \author{B.~Golob}\affiliation{University of Ljubljana, Ljubljana}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
% \author{M.~Grosse~Perdekamp}\affiliation{RIKEN BNL Research Center, Upton, New York 11973} % RIKEN
% \author{H.~Guler}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{R.~Guo}\affiliation{National Kaohsiung Normal University, Kaohsiung} % Kaohsiung
  \author{J.~Haba}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{C.~Hagner}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
% \author{F.~Handa}\affiliation{Tohoku University, Sendai} % Tohoku
% \author{K.~Hara}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{T.~Hara}\affiliation{Osaka University, Osaka} % Osaka
% \author{N.~C.~Hastings}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{K.~Hasuko}\affiliation{RIKEN BNL Research Center, Upton, New York 11973} % RIKEN
  \author{K.~Hayasaka}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{H.~Hayashii}\affiliation{Nara Women's University, Nara} % Nara
 \author{M.~Hazumi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{E.~M.~Heenan}\affiliation{University of Melbourne, Victoria} % Melbourne
% \author{I.~Higuchi}\affiliation{Tohoku University, Sendai} % Tohoku
% \author{T.~Higuchi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{L.~Hinz}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
% \author{T.~Hojo}\affiliation{Osaka University, Osaka} % Osaka
  \author{T.~Hokuue}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{Y.~Hoshi}\affiliation{Tohoku Gakuin University, Tagajo} % TohokuGakuin
% \author{K.~Hoshina}\affiliation{Tokyo University of Agriculture and Technology, Tokyo} % TUAT
  \author{S.~Hou}\affiliation{National Central University, Chung-li} % NCU
  \author{W.-S.~Hou}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{Y.~B.~Hsiung}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{H.-C.~Huang}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
% \author{T.~Igaki}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{Y.~Igarashi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{T.~Iijima}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{A.~Imoto}\affiliation{Nara Women's University, Nara} % Nara
  \author{K.~Inami}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{A.~Ishikawa}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{H.~Ishino}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
% \author{K.~Itoh}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
  \author{R.~Itoh}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{M.~Iwamoto}\affiliation{Chiba University, Chiba} % Chiba
  \author{M.~Iwasaki}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
  \author{Y.~Iwasaki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{M.~Jones}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
% \author{R.~Kagan}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
% \author{H.~Kakuno}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
  \author{J.~H.~Kang}\affiliation{Yonsei University, Seoul} % Yonsei
  \author{J.~S.~Kang}\affiliation{Korea University, Seoul} % Korea
  \author{P.~Kapusta}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
% \author{S.~U.~Kataoka}\affiliation{Nara Women's University, Nara} % Nara
  \author{N.~Katayama}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{H.~Kawai}\affiliation{Chiba University, Chiba} % Chiba
% \author{H.~Kawai}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
% \author{Y.~Kawakami}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{N.~Kawamura}\affiliation{Aomori University, Aomori} % Aomori
  \author{T.~Kawasaki}\affiliation{Niigata University, Niigata} % Niigata
% \author{N.~Kent}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{H.~R.~Khan}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
% \author{A.~Kibayashi}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
  \author{H.~Kichimi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{H.~J.~Kim}\affiliation{Kyungpook National University, Taegu} % Kyungpook
% \author{H.~O.~Kim}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
% \author{Hyunwoo~Kim}\affiliation{Korea University, Seoul} % Korea
  \author{J.~H.~Kim}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
  \author{S.~K.~Kim}\affiliation{Seoul National University, Seoul} % Seoul
  \author{S.~M.~Kim}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
% \author{T.~H.~Kim}\affiliation{Yonsei University, Seoul} % Yonsei
% \author{K.~Kinoshita}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
% \author{S.~Kobayashi}\affiliation{Saga University, Saga} % Saga
  \author{P.~Koppenburg}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{S.~Korpar}\affiliation{University of Maribor, Maribor}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
  \author{P.~Kri\v zan}\affiliation{University of Ljubljana, Ljubljana}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
  \author{P.~Krokovny}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{R.~Kulasiri}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
% \author{S.~Kumar}\affiliation{Panjab University, Chandigarh} % Panjab
  \author{C.~C.~Kuo}\affiliation{National Central University, Chung-li} % NCU
% \author{H.~Kurashiro}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
% \author{E.~Kurihara}\affiliation{Chiba University, Chiba} % Chiba
% \author{A.~Kusaka}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
% \author{A.~Kuzmin}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{Y.-J.~Kwon}\affiliation{Yonsei University, Seoul} % Yonsei
% \author{J.~S.~Lange}\affiliation{University of Frankfurt, Frankfurt} % Frankfurt
% \author{G.~Leder}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
  \author{S.~E.~Lee}\affiliation{Seoul National University, Seoul} % Seoul
  \author{S.~H.~Lee}\affiliation{Seoul National University, Seoul} % Seoul
% \author{Y.-J.~Lee}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{T.~Lesiak}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
  \author{J.~Li}\affiliation{University of Science and Technology of China, Hefei} % USTC
% \author{A.~Limosani}\affiliation{University of Melbourne, Victoria} % Melbourne
  \author{S.-W.~Lin}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{D.~Liventsev}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
% \author{J.~MacNaughton}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
  \author{G.~Majumder}\affiliation{Tata Institute of Fundamental Research, Bombay} % Tata
  \author{F.~Mandl}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
% \author{D.~Marlow}\affiliation{Princeton University, Princeton, New Jersey 08545} % Princeton
% \author{T.~Matsuishi}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{H.~Matsumoto}\affiliation{Niigata University, Niigata} % Niigata
% \author{S.~Matsumoto}\affiliation{Chuo University, Tokyo} % Chuo
  \author{T.~Matsumoto}\affiliation{Tokyo Metropolitan University, Tokyo} % TMU
% \author{A.~Matyja}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
% \author{Y.~Mikami}\affiliation{Tohoku University, Sendai} % Tohoku
  \author{W.~Mitaroff}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
  \author{K.~Miyabayashi}\affiliation{Nara Women's University, Nara} % Nara
% \author{Y.~Miyabayashi}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{H.~Miyake}\affiliation{Osaka University, Osaka} % Osaka
  \author{H.~Miyata}\affiliation{Niigata University, Niigata} % Niigata
  \author{R.~Mizuk}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
  \author{D.~Mohapatra}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
% \author{G.~R.~Moloney}\affiliation{University of Melbourne, Victoria} % Melbourne
% \author{G.~F.~Moorhead}\affiliation{University of Melbourne, Victoria} % Melbourne
  \author{T.~Mori}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
% \author{A.~Murakami}\affiliation{Saga University, Saga} % Saga
  \author{T.~Nagamine}\affiliation{Tohoku University, Sendai} % Tohoku
  \author{Y.~Nagasaka}\affiliation{Hiroshima Institute of Technology, Hiroshima} % Hiroshima
% \author{T.~Nakadaira}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
% \author{I.~Nakamura}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{E.~Nakano}\affiliation{Osaka City University, Osaka} % OsakaCity
  \author{M.~Nakao}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{H.~Nakazawa}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{Z.~Natkaniec}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
% \author{K.~Neichi}\affiliation{Tohoku Gakuin University, Tagajo} % TohokuGakuin
  \author{S.~Nishida}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{O.~Nitoh}\affiliation{Tokyo University of Agriculture and Technology, Tokyo} % TUAT
% \author{S.~Noguchi}\affiliation{Nara Women's University, Nara} % Nara
% \author{T.~Nozaki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{A.~Ogawa}\affiliation{RIKEN BNL Research Center, Upton, New York 11973} % RIKEN
  \author{S.~Ogawa}\affiliation{Toho University, Funabashi} % Toho
  \author{T.~Ohshima}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{T.~Okabe}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{S.~Okuno}\affiliation{Kanagawa University, Yokohama} % Kanagawa
  \author{S.~L.~Olsen}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
% \author{Y.~Onuki}\affiliation{Niigata University, Niigata} % Niigata
  \author{W.~Ostrowicz}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
  \author{H.~Ozaki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{P.~Pakhlov}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
% \author{H.~Palka}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
  \author{C.~W.~Park}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
  \author{H.~Park}\affiliation{Kyungpook National University, Taegu} % Kyungpook
% \author{K.~S.~Park}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
  \author{N.~Parslow}\affiliation{University of Sydney, Sydney NSW} % Sydney
% \author{L.~S.~Peak}\affiliation{University of Sydney, Sydney NSW} % Sydney
% \author{M.~Pernicka}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
% \author{J.-P.~Perroud}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
  \author{R.~Pestotnik}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
% \author{M.~Peters}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{L.~E.~Piilonen}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
% \author{A.~Poluektov}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
% \author{F.~J.~Ronga}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{N.~Root}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
  \author{M.~Rozanska}\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow} % Krakow
  \author{H.~Sagawa}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{M.~Saigo}\affiliation{Tohoku University, Sendai} % Tohoku
% \author{S.~Saitoh}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{Y.~Sakai}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{H.~Sakamoto}\affiliation{Kyoto University, Kyoto} % Kyoto
% \author{H.~Sakaue}\affiliation{Osaka City University, Osaka} % OsakaCity
% \author{T.~R.~Sarangi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{M.~Satapathy}\affiliation{Utkal University, Bhubaneswer} % Utkal
% \author{N.~Sato}\affiliation{Nagoya University, Nagoya} % Nagoya
  \author{T.~Schietinger}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
  \author{O.~Schneider}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
  \author{P.~Sch\"onmeier}\affiliation{Tohoku University, Sendai} % Tohoku
  \author{J.~Sch\"umann}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
% \author{C.~Schwanda}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
  \author{A.~J.~Schwartz}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
% \author{T.~Seki}\affiliation{Tokyo Metropolitan University, Tokyo} % TMU
% \author{S.~Semenov}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
  \author{K.~Senyo}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{Y.~Settai}\affiliation{Chuo University, Tokyo} % Chuo
% \author{R.~Seuster}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
% \author{M.~E.~Sevior}\affiliation{University of Melbourne, Victoria} % Melbourne
% \author{T.~Shibata}\affiliation{Niigata University, Niigata} % Niigata
  \author{H.~Shibuya}\affiliation{Toho University, Funabashi} % Toho
% \author{B.~Shwartz}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
% \author{V.~Sidorov}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
% \author{V.~Siegle}\affiliation{RIKEN BNL Research Center, Upton, New York 11973} % RIKEN
  \author{J.~B.~Singh}\affiliation{Panjab University, Chandigarh} % Panjab
  \author{A.~Somov}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
  \author{N.~Soni}\affiliation{Panjab University, Chandigarh} % Panjab
  \author{R.~Stamen}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{S.~Stani\v c}\altaffiliation[on leave from ]{Nova Gorica Polytechnic, Nova Gorica}\affiliation{University of Tsukuba, Tsukuba} % Tsukuba
  \author{M.~Stari\v c}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
% \author{A.~Sugi}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{A.~Sugiyama}\affiliation{Saga University, Saga} % Saga
  \author{K.~Sumisawa}\affiliation{Osaka University, Osaka} % Osaka
  \author{T.~Sumiyoshi}\affiliation{Tokyo Metropolitan University, Tokyo} % TMU
% \author{S.~Suzuki}\affiliation{Saga University, Saga} % Saga
% \author{S.~Y.~Suzuki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{S.~K.~Swain}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{O.~Tajima}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{F.~Takasaki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{K.~Tamai}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{N.~Tamura}\affiliation{Niigata University, Niigata} % Niigata
% \author{K.~Tanabe}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
  \author{M.~Tanaka}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{G.~N.~Taylor}\affiliation{University of Melbourne, Victoria} % Melbourne
  \author{Y.~Teramoto}\affiliation{Osaka City University, Osaka} % OsakaCity
  \author{X.~C.~Tian}\affiliation{Peking University, Beijing} % Peking
% \author{S.~Tokuda}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{S.~N.~Tovey}\affiliation{University of Melbourne, Victoria} % Melbourne
% \author{K.~Trabelsi}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
% \author{T.~Tsuboyama}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{T.~Tsukamoto}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
% \author{K.~Uchida}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{S.~Uehara}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{T.~Uglov}\affiliation{Institute for Theoretical and Experimental Physics, Moscow} % ITEP
  \author{K.~Ueno}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
% \author{Y.~Unno}\affiliation{Chiba University, Chiba} % Chiba
  \author{S.~Uno}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{Y.~Ushiroda}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{G.~Varner}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
  \author{K.~E.~Varvell}\affiliation{University of Sydney, Sydney NSW} % Sydney
  \author{S.~Villa}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
  \author{C.~C.~Wang}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{C.~H.~Wang}\affiliation{National United University, Miao Li} % Lien-Ho
% \author{J.~G.~Wang}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
  \author{M.-Z.~Wang}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
% \author{M.~Watanabe}\affiliation{Niigata University, Niigata} % Niigata
% \author{Y.~Watanabe}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
% \author{L.~Widhalm}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
% \author{Q.~L.~Xie}\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing} % IHEP
% \author{B.~D.~Yabsley}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
  \author{A.~Yamaguchi}\affiliation{Tohoku University, Sendai} % Tohoku
  \author{H.~Yamamoto}\affiliation{Tohoku University, Sendai} % Tohoku
% \author{S.~Yamamoto}\affiliation{Tokyo Metropolitan University, Tokyo} % TMU
% \author{T.~Yamanaka}\affiliation{Osaka University, Osaka} % Osaka
  \author{Y.~Yamashita}\affiliation{Nihon Dental College, Niigata} % NihonDental
  \author{M.~Yamauchi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{Heyoung~Yang}\affiliation{Seoul National University, Seoul} % Seoul
% \author{P.~Yeh}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
  \author{J.~Ying}\affiliation{Peking University, Beijing} % Peking
% \author{K.~Yoshida}\affiliation{Nagoya University, Nagoya} % Nagoya
% \author{Y.~Yuan}\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing} % IHEP
% \author{Y.~Yusa}\affiliation{Tohoku University, Sendai} % Tohoku
% \author{H.~Yuta}\affiliation{Aomori University, Aomori} % Aomori
% \author{S.~L.~Zang}\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing} % IHEP
% \author{C.~C.~Zhang}\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing} % IHEP
  \author{J.~Zhang}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
  \author{L.~M.~Zhang}\affiliation{University of Science and Technology of China, Hefei} % USTC
  \author{Z.~P.~Zhang}\affiliation{University of Science and Technology of China, Hefei} % USTC
% \author{Y.~Zheng}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
 \author{V.~Zhilich}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
% \author{T.~Ziegler}\affiliation{Princeton University, Princeton, New Jersey 08545} % Princeton
  \author{D.~\v Zontar}\affiliation{University of Ljubljana, Ljubljana}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
% \author{D.~Z\"urcher}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
\collaboration{The Belle Collaboration}


