Search for the \boldmath$\btodgamma$ process
Belle Collaboration
%------------------------------------------------------ We report the results of a search for the flavor-changing neutral current process $\btodgamma$ using a sample of 275 million $B$ meson pairs accumulated by the Belle detector at KEKB. We find no significant signal for the exclusive decays $\BtoRMG$, $\BtoRBG$, or $\BtoOG$. Assuming an isospin relation between the three modes, we set an upper limit for the combined branching fraction $\Br(\BtoROG)$, of $\ULROG$ at the 90\% confidence level. This limit can be used to constrain the ratio of CKM matrix elements $|\Vtd/\Vts|$.
b2dgamma.tex

           %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
           %                                                %
           %  Search for the b --> d gamma process          %
           %                                                %
           %  The Belle Collaboration                       %
           %                                                %
           %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


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% (1) for PRL submission
%\documentclass[aps,prl,preprint,superscriptaddress,showpacs]{revtex4}
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%\documentclass[aps,prl,preprint,tightenlines,superscriptaddress,showpacs]{revtex4}
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% size and color of figures, Belle logo, preprint numbers
\if\mystyle4
  \typeout{PREPRINT!!!!}
 \def\figonescale{0.7}
 \def\figtwoscale{0.8}
 \def\figthreescale{0.8}
  \def\bellelogo{\vbox to 16mm{
                 \vss\hbox{\resizebox{!}{3cm}{
                 \includegraphics{belle-logo.eps}}}}\vspace{-1cm}}
  \def\preprintA{\hbox{\hfil BELLE-CONF-0401}}
  \def\preprintB{\hbox{\hfil ICHEP 11-0646}}
  \def\preprintC{}
\else
 \def\figonescale{0.4}
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 \def\bellelogo{}
 \def\preprintA{}
 \def\preprintB{}
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\fi

\def\mydate{\date{May 30 2005}}

\usepackage{graphicx}
%\usepackage{ulem}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PARTICLES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\KP{K^+}
\def\KM{K^-}
\def\KZ{K^0}
\def\KS{{K^0_S}}
\def\KL{{K^0_L}}
\def\piZ{{\pi^0}}
\def\piP{{\pi^+}}
\def\piM{{\pi^-}}
\def\rhoP{{\rho^+}}
\def\rhoM{{\rho^-}}
\def\rhoZ{{\rho^0}}
\def\Kstar{{K^*}}
\def\KstarZ{{K^{*0}}}
\def\KstarP{{K^{*+}}}
\def\KstarM{{K^{*-}}}
\def\KstarB{{\Kbar^{*0}}}
\def\omegaG{{\omega\gamma}}
\def\rhoG{{\rho\gamma}}
\def\rhoPG{{\rhoP\gamma}}
\def\rhoMG{{\rhoM\gamma}}
\def\rhoZG{{\rhoZ\gamma}}
\def\ROG{{(\rho,\omega)\gamma}}
\def\KstarG{{\Kstar\gamma}}
\def\KstarZG{{\KstarZ\gamma}}
\def\KstarPG{{\KstarP\gamma}}
\def\KstarMG{{\KstarM\gamma}}
\def\KstarBG{{\KstarB\gamma}}
\def\KPPM{\KP\piM}
\def\KSPZ{\KS\piZ}
\def\KSPP{\KS\piP}
\def\KPPZ{\KP\piZ}
\def\Jpsi{{J/\psi}}
\def\uubar{u\overline{u}{}}
\def\ddbar{d\overline{d}{}}
\def\ssbar{s\overline{s}{}}
\def\ccbar{c\overline{c}{}}
\def\qqbar{q\overline{q}{}}
\def\fbar{\overline{f}{}}
\def\Bbar{\overline{B}{}}
\def\Dbar{\overline{D}{}}
\def\Kbar{\overline{K}{}}
\def\pbar{\overline{p}{}}
\def\nubar{\overline{\nu}{}}
\def\sbar{\overline{s}{}}
\def\cbar{\overline{c}{}}
\def\bbar{\overline{b}{}}
\def\Xsbar{\overline{X}_s{}}
\def\epem{e^+e^-{}}
\def\mumu{\mu^+\mu^-{}}
\def\elel{\ell^+\ell^-{}}
\def\BBbar{B\Bbar}
\def\Bd{B_d^0{}}
\def\Bs{B_s^0{}}
\def\Bds{B_{d,s}^0{}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PROCESSES - radiatives %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\btosgamma{b\to s\gamma}
\def\bbartosbargamma{\bbar\to \sbar\gamma}
\def\btodgamma{b\to d\gamma}
\def\btosdgamma{b\to (s,d)\gamma}

\def\BtoRG{B\to \rho\gamma}
\def\BtoRPG{B^+\to \rho^+\gamma}
\def\BtoRMG{B^-\to \rho^-\gamma}
\def\BtoRZG{B^0\to \rho^0\gamma}
\def\BtoRBG{\Bbar^0\to \rho^0\gamma}
\def\BtoROG{B\to (\rho,\omega)\gamma}
\def\BtoOG{\Bbar^0\to \omega\gamma}

\def\BtoKG{B\to K^*\gamma}

\def\Btorhogamma{B\to \rho\gamma}
\def\Btoomegagamma{B\to \omega\gamma}
\def\BtoXsgamma{B\to X_s\gamma}
\def\BtoXdgamma{B\to X_d\gamma}
\def\BtoKstargamma{B\to K^*\gamma}
\def\BbartoKstarbargamma{\Bbar\to \Kbar^*\gamma}
\def\BtoKZG{B^0\to K^{*0}\gamma}
\def\BtoKPG{B^+\to K^{*+}\gamma}
\def\BtoKBG{\Bbar^0\to \Kbar^{*0}\gamma}
\def\BtoKMG{B^-\to K^{*-}\gamma}
\def\BtoKstarZG{B^0\to K^{*0}\gamma}
\def\BtoKstarPG{B^+\to K^{*+}\gamma}
\def\BtoKXgamma{B\to K_X\gamma}
\def\BtoVgamma{B\to V\gamma}
\def\BtoKstarzerogamma{B^0\to K^{*0}\gamma}
\def\BtoKstarplusgamma{B^+\to K^{*+}\gamma}
\def\Btorhozerogamma{B^0\to \rho^0\gamma}
\def\Btorhoplusgamma{B^+\to \rho^+\gamma}
\def\BtoKSphigamma{B^0\to\KS\phi\gamma}
\def\BtoKPphigamma{B^+\to\KP\phi\gamma}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PROCESSES - electroweak %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\btosll{b\to s\elel}