\begin{abstract}
We report measurements of $B$ to pseudoscalar-pseudoscalar decays with 
at least one $\eta$ meson in the final state using $140 \mathrm{~fb}^{-1}$ of 
data collected by the Belle detector at KEKB $e^+ e^-$ collider.  
We observe the decay  $\btoetapi$ and find  evidence of  $\btoetak$; the 
measured branching fractions are
$\br(\btoetapi) = ( 4.8^{+0.8}_{-0.7} \mathrm{(stat)} \pm 0.3
 \mathrm{(sys)}) \times 10^{-6}$ and
$\br(\btoetak) = ( 2.1\pm 0.6 \mathrm{(stat)} \pm 0.2
\mathrm{(sys)}) \times 10^{-6}$. Their corresponding $CP$ violating
asymmetries are measured to be $0.07\pm 0.15 \mathrm{(stat)} 
\pm 0.03 \mathrm{(sys)}$ for $\eta \pi^\pm$ and $-0.49\pm 0.31 \mathrm{(stat)} 
\pm 0.07  \mathrm{(sys)}$ for $\eta K^\pm$. No significant signals are found for
neutral $B\to \eta h$ decays. We report the following upper limits on branching 
fractions at the 90\% confidence level: 
$\br(\btoetakz)< 2.0\times 10^{-6}, \;
\br(\btoetapiz)<2.5 \times 10^{-6}$ and 
$\br (\btoetaeta) <2.0 \times 10^{-6}$.
 