\def\BtoXsll{B\to X_s\elel}
\def\BtoXsee{B\to X_s \epem}
\def\BtoXsmumu{B\to X_s\mumu}
\def\BtoKll{B\to K\elel}
\def\BtoKee{B\to K\epem}
\def\BtoKmumu{B\to K\mumu}
\def\Xsll{X_s\elel}
\def\Xsee{X_s\epem}
\def\Xsmumu{X_s\mumu}
\def\Kll{K\elel}
\def\Kstarll{K^*\elel}
\def\BtoKstarll{B\to K^*\elel}
\def\BtoKstaree{B\to K^*\epem}
\def\BtoKstarmumu{B\to K^*\mumu}
\def\BtoKorKstarll{B\to K^{(*)}\elel}
\def\BtoXdll{B\to X_d\elel}
\def\Btoll{B^0\to\elel}
\def\Btoee{B^0\to\epem}
\def\Btomumu{B^0\to\mumu}
\def\Btoemu{B^0\to e^\pm\mu^\mp}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PROCESSES - else %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\btos{b\to s}
\def\btod{b\to d}
\def\btoc{b\to c}
\def\btou{b\to u}
\def\btosg{b\to sg}

\def\BtoKpi{B\to K\pi}
\def\BtophiK{B\to\phi K}
\def\Btopipi{B\to\pi\pi}
\def\BtoDspi{B\to D_s\pi}
\def\BtoDZpi{B^-\to D^0\pi^-}

\def\Btopilnu{B\to\pi\ell\nu}
\def\Btorholnu{B\to\rho\ell\nu}
\def\Btoomegalnu{B\to\omega\ell\nu}

\def\BtoJpsiKS{B\to\Jpsi\KS}
\def\BtophiKS{B\to\phi\KS}
\def\BtoetapKS{B\to\eta'\KS}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% UNITS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\ps{\mbox{~ps}}
\def\um{\mbox{~}\mu\mbox{m}}
\def\mm{\mbox{~mm}}
\def\cm{\mbox{~cm}}

\def\lumiunit{\mbox{~cm}^{-2}\mbox{s}^{-1}}

\def\nb{\mbox{~nb}}
\def\nbinv{\mbox{~nb}^{-1}}
\def\pbinv{\mbox{~pb}^{-1}}
\def\fbinv{\mbox{~fb}^{-1}}
\def\abinv{\mbox{~ab}^{-1}}

\def\GeV{\mbox{~GeV}}
\def\GeVc{\mbox{~GeV}/c}
\def\GeVcc{\mbox{~GeV}/c^2}
\def\MeV{\mbox{~MeV}}
\def\MeVc{\mbox{~MeV}/c}
\def\MeVcc{\mbox{~MeV}/c^2}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OTHER SYMBOLS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\Vud{V_{ud}}
\def\Vus{V_{us}}
\def\Vub{V_{ub}}
\def\Vcd{V_{cd}}
\def\Vcs{V_{cs}}
\def\Vcb{V_{cb}}
\def\Vtd{V_{td}}
\def\Vts{V_{ts}}
\def\Vtb{V_{tb}}

\def\Order#1{{\cal O}(#1)}
\def\Br{{\cal B}}
\def\Lumi{{\cal L}}

\def\Lpi{L_\pi}
\def\LK{L_K}
\def\LpiK{{\cal L}_{\pi/K}}

\def\Mbc{M_{\rm bc}}
\def\DeltaE{\Delta{E}}
\def\Ebeam{E^*_{\rm beam}{}}
\def\EB{E_B^*{}}
\def\pB{p_B^*{}}
\def\Emiss{E_{\rm miss}}
\def\Pmiss{P_{\rm miss}}
\def\pCM{p^{\rm CM}}

\def\Mll{M_{\elel}}
\def\MKpi{M_{K\pi}}
\def\Mpipi{M_{\pi\pi}}

\def\shat{\hat{s}}
\def\Cseveneff{C_7^{\rm eff}}
\def\Cnineeff{C_9^{\rm eff}}
\def\Cteneff{C_{10}^{\rm eff}}
\def\Cseven{C_7}
\def\Cnine{C_9}
\def\Cten{C_{10}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% SHORTHANDS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\eKS{\epsilon_{\KS}}
\def\eKP{\epsilon_{\KP}}
\def\epiZ{\epsilon_{\piZ}}
\def\epiP{\epsilon_{\piP}}

\def\eKSeKPdata{(\eKS/\eKP)_{\rm data}}
\def\eKSeKPMC{(\eKS/\eKP)_{\rm MC}}
\def\epiZepiPdata{(\epiZ/\epiP)_{\rm data}}
\def\epiZepiPMC{(\epiZ/\epiP)_{\rm MC}}

\def\Btorhogamma{B\to \rho\gamma}
\def\BtoKstargamma{B\to K^*\gamma}
\def\BtoVgamma{B\to V\gamma}
\def\BtoKstarzerogamma{B^0\to K^{*0}\gamma}
\def\BtoKstarplusgamma{B^+\to K^{*+}\gamma}
\def\Btorhozerogamma{B^0\to \rho^0\gamma}
\def\Btorhoplusgamma{B^+\to \rho^+\gamma}

\def\Egamma{E^*_\gamma}
\def\EgammaMomII{\langle\Egamma^2\rangle-\langle\Egamma\rangle^2}

\def\Acp{A_{CP}}
\def\Deltapz{\Delta_{+0}}
\def\tauBratio{{\tau_{B^+}\over\tau_{B^0}}}

\def\MXs{M(X_s)}

\def\AFB{A_{FB}}

\def\piZeta{\piZ/\eta}

\def\costhetahel{{\cos\theta_{\rm hel}}}
\def\thetaB{{\theta^*_B}}
\def\cosB{{\cos\thetaB}}

\def\redto{\red\Rightarrow}

\def\calF{{\cal F}}
\def\calLs{{\cal L}_s}
\def\calLc{{\cal L}_c}
\def\calR{{\cal R}}
\def\calL{{\cal L}}

\def\Deltaz{\Delta{z}}
\def\thetahel{\theta_{\rm hel}}
\def\coshel{\cos\thetahel}

\def\Lzero{{\cal L}_0}
\def\Lmax{{\cal L}_{\rm max}}

\def\PM#1#2{\,^{+#1}_{-#2}{}}
\def\EM#1{\times10^{-#1}}

\def\etal{\textit{et al.}}
\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)} % {journal}{vol}{page}{year}
\def\NCA{Nuovo Cimento}                      % Some useful journal names
\def\NIMA{Nucl. Instrum. Meth. A}
\def\NPB{Nucl. Phys. B}
\def\PLB{Phys. Lett. B}
\def\PRL{Phys. Rev. Lett.}
\def\PRD{Phys. Rev. D}
\def\ZPC{Z. Phys. C}
\def\EPJD{Eur. Phys. J. direct C}
\def\EPJC{Eur. Phys. J. C}
\def\JPG{J. Phys. G}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MACROS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\makeatletter
\def\mygraphic@[#1,#2]#3{\resizebox{#1}{#2}{\includegraphics{#3}}}
\def\mygraphics{\@ifnextchar[{\mygraphic@}{\mygraphic@[\textwidth,!]}}
\def\myep@[#1]#2{\resizebox{#1\textwidth}{!}{\includegraphics{#2}}}
\def\myeps{\@ifnextchar[{\myep@}{\myep@[1]}}
\makeatother

%%
\def\EffKaon{76\mbox{--}80\%} % kaon-id eff for atc<0.4, 76(80)% for K*0(+)
\def\EffPionR{89\%}  % pion-id efficiency for atc>0.85

% rho0 gamma  pi+ 4017/4494 => 89.4 +/- 0.5 %
%             pi- 4017/4539 => 88.5 +/- 0.5 %
% rho+ gamma      3888/4309 => 90.2 +/- 0.5 %
% omega gamma     3357/3443 => 93.7 +/- 0.4 %

\def\EffPionO{94\%}  % pion-id efficiency for atc>0.8
\def\FakePionR{{\sim}10\%} % K->pi fake rate, atc>0.85, 8.6(12.4)% for K*0(+)
%\def\FakePionO{\TBF{xx.x\%}} % K->pi fake rate for atc>0.8

\def\EffVtxVeryRough{85\%} % typical vertexing efficiency
\def\EffVtxS{97\%} % vertexing efficiency for signal MC (too high?)
\def\EffVtxC{85\%} % vertexing efficiency for continuum
\def\EffVtxSii{85\%} % vertexing efficiency for signal MC (SVD2)
\def\EffVtxCii{81\%} % vertexing efficiency for continuum (SVD2)


\def\drcut{2\cm}
\def\dzcut{5\cm}
\def\ptrkcut{100\MeVc}

\def\effRPG{(5.5\pm0.4)\%}
\def\effRZG{(3.9\pm0.3)\%}
\def\effOMG{(3.9\pm0.4)\%}

%\def\sROG{1.9}
%\def\sRPG{2.1}
%\def\sRZG{0.6}
%\def\sOMG{0.2}
\def\sROG{1.2}
\def\sRPG{1.7}
\def\sRZG{0.3}
\def\sOMG{0.1}

%\def\BrROG{(0.72\PM{0.43}{0.39}\PM{0.28}{0.27})\EM6}
\def\BrROG{(0.72\PM{0.43}{0.39}\pm{0.28})\EM6}
\def\BrRPG{(1.24\PM{0.67}{0.61}\pm{0.26})\EM6}
\def\BrRZG{(0.18\PM{0.33}{0.25}\pm{0.10})\EM6}
\def\BrOMG{(0.08\PM{0.39}{0.31}\pm{0.19})\EM6}


\def\nRPG{18.7\PM{10.1}{\phantom{1}9.2}}
\def\nRZG{\phantom{1} 1.9\PM{2.8}{2.7\phantom{1}}}
\def\nOMG{\phantom{1} 0.9\PM{4.2}{3.3\phantom{1}}}


\def\ULROG{1.4\EM6}
\def\ULRPG{2.2\EM6}
\def\ULRZG{0.8\EM6}
\def\ULOMG{0.8\EM6}

\def\RatioROGoverKG{0.019\PM{0.012}{0.010}\PM{0.008}{0.007}} %+0.0075
\def\ULROGoverKG{0.035}
\def\RatioVtdoVts{0.15\PM{0.06}{0.05}}
%\def\ULVtdoVts{0.21}
\def\ULVtdoVts{0.22}