\end{abstract}

\pacs{13.25.Hw, 12.15.Hh, 11.30.Er}

\maketitle

%%%% >>>> keep the final version single-spaced
\tighten

{\renewcommand{\thefootnote}{\fnsymbol{footnote}}}
\setcounter{footnote}{0}
Charmless $B$ decays provide a  rich sample to understand  $B$ decay
dynamics and to search for $CP$ violation. An unexpectedly large 
$B\to\eta^\prime K$ branching fraction \cite{etapetac,etapk} 
has stimulated much theoretical
interest. It was suggested even before the $\eta^\prime K$ measurement that
 two $b\to s$ 
penguin amplitudes are constructive in  $B\to \eta^\prime K$ decays 
but destructive in $B\to \eta K$ \cite{lipkin}. The situation is reversed
for $B\to \eta^\prime K^*$ and $B\to \eta K^*$ decays. 
 Experimental results have more or 
less confirmed this picture; however, precise measurements of  branching
fractions are needed to quantitatively understand the contribution of each 
diagram. It was also pointed out that in the $\eta K$ mode the suppressed 
penguin amplitudes may interfere  with the CKM suppressed $b\to u$
(tree) amplitude and result in  direct $CP$ violation \cite{etakt}. 
The penguin-tree 
interference may also be large in $B^+\to\eta^\prime \pi^+$ \cite{CC} and 
$B^+\to\eta \pi^+$ decays; however, theoretical expectations for the 
partial rate asymmetry $(A_{CP})$ can be either positive or negative
\cite{etakt,etapit}. Recently, the BaBar Collaboration has reported  large 
negative $A_{CP}$ values in both $\eta K^+$ 
and $\eta \pi^+$, which are $\sim 2 \sigma$ away from zero \cite{babar}.
However, more data  are needed to verify these large $CP$ violating 
asymmetries. 
Furthermore, branching fractions and partial rate asymmetries in charmless 
$B$ decays can be used to understand the tree and penguin contributions and
provide constraints on the third unitarity triangle angle $\phi_3$ 
\cite{rosner}.      