\begin{document}

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

\bellelogo

\preprint{\vbox{
  \preprintA
  \preprintB
  \preprintC
}}

\title{Search for the \boldmath$\btodgamma$ process}


%\author{Belle Collaboration}
%\input{author.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% Paper:    b -> d gamma
%%% Journal:  Physical Review Letters
%%% Contacts: D. Mohapatra (dmohapat@vt.edu)
%%%           M. Nakao (mikihiko.nakao@kek.jp)
%%%           B. Yabsley (yabsley@bmail.kek.jp)
%%% 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{University of Cincinnati, Cincinnati, Ohio 45221}
\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{Kyungpook National University, Taegu}
\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne}
\affiliation{University of Ljubljana, Ljubljana}
\affiliation{University of Melbourne, Victoria}
\affiliation{Nagoya University, Nagoya}
\affiliation{Nara Women's University, Nara}
\affiliation{National Central University, Chung-li}
\affiliation{National United University, Miao Li}
\affiliation{Department of Physics, National Taiwan University, Taipei}
\affiliation{H. Niewodniczanski Institute of Nuclear Physics, Krakow}
\affiliation{Nippon Dental University, Niigata}
\affiliation{Niigata University, Niigata}
\affiliation{Nova Gorica Polytechnic, Nova Gorica}
\affiliation{Osaka City University, Osaka}
\affiliation{Osaka University, Osaka}
\affiliation{Panjab University, Chandigarh}
\affiliation{Peking University, Beijing}
\affiliation{Princeton University, Princeton, New Jersey 08544}
\affiliation{University of Science and Technology of China, Hefei}
\affiliation{Seoul National University, Seoul}
\affiliation{Shinshu University, Nagano}
\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{University of Tsukuba, Tsukuba}
\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061}
\affiliation{Yonsei University, Seoul}
   \author{D.~Mohapatra}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
   \author{M.~Nakao}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{B.~D.~Yabsley}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
 \author{K.~Abe}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{K.~Abe}\affiliation{Tohoku Gakuin University, Tagajo} % TohokuGakuin
   \author{H.~Aihara}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
   \author{K.~Arinstein}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
   \author{Y.~Asano}\affiliation{University of Tsukuba, Tsukuba} % Tsukuba
   \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{E.~Barberio}\affiliation{University of Melbourne, Victoria} % Melbourne
   \author{M.~Barbero}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
   \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{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{Y.~Chao}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
   \author{A.~Chen}\affiliation{National Central University, Chung-li} % NCU
   \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{A.~Chuvikov}\affiliation{Princeton University, Princeton, New Jersey 08544} % Princeton
   \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{J.~Dragic}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{S.~Eidelman}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
   \author{T.~Gershon}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \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{A.~Gori\v sek}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
   \author{T.~Hara}\affiliation{Osaka University, Osaka} % Osaka
   \author{K.~Hayasaka}\affiliation{Nagoya University, Nagoya} % Nagoya
   \author{M.~Hazumi}\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.~Hokuue}\affiliation{Nagoya University, Nagoya} % Nagoya
   \author{Y.~Hoshi}\affiliation{Tohoku Gakuin University, Tagajo} % TohokuGakuin
   \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{T.~Iijima}\affiliation{Nagoya University, Nagoya} % Nagoya
   \author{K.~Ikado}\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{M.~Iwasaki}\affiliation{Department of Physics, University of Tokyo, Tokyo} % Tokyo
   \author{Y.~Iwasaki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{J.~H.~Kang}\affiliation{Yonsei University, Seoul} % Yonsei
   \author{J.~S.~Kang}\affiliation{Korea University, Seoul} % Korea
   \author{H.~Kawai}\affiliation{Chiba University, Chiba} % Chiba
   \author{T.~Kawasaki}\affiliation{Niigata University, Niigata} % Niigata
   \author{H.~R.~Khan}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
   \author{H.~J.~Kim}\affiliation{Kyungpook National University, Taegu} % Kyungpook
   \author{S.~M.~Kim}\affiliation{Sungkyunkwan University, Suwon} % Sungkyunkwan
   \author{K.~Kinoshita}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
   \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{C.~C.~Kuo}\affiliation{National Central University, Chung-li} % NCU
   \author{A.~Kuzmin}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
   \author{Y.-J.~Kwon}\affiliation{Yonsei University, Seoul} % Yonsei
   \author{G.~Leder}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
   \author{S.~E.~Lee}\affiliation{Seoul National University, Seoul} % Seoul
   \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{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \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{G.~Majumder}\affiliation{Tata Institute of Fundamental Research, Bombay} % Tata
   \author{F.~Mandl}\affiliation{Institute of High Energy Physics, Vienna} % Vienna
   \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{H.~Miyata}\affiliation{Niigata University, Niigata} % Niigata
   \author{G.~R.~Moloney}\affiliation{University of Melbourne, Victoria} % Melbourne
   \author{T.~Nagamine}\affiliation{Tohoku University, Sendai} % Tohoku
   \author{Y.~Nagasaka}\affiliation{Hiroshima Institute of Technology, Hiroshima} % Hiroshima
   \author{E.~Nakano}\affiliation{Osaka City University, Osaka} % OsakaCity
   \author{H.~Nakazawa}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \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{T.~Nozaki}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{S.~Ogawa}\affiliation{Toho University, Funabashi} % Toho
   \author{T.~Ohshima}\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.~Park}\affiliation{Kyungpook National University, Taegu} % Kyungpook
   \author{R.~Pestotnik}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
   \author{L.~E.~Piilonen}\affiliation{Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061} % VPI
   \author{Y.~Sakai}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{T.~R.~Sarangi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{N.~Sato}\affiliation{Nagoya University, Nagoya} % Nagoya
   \author{N.~Satoyama}\affiliation{Shinshu University, Nagano} % Shinshu
   \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{J.~Sch\"umann}\affiliation{Department of Physics, National Taiwan University, Taipei} % Taiwan
   \author{A.~J.~Schwartz}\affiliation{University of Cincinnati, Cincinnati, Ohio 45221} % Cincinnati
   \author{K.~Senyo}\affiliation{Nagoya University, Nagoya} % Nagoya
   \author{M.~E.~Sevior}\affiliation{University of Melbourne, Victoria} % Melbourne
   \author{H.~Shibuya}\affiliation{Toho University, Funabashi} % Toho
   \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}\affiliation{Nova Gorica Polytechnic, Nova Gorica} % NovaGorica
   \author{M.~Stari\v c}\affiliation{J. Stefan Institute, Ljubljana} % Ljubljana
   \author{T.~Sumiyoshi}\affiliation{Tokyo Metropolitan University, Tokyo} % TMU
   \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{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{K.~Trabelsi}\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{S.~Uno}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{G.~Varner}\affiliation{University of Hawaii, Honolulu, Hawaii 96822} % Hawaii
   \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{Y.~Watanabe}\affiliation{Tokyo Institute of Technology, Tokyo} % TIT
   \author{Q.~L.~Xie}\affiliation{Institute of High Energy Physics, Chinese Academy of Sciences, Beijing} % IHEP
   \author{Y.~Yamashita}\affiliation{Nippon Dental University, Niigata} % NihonDental
   \author{M.~Yamauchi}\affiliation{High Energy Accelerator Research Organization (KEK), Tsukuba} % KEK
   \author{Heyoung~Yang}\affiliation{Seoul National University, Seoul} % Seoul
   \author{J.~Ying}\affiliation{Peking University, Beijing} % Peking
   \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{V.~Zhilich}\affiliation{Budker Institute of Nuclear Physics, Novosibirsk} % BINP
   \author{D.~Z\"urcher}\affiliation{Swiss Federal Institute of Technology of Lausanne, EPFL, Lausanne} % Lausanne
\collaboration{The Belle Collaboration}


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

\mydate

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract} %------------------------------------------------------

  We report the results of a search for the flavor-changing neutral
  current process $\btodgamma$ using a sample of 275 million $B$ meson
  pairs accumulated by the Belle detector at KEKB.  We find no
  significant signal for the exclusive decays $\BtoRMG$, $\BtoRBG$, or
  $\BtoOG$. Assuming an isospin relation between the three modes, we
  set an upper limit for the combined branching fraction
  $\Br(\BtoROG)$, of $\ULROG$ at the 90\% confidence level.  This
  limit can be used to constrain the ratio of CKM matrix elements
  $|\Vtd/\Vts|$.

\end{abstract}

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

\pacs{11.30.Hv, 13.40.Hq, 14.65.Fy, 14.40.Nd}

% 11.30.Hv = Flavor symmetries
% 13.20.He = Leptonic and semileptonic decays of bottom mesons
% 13.40.Hq = Leptonic and semileptonic decays of bottom mesons
% 14.40.Nd = Properties of Bottom mesons
% 14.65.Fy = Properties of Bottom quarks
%\input author.tex
\maketitle



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MAIN TEXT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



                       %%%%%%%%%%%%%%%%%%%%%%
                       %%%  INTRODUCTION  %%%
                       %%%%%%%%%%%%%%%%%%%%%%


The $\btodgamma$ process, shown in Fig.~\ref{fig:diagram}(a), is a
flavor changing neutral current transition that proceeds via loop
diagrams in the Standard Model (SM).  It is suppressed with respect to
$\btosgamma$ by the Cabibbo-Kobayashi-Maskawa (CKM) factor
$|\Vtd/\Vts|^2 \sim 0.04$ with a large uncertainty due to the lack of
precise knowledge of $\Vtd$. The exclusive modes $B \to \rho \gamma$
and $B \to \omega \gamma$, which are presumably the easiest modes to
search for, have not yet been observed~\cite{bib:babar-rhogam}.
%Calculations based on the rate for 
%the corresponding exclusive decay $\BtoKG$, the $|\Vtd/\Vts|^2$ suppression,
%and corrections due to form factors, $SU(3)$ breaking
%effects, 
Calculations based on the measured rate for the $\btosgamma$ process
$\BtoKG$ that include $|\Vtd/\Vts|^2$ suppression, corrections due to
form factors, $SU(3)$ breaking effects, and, for $B^-$ decay, the
additional annihilation diagram of Fig.~\ref{fig:diagram}(b), predict
branching fractions in the range $(0.9\mbox{--}2.7)\EM6$
%in the SM 
~\cite{bib:ali-parkhomenko,bib:bosch-buchalla}.  Measurement of these
exclusive branching fractions would improve the constraints on
$|\Vtd/\Vts|$ in the context of the SM, and provide sensitivity to
physics beyond the SM that is complementary to that from $\btosgamma$.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FIGURES 1--------------------------------------------------------------

\begin{figure}[ht]
\begin{center}
\vspace*{24pt}
\myeps[\figonescale]{fig1.eps}
\caption{(a) Loop diagram for $\btodgamma$ and (b) annihilation diagram
  for $\BtoRMG$ only.}
\label{fig:diagram}
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

In this paper, we report the results of a search for the $\btodgamma$
process using a sample of $(275\pm3)$ million $B$ meson pairs
accumulated at the $\Upsilon(4S)$ resonance.  The data are produced in
$\epem$ annihilation at the KEKB energy-asymmetric (3.5 on 8 GeV)
collider~\cite{bib:kekb} and collected with the Belle
detector~\cite{bib:belle-detector}.  The Belle detector includes a
silicon vertex detector (SVD), a central drift chamber (CDC), aerogel
threshold Cherenkov counters (ACC), time-of-flight (TOF) scintillation
counters, and an electromagnetic calorimeter (ECL) comprised of CsI(Tl)
crystals located inside a 1.5 T superconducting solenoid coil.  An iron
flux-return located outside of the coil is instrumented to identify
muons (KLM).  The dataset consists of two subsets: the first 152 million
$B$ meson pairs were collected with a 2.0 cm radius beampipe and a 3-layer SVD, and the
remaining 123 million $B$ meson pairs with a 1.5 cm radius beampipe, a
4-layer SVD and a small-cell inner drift chamber~\cite{bib:svd2}.



                      %%%%%%%%%%%%%%%%%%%%%%%%
                      %%%  RECONSTRUCTION  %%%
                      %%%%%%%%%%%%%%%%%%%%%%%%


We reconstruct the following final states: $\BtoRMG$, $\BtoRBG$, and
$\BtoOG$.  Charge conjugate modes are implicitly included throughout
this paper.  We also reconstruct control samples of $\BtoKMG$ and
$\BtoKBG$ decays.  The following decay chains are used to reconstruct
the intermediate states: $\rhoM\to\piM\piZ$, $\rhoZ\to\piP\piM$,
$\omega\to\piP\piM\piZ$, $\KstarM\to\KM\piZ$, $\KstarB\to\KM\piP$, and
$\piZ\to\gamma\gamma$.

Photon candidates are reconstructed from isolated clusters in the ECL
that have no corresponding charged track, and a shower shape that is
consistent with that of a photon.  A photon in the barrel region of
the ECL ($33^\circ<\theta_\gamma<128^\circ$ in the laboratory frame)
with a center-of-mass (c.m.)\ energy in the range
$1.8\GeV<\Egamma<3.4\GeV$ is selected as the primary photon candidate.
To suppress backgrounds from $\piZ\to\gamma\gamma$ and
$\eta\to\gamma\gamma$ decays, we veto the event if the reconstructed
mass of the primary photon and any other photon of energy 30 (200) MeV
or more is within a $\pm3\sigma$ window, i.e., $\pm18$ $(\pm
32)\MeVcc$, around the $\piZ$ ($\eta$) mass.  This set of criteria is
referred to as the $\piZeta$ veto.  For the primary photon, we sum the
energy deposited in arrays of $3\times3$ and $5\times5$ ECL cells
around the maximum energy cell; if their ratio is less than 0.95, the
event is vetoed.

Neutral pions are formed from photon pairs with invariant masses
within $\pm 10$ ($16$)$\MeVcc$ of the nominal $\piZ$ mass,
corresponding to a ${\sim}2 \sigma$ $({\sim}3\sigma)$ window for the
$\rhoMG$ and $\KstarMG$ ($\omegaG$) modes.  The photon momenta are
then recalculated with a $\piZ$ mass constraint.  We require the
energy of each photon to be greater than 30 MeV.  We also require the
{c.m.}  momentum of the $\piZ$ to be greater than $0.5\GeVc$ for the
$\rhoMG$ and $\KstarMG$ modes.

Charged pions and kaons are reconstructed as tracks in the CDC and
SVD.  Each track is required to have a transverse momentum greater
than $\ptrkcut$ and distance of closest approach to the interaction
point
%within 
of less than $\drcut$ in radius and $\pm\dzcut$ along the $z$-axis,
which is aligned opposite to the positron beam.  We do not use the
track to form the signal candidate if, when combined with any other
track, it forms a $\KS$ candidate with an invariant mass within
$\pm10\MeVcc$ of the nominal $\KS$ mass and a displaced vertex that is
consistent with a $\KS$.  We determine the pion ($\Lpi$) and kaon
($\LK$) likelihoods from ACC, CDC and TOF information, and form a
likelihood ratio $\Lpi/(\Lpi + \LK)$ to separate pions from kaons.  We
select pions using criteria which have an efficiency of $\EffPionR$
and for which $\FakePionR$ of kaons are misidentified as pions.  For
the $\omegaG$ mode, we relax the requirement to select $\EffPionO$ of
pions.  (In the $\KstarG$ modes, we select kaons with an efficiency of
$\EffKaon$.)  In addition, we remove tracks that are consistent with
being electrons or muons.

Invariant masses for the $\rho$ and $\omega$ candidates are required
to be within windows of $\pm150\MeVcc$ and $\pm30\MeVcc$,
respectively, around their nominal masses.