In this paper, we report  measurements of branching fractions and partial
rate asymmetries for  $B\to\eta h$ decays, where $h$ could be a 
$K,\; \pi$ or $\eta$ meson. The partial rate asymmetry is measured for the
charged $B$ decays and  defined to be:
\begin{eqnarray*}
\acp=\frac{N( B^- \to \eta h^-)-N(B^+ \to \eta h^+)}
{N(B^- \to \eta h^-)+N(B^+ \to \eta h^+)},
\end{eqnarray*}
where $N(B^-)$ is the yield for the $B^- \to \eta h^-$ decay and
$N(B^+)$ denotes that of the charge conjugate mode.
 The data sample consists of 152 
million \bb pairs (140 fb$^{-1}$) collected
with the Belle detector at the KEKB $e^+e^-$ asymmetric-energy  
(3.5 on 8~GeV) collider~\cite{KEKB} operating at the $\Upsilon(4S)$ resonance.



The Belle detector is a large-solid-angle magnetic
spectrometer that
consists of a three-layer silicon vertex detector (SVD),
a 50-layer central drift chamber (CDC), an array of
aerogel threshold \v{C}erenkov counters (ACC),
a barrel-like arrangement of time-of-flight
scintillation counters (TOF), and an electromagnetic calorimeter (ECL)
comprised of CsI(Tl) crystals located inside
a superconducting solenoid coil that provides a 1.5~T
magnetic field.  An iron flux-return located outside of
the coil is instrumented to detect $K_L^0$ mesons and to identify
muons (KLM).  The detector
is described in detail elsewhere~\cite{Belle}.

Two $\eta$ decay channels are considered in this analysis: 
$\eta\to \gamma\gamma$ ($\eta_{\gamma\gamma}$) and $\eta\to \pi^+\pi^-\pi^0$
 ($\etapi$).  In the $\etagg$ reconstruction, each photon is required to have 
a minimum laboratory energy of 50 MeV and the energy asymmetry, 
defined as the absolute value of the energy difference in the laboratory frame
between the two photons divided by their energy sum, 
must be less than 0.9. 
Furthermore, we remove  $\eta$ candidates if either one of the daughter 
photons can pair with any other photon  to form a $\pi^0$ candidate. Candidate $\etapi$ mesons are reconstructed by combining a $\pi^0$ with a pair
of oppositely charged tracks that originate from the interaction point (IP).
We make the following requirements for the invariant mass  on 
the $\eta$ candidates: 516 MeV/$c^2 < M_{\gamma\gamma} < 569$ MeV/$c^2$ for 
$\etagg$ and 539 MeV/$c^2 < M_{3\pi} <556$ MeV/$c^2$ for $\etapi$. After the 
selection of each 
candidate, an $\eta$ mass constraint is implemented  by readjusting the momenta
of the daughter particles.   

Candidate neutral pions are selected by requiring the
two-photon invariant mass to be in the mass window between 115 MeV/$c^2$ and 
152 MeV/$c^2$. The momentum of each photon is then readjusted to
constrain the mass of the photon pair to be the nominal $\pi^0$ mass. 
To reduce the low energy photon background,  
each photon is required to have a minimum energy of 50 MeV and the 
$\pi^0$ momentum 
must be above 250 MeV/$c$ in the laboratory frame. 
Charged tracks are required to come from the IP.  Charged kaons and pions 
that form $B$ candidates with $\eta$ mesons
are identified by combining information from the CDC ($dE/dx$),
the TOF and the ACC to form a $K(\pi)$ likelihood $L_K(L_\pi)$. 
Discrimination between kaons and pions is achieved through
the likelihood ratio $L_{K}$/($L_{\pi}+L_{K}$). Charged tracks with  
likelihood ratios greater than 0.6 are regarded as kaons, and less than 0.4
as pions. The typical kaon and pion identification efficiencies for 2.5 GeV/$c$
tracks are  $(85.0\pm 0.2)$\% and $(89.3\pm 0.2)$\%, respectively. With the
same track momentum, the rate for  pions to be misidentified as kaons is 
$(7.3 \pm 0.2)$\% while the rate for  kaons  to be misidentified as pions is
$(10.6 \pm 0.2)$\%.
Furthermore, charged tracks that are positively identified as 
electrons or muons are rejected. $K^0_S$ candidates 
 are reconstructed from  pairs of oppositely charged tracks
 with invariant mass ($M_{\pi\pi}$) between 480 to 516 MeV/$c^2$.
Each candidate must have a displaced vertex with a flight direction
 consistent with a $K^0_S$ originating from the IP.

Candidate $B$ mesons are identified using the beam constrained mass,
$\Mbc =  \sqrt{E^2_{\mbox{\scriptsize beam}} - P_B^2}$,
and the energy difference, $\Delta E = E_B  - E_{\mbox{\scriptsize beam}}$,
where $E_{\mbox{\scriptsize beam}}$ is the run-dependent beam energy in the
$\Upsilon(4S)$ rest frame and  is determined  from
$B\to D^{(*)}\pi$ events,
and $P_{B}$ and $E_B$ are the momentum and energy of  the
$B$ candidate in the $\Upsilon(4S)$ rest frame. The resolutions on $\Mbc$ and 
$\de$ are around 3 MeV/$c^2$ and $\sim$ 20--30 MeV, respectively.  
Events with $\Mbc >5.2$ GeV/$c^2$ and $|\de|<0.3$ GeV are selected for the 
 analysis.   

The dominant background comes from the $e^+e^-\rightarrow q\bar{q}$ continuum, 
where $q= u, d, s$ or $c$. To distinguish signal from the jet-like continuum 
background,  event shape variables and the $B$ flavor tagging information 
are employed. We form a Fisher discriminant \cite{fisher} from seven
variables that quantify event topology.  The Fisher variables include
the angle $\theta_T$ between the thrust axis \cite{thrust} of the $B$ candidate
and the thrust axis of the rest of the event, five modified Fox-Wolfram
 moments \cite{sfw}, and a measure of the momentum transverse to the event 
thrust axis ($S_\perp$)  \cite{sperp}. The  probability density functions (PDF)
for this discriminant  and $\cos\theta_B$, where $\theta_B$ is the angle
between the $B$ flight direction and the beam direction
in the $\Upsilon(4S)$ rest frame,  are obtained using events in  signal 
Monte Carlo (MC) and data with $\Mbc< 5.26$ GeV/$c^2$ for signal and 
$q \bar{q}$ background, respectively. These two variables are then combined to 
form a likelihood ratio $\LR = {\calL}_s/({\calL}_s + {\calL}_{q \bar{q}})$,
where ${\calL}_{s (q \bar{q})}$ is the product of signal ($q \bar{q}$) 
probability densities.