$B$ candidates are reconstructed by combining a $\rho$ or $\omega$
candidate and the primary photon using two variables: the beam-energy
constrained mass $\Mbc = \sqrt{ (\Ebeam/c^2)^2 - |p_{B}^*/c|^{2}}$ and
the energy difference $\Delta E = E^*_{B} - \Ebeam$; $p^*_{B}$ and
$E^*_B$ are the {c.m.}\ momentum and energy of the $B$ candidate, and
$\Ebeam$ is the {c.m.}\ beam energy.  The magnitude of the photon
momentum is replaced by $(\Ebeam - E_{\rho/\omega}^*)/c$ when the
momentum $p^*_{B}$ is calculated.  To optimize the event selection, we
study Monte Carlo (MC) events in the region
$-0.10\GeV<\DeltaE<0.08\GeV$ and $5.273\GeVcc<\Mbc<5.285\GeVcc$: we
choose selection criteria to maximize $N_S/\sqrt{N_B}$, where $N_S$ is
the MC signal yield assuming the SM branching fractions in
Ref.~\cite{bib:ali-parkhomenko}, and $N_B$ is the expected background
yield.


                      %%%%%%%%%%%%%%%%%%%%%%%%
                      %%%  BACKGROUND      %%%
                      %%%%%%%%%%%%%%%%%%%%%%%%

The dominant background arises from continuum events
($\epem\to\qqbar(\gamma)$), where the accidental combination of a
$\rho$ or $\omega$ candidate with a photon forms a $B$ candidate.  We
suppress this background using the following quantities:
%
(1) $\calF$, a Fisher discriminant 
\cite{bib:fisher} constructed from 16 modified Fox-Wolfram
moments~\cite{bib:belle-pi0pi0,bib:fox-wolfram} and the scalar sum of
the transverse momentum of all charged tracks and photons.
%
(2) $\cosB$, where $\thetaB$ is the {c.m.}\ polar angle of the $B$
candidate direction: true $B$ mesons follow a $1-\cos^2\thetaB$
distribution, while candidates in the continuum background are
uniformly distributed.
%
(3) $\Delta z$, the separation between the decay vertex of the candidate
$B$ meson and the origin of the remaining tracks in the event along the
$z$-axis.  The two vertices are 
%available 
reconstructed in about $\EffVtxVeryRough$ of
the $\rhoZG$ and $\omegaG$ events.  Discrimination is provided due to
the displacement of the signal $B$ decay vertex from the other $B$, 
%while tracks from continuum events 
as tracks from continuum events typically have a common vertex.
%
% In about
% $\EffVtxVeryRough$ of events for the $\rhoZG$ and $\omegaG$ modes, a fit
% can be successfully performed to determine the decay vertex of the
% candidate $B$ meson as well as the origin of the remaining tracks in the
% event.  The separation $\Delta z$ between these two vertices along the
% $z$-axis discriminates between continuum events, which have a common
% vertex, and signal events, whose decay vertices are displaced.
%
(4)
%
A tagging quality $r$ which indicates the level of confidence in the
$B$-flavor determination described in Ref.~\cite{bib:hamlet}.  The
algorithm provides additional discrimination between signal and
continuum background where no true $B$ meson is present.

For each of the quantities $\calF$, $\cosB$ and $\Deltaz$, we
construct one-dimensional likelihood distributions for signal and
continuum events.  Signal distributions are modeled with an asymmetric
Gaussian function for $\calF$, ${3\over2}(a_0-a_2\cos^2\thetaB)$ for
$\cos\thetaB$, and an exponential convolved with a Gaussian resolution
function for $\Deltaz$. Continuum background distributions are modeled
with an asymmetric Gaussian for $\calF$, $(b_0-b_2\cos^2\thetaB)$ for
$\cos\thetaB$, and a sum of three Gaussians with a common mean for
$\Deltaz$; the coefficients $a_0$, $a_2$, $b_0$ are close to unity
while the coefficient $b_2$ is close to zero. The $\Delta z$
likelihood distribution for continuum is determined from data in the
sideband region $5.20\GeVcc<\Mbc<5.24\GeVcc$, $|\DeltaE|<0.3\GeV$; we
treat the two subsets of the data separately, as the vertex resolution
is improved in the subset with the 4-layer SVD.  The $\calF$ and
$\cosB$ likelihood distributions are determined from MC samples.



We form product likelihoods $\calLs$ and $\calLc$ for signal and
continuum background, respectively, from the likelihood distributions
for $\calF$, $\cosB$ and (where available) $\Deltaz$, since these
quantities are independent.  In the plane $(r,\calR)$ defined by the
tagging quality $r$ and the likelihood ratio $\calR=\calLs/(\calLs +
\calLc)$, signal tends to populate the edges at $r=1$ and $\calR=1$,
while continuum tends to populate the edges at $r=0$ and $\calR=0$.
We select the events in a signal enriched region defined by $\calR >
\calR_1$ for $r>r_1$, and $\calR > 1 - \alpha(1 + r)$ for $r_2<r<r_1$,
where the parameters $r_1$, $r_2$, $\calR_1$ and $\alpha$ are mode-
and subset-dependent and are determined so that $N_S/\sqrt{N_S+N_B}$
is maximized (we use this quantity instead of $N_S/\sqrt{N_B}$ because
of the limited size of the MC simulation sample used in this
procedure).  The values are $r_1=0.85$, $r_2=0.01$, $\calR_1=0.8$ and
$\alpha=0.025$ for the first subset of the $\rhoZG$ mode; similar
values are used for the other subsets.  We define the rest of the area
as the background enriched region.

% We determine the $\Delta z$ likelihood function separately for the two
% datasets as the vertex resolution is improved in the second dataset.  As
% a consequence, we introduce two sets of selection criteria for each
% decay mode.

We consider the following $B$ decay backgrounds: $\BtoKG$, other $B\to
X_s\gamma$ processes, $B\to\rho\piZ$ and $\omega\piZ$, $B\to\rho\eta$
and $\omega\eta$, $B^-\to\rho^-\rho^0$, other charmless $B$ decays, and
the $b\to c$ transition.  We find the $b\to c$ background to be negligible.
The $\BtoKG$ background may mimic the signal decay $\BtoRG$ if the kaon
from $K^*$ is misidentified as a pion. To suppress
$\BtoKG$ events we calculate $\MKpi$, where the kaon mass is assigned to one
of the charged pion candidates, and reject the candidate if $\MKpi<0.96$
($0.92$) $\GeVcc$ for the $\rhoZG$ ($\rhoMG$) mode.  The decay chain
$\BtoKBG$, $\Kbar^{*0}\to\KS\piZ$, $\KS\to\piP\piM$ has a small
contribution to $\BtoOG$ due to the tail of the $K^*$ Breit-Wigner 
lineshape. In addition, $\BtoKG$ and other $\BtoXsgamma$ decays contribute
to the background when the $\rho$ and $\omega$ candidates are selected
from a random combination of particles.