Additional background discrimination is provided by the quality of 
the$B$ flavor tagging of the accompanying $B$ meson.
We use the standard Belle $B$ tagging package \cite{tagging},  
which gives two outputs:
a discrete variable $(q)$ indicating the $B$ flavor and a dilution factor ($r$)
ranging from zero for no flavor information to unity for unambiguous
flavor assignment. We divide the data into six $r$ regions.
Continuum suppression is achieved by applying a mode dependent requirement on 
$\LR$ for events in each $r$ region based on 
$N_s^{\rm exp}/\sqrt{N_s^{\rm exp}+N_{q\bar{q}}^{\rm exp}}$,
where $N_s^{\rm exp}$ is the expected signal  from MC and
$N_{q\bar{q}}^{\rm exp}$ denotes the number of background events estimated from data.
This $\LR$ requirement retains 58--86\% of the signal  while reducing 
96--82\% of 
the background. From MC all other backgrounds are found to be negligible 
 except for the 
$\eta K^+ \leftrightarrow \eta \pi^+$ reflection, due to 
$K^+\leftrightarrow \pi^+$ 
misidentification, and the $\eta K^*(892) (\eta\rho(770))$ feed-down to the
$\eta K (\eta \pi)$ modes. We include these two components in the fit used 
to extract the signal.  

The signal yields and branching fractions are obtained using an extended 
unbinned maximum-likelihood (ML) fit with input variables $\Mbc$ and $\de$.
The likelihood is defined as: 
\begin{eqnarray*}
  \mathcal{L} = {\rm exp}\; (-\sum_j N_j) \prod^N_i \; [\; \sum N_j P_j(\Mbc{}_i,\de{}_i) \; ],
\end{eqnarray*}
where $N_j$ is the yield of category $j$ (signal, continuum background, 
reflection, $\eta K^*/\eta\rho$), $P_j (\Mbc{}_i,\de{}_i)$ is the 
probability density for the $i$th event and $N$ is the total number of events.  
The PDFs for the signal, the reflection background and the $\eta K^*/\eta \rho$
feed-down are modeled with two-dimensional $\Mbc$-$\de$ smooth functions obtained
using MC. The signal peak positions and resolutions in $\Mbc$ and $\de$
are adjusted according to the data-MC differences using large control samples 
of $B\to D\pi$  and $\overline{D}{}^0\to K^+\pi^-\pi^0/\pi^0\pi^0$ decays. 
The continuum background in $\de$ is described by a first or second order
polynomial while the $\Mbc$ distribution is parameterized by an 
ARGUS function, $f(x) = x \sqrt{1-x^2}\;{\rm exp}\;[ -\xi (1-x^2)]$, where 
$x$ is $\Mbc$ divided by half of the total center of mass energy \cite{argus}. 
Thus the continuum 
PDF is the product of an ARGUS function and a polynomial, where
$\xi$ and the coefficients of the polynomial are free parameters. 
Since $B\to\eta K^*$ branching fractions are well measured 
($\sim 20 \times 10^{-6}$) \cite{etapetac,etakst}, their feed-down  
to the $\eta K$ modes are fixed from MC in the likelihood fit. Since  the 
decay $B^+\to \eta \rho^+$  is experimentally poorly constrained, the amount of this background  in the
$\eta \pi$ modes is allowed to float in the fit. In the charged $B$ modes,
the normalizations of the reflections are fixed to  expectations 
based on the $B^+\to \eta K^+$ and $B^+\to \eta \pi^+$  branching fractions and 
$K^+\leftrightarrow \pi^+$ fake rates, measured using   
$\overline{D}{}^0 \to K^+\pi^-$ data. The reflection yield is first estimated
with the assumed $\eta K^+$ and $\eta\pi^+$ branching fractions and is then
recalculated according to our measured branching fractions. No $\bb$ 
contributions
are included for the $B^0\to \eta \eta$ mode.
  

\begin{table*}[th]
\caption{ Detection efficiency ($\epsilon$), product of daughter branching 
fractions ( $\prod \br_i$), yield,
significance (Sig.), measured branching fraction ($\mathcal{B}$), 
the 90\% C.L. upper limit (UL) and $A_{CP}$ for the $B\to \eta h$ decays. 
The first errors
in columns 4, 6 and 8 are statistical and the second errors are systematic.}

\begin{tabular}{lccccccc} \hline\hline
Mode & $\epsilon(\%)$ & $\prod \br_i (\%)$ &  Yield & \hspace{0.2cm}Sig. 
\hspace{0.2cm} & $\mathcal{B} (10^{-6})$  & UL$(10^{-6}$)& $A_{CP}$ \\
\hline
\hline
 \btoetapi &
        & & & 8.0 & $4.8\pm 0.7\pm 0.3$ &
         & $0.07\pm 0.15 \pm 0.03$
        \\
\hspace{0.4cm}$\etagg \pi^+$ &
        $23.3$ &39.4 & $73.4^{+13.5}_{-12.7}\pm 2.0$ & 7.0 & $5.3^{+1.0}_{-0.9}
\pm 0.3$  &  & $0.11 \pm 0.17 \pm 0.03$
        \\
\hspace{0.4cm}$\eta_{3\pi} \pi^+$ &
        $14.8$ & 22.6& $19.6^{+7.0}_{-6.1}\pm 0.7$ & 3.9 & $3.8^{+1.4}_{-1.2} \pm 0.3$
  &          & $-0.11^{+0.35+0.04}_{-0.33-0.05}$
        \\
 \btoetak &
      & & & 3.7 & $2.1\pm 0.6 \pm 0.2$ &  & $-0.49\pm 0.31 \pm 0.07$ \\
  \hspace{0.4cm}$\etagg K^+$ &
       $21.1$ & $39.4$ & $28.0^{+10.0}_{-9.1}\pm 1.6$ & $3.3$ & $2.2^{+0.8}_{-0.7}\pm
       0.2$ &  & $-0.45^{+0.35}_{-0.31}\pm 0.07$ \\
  \hspace{0.4cm}$\eta_{3\pi} K^+$ &
       $13.8$ & $22.6$ & $7.4^{+5.4}_{-4.5}\pm 0.5$ & 1.7 & $1.5^{+1.1}_{-0.9}\pm 0.2$
       &  & $-0.78^{+1.03+0.11}_{-0.76-0.12}$ \\
 $B^0\to \eta K^0$ &
      & & & 0.4 & $0.3^{+0.9}_{-0.7}\pm 0.1$ & $<2.0$ & \\
  \hspace{0.4cm}$\etagg K^0$ & $22.9$ & $13.6$ & $-1.9^{+4.3}_{-3.1}\pm 0.3$ 
      &$-$  & $-0.4^{+0.9}_{-0.7}\pm 0.1$ & & \\
  \hspace{0.4cm}$\eta_{3\pi} K^0$ & $12.2$ & $7.8$ & $3.5^{+3.6}_{-2.7}\pm 0.2$
      &  1.3& $2.4^{+2.5}_{-1.9}\pm \pm 0.3$ & &\\
 $B^0\to \eta \pi^0$ &
      & & & 1.8 &  $1.2\pm 0.7\pm 0.1 $ & $<2.5$ & \\
  \hspace{0.4cm}$\etagg \pi^0$ & 17.0 & 39.0 & 
       $18.2^{+8.9+0.8}_{-8.0-0.7}$ & 2.4 & $1.8^{+0.9}_{-0.8}\pm 0.2$ & & \\
  \hspace{0.4cm}$\eta_{3\pi} \pi^0$ &11.2 & 22.3 & $-3.0^{+5.0}_{-4.0}\pm 0.3$ 
      &$-$ & $-0.8^{+1.3}_{-0.8}\pm 0.1$& & \\
 $B^0\to \eta \eta$ &
     & & &1.1 & $0.7^{+0.7}_{-0.6}\pm 0.1$  &$<2.0$ &  \\
  \hspace{0.4cm}$\etagg \etagg$ & 16.9 & 15.5 & $-1.5^{+2.7}_{-1.6}\pm 0.1$ & 
         $-$   & $-0.4^{+0.7}_{-0.4}\pm 0.0$ & & \\
  \hspace{0.4cm}$\etagg \eta_{3\pi}$ & 11.3 & 17.8 &$7.3^{+4.5}_{-4.0}\pm 0.2$ 
         &2.2 & $2.3^{+1.4}_{-1.2}\pm 0.2$ &  & \\
  \hspace{0.4cm}$\eta_{3\pi}\eta_{3\pi}$ & 7.7 &5.1&$0.3^{+2.0}_{-1.2}\pm 0.1$ &
         0.2 & $0.5^{+3.1}_{-1.9}\pm 0.1$ & & \\
\hline
\hline
\end{tabular}
\label{tab:result}
\end{table*}

In Table ~\ref{tab:result}  we show the measured branching
 fractions for each decay mode
as well as  other quantities associated with the measurements.
The efficiency for each mode is determined using  MC simulation and
corrected for the discrepancy between data and MC using the control samples. 
The only discrepancy we find is the performance of particle identification, 
which
results in a 4.3\% correction for the  $\eta \pi^+$ mode and 1.7\% for 
$B\to \eta K^+$.  
The combined branching fraction of the two $\eta$ decay modes is obtained 
from a simultaneous  likelihood fit to all the sub-samples with a common 
branching fraction. 
Systematic uncertainties in the fit due to the uncertainties in the signal PDFs
are estimated by performing the fit after varying their peak positions and 
resolutions by one standard deviation. In the $\eta K$ modes, we also vary the expected $\eta K^*$ 
feed-down by one standard deviation to check the yield difference. 
The quadratic 
sum of the deviations from the central value gives the systematic 
uncertainty in the fit,
which ranges from 3\% to 6\%. For each systematic check, the 
statistical significance is taken as the square root of
the difference between the value of $-2\ln\calL$ for zero signal yield and the
best-fit value. We regard the smallest value as our significance incuding 
the systematic uncertainty. 
The number of $B^+B^-$ and $B^0\overline{B}{}^0$ pairs are assumed to be
equal.


The performance of the $\LR$ requirement is 
studied by 
checking the data-MC efficiency ratio using the $B^+\to \overline{D}{}^0 \pi^+$ 
control sample. The obtained error is 2.4--3.5\%. The
 systematic errors on the charged track reconstruction
are estimated to be around $1$\% per track using  partially
reconstructed $D^*$ events, and  verified by comparing the ratio of
$\eta\to \pi^+\pi^-\pi^0$ to $\eta\to \gamma\gamma$
in data with MC expectations. The $\pi^0$ and $\eta_{\gamma\gamma}$ 
reconstruction efficiency is verified by comparing the $\pi^0$
decay angular distribution with the MC prediction, and by measuring the ratio 
of the branching fractions for the two $\eta$ decay channels: 
$\eta\to \gamma\gamma$
and $\eta\to \pi^0\pi^0\pi^0$. We assign 3.5\% error for the 
$\pi^0$ and $\etagg$ reconstruction. The $K_S^0$ reconstruction is verified by 
comparing the  ratio of $D^+\to K_S^0\pi^+$ and $D^+\to K^-\pi^+\pi^+$ yields. 
The resulting $K_S^0$ detection systematic error is 
4.4\%. The 
uncertainty in the number of $\bb$ events is 1\%. The final systematic error is
obtained by first summing all correlated errors linearly and then quadratically
summing the uncorrelated errors.  

 
\begin{figure}[htb]
\includegraphics[width=0.7\textwidth]{fig1.eps}
\caption{$\Mbc$ and $\de$ projections for (a,b) $\btoetapi$, (c,d) $\btoetak$,
(e,f) $\btoetakz$, (g,h) $\btoetapiz$ and (i,j) $\btoetaeta$ decays with 
the $\etagg$ and $\etapi$ modes combined. Open
histograms are data, solid curves are the fit functions, dashed lines show
the continuum contributions and shaded histograms are the $\eta K^*/\eta \rho$
contributions.  The small contributions around $\Mbc = 5.28$ GeV/$c^2$ and 
$\de =\pm 0.05$
GeV in (a)-(d) are the backgrounds from $\btoetak$ and $\btoetapi$.  
}
\label{fig:mbde}
\end{figure}


 Figure \ref{fig:mbde} shows the $\Mbc$ and $\de$ projections after requiring
events to satisfy $-0.10$ GeV $<\de<0.08$ GeV ($-0.15$ GeV $<\de<0.10$ GeV for 
the $\etagg$ and $\eta \pi^0$ modes) and $\Mbc>5.27$ GeV/$c^2$, respectively.
No significant signals are observed for the neutral $B$ meson modes; for these
modes we
set branching fraction upper limits at the 90\% confidence level. The  
upper limit for each mode is determined using the combined likelihood 
for the two $\eta$ decay channels with
the reconstruction efficiency reduced by $1 \sigma$. We vary
the signal PDF and the expected $\eta K^*$ feed-down in the $\eta K^0$ mode to 
compute the likelihood as a function of branching fraction; the largest 
branching fraction that covers 90\% of the 
likelihood area is chosen to be the upper limit.
 