Charmless decays $B\to\rho\piZ$, $\omega\piZ$, $\rho\eta$, and
$\omega\eta$ may mimic the signal if a photon from $\piZ$ or
$\eta\to\gamma\gamma$ decay is soft and undetected by the $\piZeta$
veto.  To suppress this background, we reject the candidate if
$|\coshel|>0.8$ ($0.6$) for the $\rhoZG$ and $\omegaG$ ($\rhoMG$)
modes, where the helicity angle $\thetahel$ is the angle between the
$\piP$ and $B$ momentum vectors in the $\rho$ rest frame, or the angle
between the normal to the $\omega$ decay plane and the $B$ momentum
vector in the $\omega$ rest frame.  The decay $B^-\to\rho^-\rho^0$,
$\rho^-\to\pi^-\pi^0$ also contributes to the $\BtoRZG$ mode when a
pion from the $\rho^-$ decay and a photon from the $\piZ$ decay are
both soft and undetected.  Other charmless decays have very small
contributions and are considered as an additional background component
when we extract the signal yield.


                       %%%%%%%%%%%%%%%%%%%%%%
                       %%%  EFFICIENCY    %%%
                       %%%%%%%%%%%%%%%%%%%%%%

The reconstruction efficiency for each mode is defined as the fraction
of the signal yield remaining after all selection criteria, where the
signal yield is determined from an extended unbinned maximum likelihood
fit to the MC sample.
%%
%%The reconstruction efficiency for each mode is defined by the fraction
%%of the signal yield from an extended unbinned maximum likelihood fit,
%%using a sum of signal and background components, to the MC sample after
%%all selection criteria.
%%
Each signal distribution is modeled as the product of a Gaussian in
$\Mbc$ and a Crystal Ball lineshape \cite{bib:cbls} in $\DeltaE$ to
reproduce the asymmetric ECL energy response for $\DeltaE$.  The
background component is modeled as the product of a linear function
for $\DeltaE$ and an ARGUS function \cite{bib:argus-function} for
$\Mbc$.  The efficiencies are listed in Table~\ref{tbl:results}.
%
The systematic error on the efficiency is the quadratic sum of the
following contributions, estimated using control samples: the photon
detection efficiency (2.2\%) as measured in radiative Bhabha events;
charged tracking efficiency (1.0\% per track), from partially
reconstructed $D^{*+}\to D^0\piP$, $D^0\to\KS\piP\piM$,
$\KS\to\piP(\piM)$; charged pion identification (1.0\% per pion) from
$D^{*+}\to D^0\piP$, $D^0\to\KM\piP$; neutral pion detection
(4.6--7.3\%) from $\eta$ decays to $\gamma\gamma$, $\piP\piM\piZ$ and
$3\piZ$; $\calR$-$r$ and $\piZeta$ veto requirements (5.4\%) from
$B^-\to D^0\pi^-$, $D^0\to\KM\piP$; and uncertainty due to limited 
MC statistics (0.9--1.5\%).


                       %%%%%%%%%%%%%%%%%%%%%%
                       %%%  FITTING       %%%
                       %%%%%%%%%%%%%%%%%%%%%%

We perform an unbinned maximum likelihood fit to the data in the
($\Mbc$, $\DeltaE$) region bounded by $|\DeltaE|<0.3\GeV$ and
$\Mbc>5.2\GeVcc$, simultaneously for the three signal modes
%(collectively referred to as $\BtoROG$)
and the two $\BtoKG$ modes; the latter are used to determine the residual
$K^*\gamma$ backgrounds in the signal modes.  We fit the two data
subsets simultaneously, so that in total ten distributions are
included in the fit.  We define the combined branching fraction
$\Br(\BtoROG) \equiv \Br(\BtoRMG)$, assuming the isospin relation
\cite{bib:ali-1994} $\Br(\BtoRMG) = 2\tauBratio\Br(\BtoRBG) =
2\tauBratio\Br(\BtoOG)$; we use $\tauBratio = 1.086\pm0.017$
\cite{bib:pdg2004}.  We also assume $\Br(\BtoKG)\equiv\Br(\BtoKMG) =
\tauBratio\Br(\BtoKBG)$.

We describe the events in the fit region using a sum of functions for the signal,
continuum, $\KstarG$, and other background hypotheses.  Signal parameters
for $\Mbc$ and $\DeltaE$ are calibrated using $\BtoDZpi$
and $\BtoKG$ samples, respectively.
%  Those for $\DeltaE$ are calibrated using the result of a fit
%to the $\DeltaE$ distribution of the $\BtoKG$ control sample, in which
%the mean and the width are allowed to float.  
%
We use the combined branching fractions $\BtoROG$ and $\BtoKG$ as free
parameters.
% , from which the signal yield for each channel is deduced
% using the efficiency for each mode.  
% We assume the efficiency systematic
% errors are fully correlated when we evaluate the systematic error.  
The
continuum background is modeled as the product of a linear function in
$\DeltaE$ whose slope is allowed to float, and an ARGUS function in
$\Mbc$ whose parameters are fixed from a comparison between data and MC
in the background enriched region and MC in the signal enriched region.
The continuum contribution in the data is allowed to float.  The
size of the $\KstarG$ background component in each $\ROG$ channel is
constrained using the fit to the $\KstarG$ events.  The levels of
the other backgrounds are fixed using known branching fractions or upper
limits.
%
% The free parameters in the fit are therefore the branching
% fractions for $\BtoROG$ and $\BtoKG$, five continuum fractions, and five
% continuum $\DeltaE$ slopes.


                       %%%%%%%%%%%%%%%%%%%%%%
                       %%%  RESULTS       %%%
                       %%%%%%%%%%%%%%%%%%%%%%

Results of the fit are shown in Fig.~\ref{fig:simfit} and listed in
Table~\ref{tbl:results}. The significance of the fit,
$\sqrt{-2\ln(\Lzero/\Lmax)}$, is found to be $\sROG\sigma$; where
$\Lmax$ ($\Lzero$) is the maximum likelihood from the fit when the
signal branching fraction is floated (set to zero).  To include the
effect of possible systematic error in this calculation, we change
each parameter by $\pm1\sigma$ in the direction that gives the smaller
resulting significance.  The systematic error in the signal yield is
estimated by varying each of the fixed parameters by $1\sigma$, and
then taking the quadratic sum of the deviations in the signal yield
from the nominal value.  The combined branching fraction is
$\Br(\BtoROG)=\BrROG$, where the first and second errors are
statistical and systematic, respectively.