Significant signals are observed for charged $B$ decays. We investigate
their partial rate asymmetries by extracting signal yields separately from the 
 $B^+$ and $B^-$ samples. Unbinned maximum likelihood fits are performed 
independently for the two $\eta$ decay modes in order to reduce the 
systematic uncertainties. The same signal and background PDFs as used in the 
branching fraction measurement 
are applied. The parameters of the continuum PDF are fixed according to
the branching fraction results. Contributions from 
$\bb$ backgrounds are required to be equal for the $B^+$ and $B^-$ samples. 
 Figure \ref{fig:acp} shows the $\Mbc$ and $\de$ projections. 
  The $A_{CP}$ results for the two $\eta$ decay modes are combined
assuming that the errors are Gaussian. Systematic errors due to  
uncertainties  in the signal PDF are estimated by varying the peak positions and
resolutions. We also check the $A_{CP}$ values after varying the amount of the
expected $\eta K^*$ feed-down and the reflection background. The $\bb$ 
contributions are allowed to be different for the two samples to obtain
the systematic error. The largest 
uncertainty is the asymmetry of the reflection.  A possible detector bias in $A_{CP}$ 
is studied using $B\to D\pi^+$ decays. The obtained 
uncertainty is 0.5\%. Each $A_{CP}$ deviation is added quadratically to provide
the total systematic uncertainty.   
   
In summary, we have  observed  $\btoetapi$ and found evidence for 
$\btoetak$; the 
measured branching fractions and partial rate asymmetries are summarized
in Table \ref{tab:result}.  We conclude that the $B^+\to \eta \pi^+$ 
 branching fraction is larger than that of  $B^+\to \eta K^+$. 
The measured $\btoetapi$ branching fraction  is 
consistent with an earlier result published by the BaBar Collaboration; 
however, unlike the large negative $A_{CP}$
measured by BaBar, the central value in this analysis
is small and positive, and is consistent with no asymmetry. For the decay 
$\btoetak$, the measured 
branching fraction is 40\% lower than the published result of the BaBar 
experiment, corresponding 
to a 1.3 $\sigma$ deviation. It is interesting to note that although the 
errors are still large, both experiments  suggest
a large negative $A_{CP}$ value for $\btoetak$, which is anticipated by some
theories \cite{etakcp}. No significant signals are found in  neutral 
$B\to\eta h$ decays and upper limits at the 90\% confidence level are given.    
 
\begin{figure}[htb]
\includegraphics[width=0.7\textwidth]{fig2.eps}
\caption{$\Mbc$ and $\de$ projections for (a,b) $B^+\to\eta \pi^+$, (c,d) 
$B^- \to \eta\pi^-$,
(e,f) $B^+\to\eta K^+$, and (g,h) $B^-\to\eta K^-$  with 
the $\etagg$ and $\etapi$ modes combined. Open
histograms are data, solid curves are the fit functions, dashed lines show
the continuum contributions and shaded histograms are the $\eta K^*/\eta \rho$
contributions.  Small curves around $\Mbc = 5.28$ GeV/$c^2$ and $\de =\pm 0.05$
GeV are the reflection background on $\btoetapi$ and $\btoetak$.}  
\label{fig:acp}
\end{figure}

%\section*{Acknowledgments}
%***** Acknowledgments *****
% Please paste this acknowledgement into your latex file. 
 %----------- Long version, for most papers ----------- 
We thank the KEKB group for the excellent operation of the
accelerator, the KEK Cryogenics group for the efficient
operation of the solenoid, and the KEK computer group and
the National Institute of Informatics for valuable computing
and Super-SINET network support. 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 Education, Science and Training;
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 01324; the
Ministry of Science and Technology of the Russian
Federation; the Ministry of Education, Science and Sport of
the Republic of Slovenia; the National Science Council and
the Ministry of Education of Taiwan; and the U.S.\
Department of Energy.

%-------- Short version, if necessary, for PRL -----------
% currently commented out
%We thank the KEKB group for the excellent operation of the
%accelerator, the KEK Cryogenics group for the efficient
%operation of the solenoid, and the KEK computer group and
%the NII for valuable computing and Super-SINET network
%support.  We acknowledge support from MEXT and JSPS (Japan);
%ARC and DEST (Australia); NSFC (contract No.~10175071,
%China); DST (India); the BK21 program of MOEHRD and the CHEP
%SRC program of KOSEF (Korea); KBN (contract No.~2P03B 01324,
%Poland); MIST (Russia); MESS (Slovenia); NSC and MOE
%(Taiwan); and DOE (USA).

\begin{thebibliography}{99}

%\bibitem{PDG}
%S. Eidelman {\it et al.}, Phys. Lett. B {\bf 592}, 1 (2004).

\bibitem{etapetac}
CLEO Collaboration, S. J. Richichi  {\it et al.}, Phys. Rev. Lett. {\bf 85},
520 (2000).

\bibitem{etapk}
 Belle Collaboration, K. Abe {\it et al.}, Phys. Lett. B
{\bf 517}, 309 (2001); 
BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. Lett. {\bf 91},
161801 (2003).

 
\bibitem{lipkin}H.J. Lipkin, Phys. Lett. B {\bf 254}, 247 (1991).

\bibitem{etakt} M. Bander, D. Silverman, and A. Soni, Phys. Rev. Lett.
{\bf 43}, 242 (1979); M.-Z. Yang and Y.-D. Yang, Nucl. Phys. B {\bf 609}, 409
(2001); M. Beneke and M. Neubert, Nucl. Phys. B {\bf 651}, 225 (2003). 


\bibitem{CC}
Throughout this paper, 
the inclusion of the charge conjugate mode decay is implied
unless otherwise stated.


\bibitem{etapit} S. Barshay, D. Rein, and L.M. Sehgal, Phys. Lett. B {\bf 259},
475 (1991); A. S. Dighe, M. Gronau, and J. L. Rosner, Phys. Rev. Lett. {\bf 79}, 4333 (1997).   

\bibitem{babar} BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. Lett.
{\bf 92}, 061801 (2004).  

\bibitem{rosner}  Y.-Y. Keum and A. I. Sanda, Phys. Rev. D 
{\bf 67}, 054009 (2003);  C.-W. Chiang, M. Gronau, J.L. Rosner and D. A. 
Suprun, Phys. Rev. D {\bf 70}, 034020 (2004).

\bibitem{KEKB}
S.~Kurokawa and E.~Kikutani, Nucl. Instr. and. Meth. A {\bf 499}, 1 (2003),
and other papers included in this volume.

\bibitem{Belle}
Belle Collaboration, A.~Abashian {\it et al.},
Nucl. Instr. and Meth. A {\bf 479}, 117 (2002).

\bibitem{fisher}R.~A.~Fisher, Ann. Eugenics {\bf 7}, 179 (1936).

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

\bibitem{sfw}
 The Fox-Wolfram moments were introduced in
 G.~C.~Fox and S.~Wolfram, Phys. Rev. Lett. {\bf 41}, 1581 (1978).
 The Fisher discriminant used by Belle, based on modified Fox-Wolfram
 moments (SFW), is described in 
 K.~Abe {\it et al.} (Belle Collab.), Phys. Rev. Lett. {\bf 87},
 101801 (2001). 

\bibitem {sperp}CLEO Collaboration, R. Ammar {\it et al.},
 Phys. Rev. Lett. {\bf 71}, 674 (1993).

\bibitem{tagging} Belle Collaboration, H. Kakuno {\it et al.}, 
Nucl. Instr. and Meth. A {\bf 533}, 516 (2004). 

\bibitem{argus} ARGUS Collaboration, H. Albrecht {\it et al.}, Phys. Lett. B
 {\bf 241}, 278 (1990).

%\bibitem{HFAG}
%Heavy Flavor Averaging Group, http://www.slac.stanford.edu/xorg/hfag.

\bibitem{etakst}BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. 
D {\bf 70}, 032006 (2004).

\bibitem{etakcp}
C.-W. Chiang,  M. Gronau, and J. L. Rosner, Phys. Rev. D
{\bf 68}, 074012 (2003);
S. Barshay and G. Kreyerhoff, Phys. Lett. B {\bf 578}, 330, (2004).
\end{thebibliography}
%

\end{document}

hep-ex0412043.extracted_bib
\begin{thebibliography}{99}

%\bibitem{PDG}
%S. Eidelman {\it et al.}, Phys. Lett. B {\bf 592}, 1 (2004).

\bibitem{etapetac}
CLEO Collaboration, S. J. Richichi  {\it et al.}, Phys. Rev. Lett. {\bf 85},
520 (2000).

\bibitem{etapk}
 Belle Collaboration, K. Abe {\it et al.}, Phys. Lett. B
{\bf 517}, 309 (2001); 
BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. Lett. {\bf 91},
161801 (2003).

 
\bibitem{lipkin}H.J. Lipkin, Phys. Lett. B {\bf 254}, 247 (1991).

\bibitem{etakt} M. Bander, D. Silverman, and A. Soni, Phys. Rev. Lett.
{\bf 43}, 242 (1979); M.-Z. Yang and Y.-D. Yang, Nucl. Phys. B {\bf 609}, 409
(2001); M. Beneke and M. Neubert, Nucl. Phys. B {\bf 651}, 225 (2003). 


\bibitem{CC}
Throughout this paper, 
the inclusion of the charge conjugate mode decay is implied
unless otherwise stated.


\bibitem{etapit} S. Barshay, D. Rein, and L.M. Sehgal, Phys. Lett. B {\bf 259},
475 (1991); A. S. Dighe, M. Gronau, and J. L. Rosner, Phys. Rev. Lett. {\bf 79}, 4333 (1997).   

\bibitem{babar} BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. Lett.
{\bf 92}, 061801 (2004).  

\bibitem{rosner}  Y.-Y. Keum and A. I. Sanda, Phys. Rev. D 
{\bf 67}, 054009 (2003);  C.-W. Chiang, M. Gronau, J.L. Rosner and D. A. 
Suprun, Phys. Rev. D {\bf 70}, 034020 (2004).

\bibitem{KEKB}
S.~Kurokawa and E.~Kikutani, Nucl. Instr. and. Meth. A {\bf 499}, 1 (2003),
and other papers included in this volume.

\bibitem{Belle}
Belle Collaboration, A.~Abashian {\it et al.},
Nucl. Instr. and Meth. A {\bf 479}, 117 (2002).

\bibitem{fisher}R.~A.~Fisher, Ann. Eugenics {\bf 7}, 179 (1936).

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

\bibitem{sfw}
 The Fox-Wolfram moments were introduced in
 G.~C.~Fox and S.~Wolfram, Phys. Rev. Lett. {\bf 41}, 1581 (1978).
 The Fisher discriminant used by Belle, based on modified Fox-Wolfram
 moments (SFW), is described in 
 K.~Abe {\it et al.} (Belle Collab.), Phys. Rev. Lett. {\bf 87},
 101801 (2001). 

\bibitem {sperp}CLEO Collaboration, R. Ammar {\it et al.},
 Phys. Rev. Lett. {\bf 71}, 674 (1993).

\bibitem{tagging} Belle Collaboration, H. Kakuno {\it et al.}, 
Nucl. Instr. and Meth. A {\bf 533}, 516 (2004). 

\bibitem{argus} ARGUS Collaboration, H. Albrecht {\it et al.}, Phys. Lett. B
 {\bf 241}, 278 (1990).

%\bibitem{HFAG}
%Heavy Flavor Averaging Group, http://www.slac.stanford.edu/xorg/hfag.

\bibitem{etakst}BaBar Collaboration, B. Aubert {\it et al.}, Phys. Rev. 
D {\bf 70}, 032006 (2004).

\bibitem{etakcp}
C.-W. Chiang,  M. Gronau, and J. L. Rosner, Phys. Rev. D
{\bf 68}, 074012 (2003);
S. Barshay and G. Kreyerhoff, Phys. Lett. B {\bf 578}, 330, (2004).
\end{thebibliography}