Since the significance is small, we quote a 90\% confidence level
upper limit $\Br_{90}$ using the formula $\int_0^{\Br_{90}}
\calL(x)dx=0.9\int_0^\infty \calL(x)dx$, where $\calL(x)$ is the
likelihood function with the branching fraction fixed at $x$.  The
systematic error is taken into account assuming a Gaussian
distribution.  We find
%
%\begin{equation}
$\Br(\BtoROG)<\ULROG$
%\end{equation}
at the 90\% confidence level.  
We also perform individual fits to the three signal modes;
% and the two $\BtoKG$ modes.  The size of the $\Kbar^{*0}\gamma$
% ($K^{*-}\gamma$) background in the $\rho^0\gamma$ ($\rho^-\gamma$)
% mode is fixed according to the fit result to the $\BtoKG$ mode.
the corresponding upper limits are listed in Table~\ref{tbl:results}.

A similar fit is performed using the ratio of branching
fractions $\Br(\BtoROG)/\Br(\BtoKG)$ instead of $\Br(\BtoROG)$, so that
the systematic error partially cancels.  We find
${\Br(\BtoROG)/\Br(\BtoKG)}<\ULROGoverKG$ at the 90\% confidence level.
One can use this result to constrain $\Vtd$: for example, using the
prescription given in Ref.~\cite{bib:ali-2004},
%
%\begin{equation}
 ${\Br(\BtoROG)\over\Br(\BtoKG)}=
 \left| {\Vtd\over\Vts} \right|^2
 {(1-m_{(\rho,\omega)}^2/m_B^2)^3 \over (1-m_{K^*}^2/m_B^2)^3}
 \zeta^2
 [1 + \Delta R]$
%\end{equation}
%
where the form factor ratio $\zeta=0.85\pm0.10$ and $SU(3)$-breaking
effect $\Delta R=0.1\pm0.1$, we obtain $|\Vtd/\Vts|<\ULVtdoVts$ at the
90\% confidence level.  This limit is slightly smaller than that
resulting from searches for $B_s$ mixing~\cite{bib:pdg2004}.

%This limit is consistent with other
%determinations of $|\Vtd/\Vts|$~\cite{bib:pdg2004}.

                       %%%%%%%%%%%%%%%%%%%%%%
                       %%%  CONCLUSION    %%%
                       %%%%%%%%%%%%%%%%%%%%%%

In conclusion, we search for the $\btodgamma$ process using a
simultaneous fit to the $\BtoROG$ and $\BtoKG$ modes.  The
upper limit we obtain is within the range of SM
predictions~\cite{bib:ali-parkhomenko,bib:bosch-buchalla} and can be
used to constrain $|\Vtd/\Vts|$.

% In summary, we investigate the $\btodgamma$ process by searching for
% $\BtoROG$ decays. We find no evidence for these decays, and constrain
% the magnitude of the ratio of CKM matrix elements $|\Vtd/\Vts|$.





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% ACKNOWLEDGEMENTS -----------------------------------------------------

%-------- Short version, if necessary, for PRL -----------
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); MHEST (Slovenia); SNSF (Switzerland); NSC and
MOE (Taiwan); and DOE (USA).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% TABLES ---------------------------------------------------------------

\begin{table*}[ht]
\caption{ Yield, significance (including systematic error), efficiency and fitted
  branching fraction (central value and 90\%
  confidence level upper limit) for each mode and for
  $\BtoROG$.}
\label{tbl:results}
\begin{ruledtabular}
\begin{tabular}{lccccc}
     &       &              &            
     & \multicolumn{2}{c}{Branching Fraction} \\
Mode & Yield & Significance & Efficiency 
     & Central Value & Upper Limit \\
% {}   & ($\pm$syst) & & (90\% C.L.) \\
\hline

$\BtoRMG$ & $\nRPG$ & $\sRPG\sigma$ & $\effRPG$ & $\BrRPG$ & $\ULRPG$ \\
$\BtoRBG$ & $\nRZG$ & $\sRZG\sigma$ & $\effRZG$ & $\BrRZG$ & $\ULRZG$ \\
$\BtoOG$  & $\nOMG$ & $\sOMG\sigma$ & $\effOMG$ & $\BrOMG$ & $\ULOMG$ \\
Combined  &---  & $\sROG\sigma$ &  ---      & $\BrROG$ & $\ULROG$ \\
%
\end{tabular}
\end{ruledtabular}
\end{table*}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FIGURES 2--------------------------------------------------------------
\begin{figure}[ht]
\begin{center}
\myeps[\figtwoscale]{fig2.eps}
\caption{Projections of the simultaneous fit results to $\Mbc$ (in the
         region $-0.10\GeV<\DeltaE<0.08\GeV$) and $\DeltaE$ (in the
         region $5.273\GeVcc<\Mbc<5.285\GeVcc$) for the individual modes
         and their sum.  Lines represent the total fit result
         (solid), signal (dashed), continuum (dotted), and $B$ decay
         background (dot-dashed) components.}
\label{fig:simfit}
\end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% REFERENCES -----------------------------------------------------------

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Belle Collaboration, A.~Abashian \etal, \Journal{\NIMA}{479}{117}{2002}.

\bibitem{bib:svd2}
Y. Ushiroda, \Journal{\NIMA}{511}{6}{2003}.
% The BELLE silicon vertex detector
% Y. Ushiroda (KEK, Tsukuba) [Nucl.Instrum.Meth.A511:6-10,September 2003]

\bibitem{bib:fisher}
R. A. Fisher, \Journal{Ann. Eugen.}{7}{179}{1936}.

\bibitem{bib:belle-pi0pi0} % for kSFW
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\end{thebibliography}

\end{document}

hep-ex0505097.extracted_bib
\begin{thebibliography}{99}

% \bibitem{bib:belle-rhogam}
% M. Nakao (for the Belle Collaboration), hep-ex/0307031.

\bibitem{bib:babar-rhogam}
% BaBar Collaboration, B.~Aubert \etal, \Journal{\PRL}{92}{111801}{2004}.
BaBar Collaboration, B.~Aubert \etal, \Journal{\PRL}{94}{011801}{2005}.

\bibitem{bib:ali-parkhomenko}
A.~Ali and A.~Ya.~Parkhomenko, \Journal{\EPJC}{23}{89}{2002}.

\bibitem{bib:bosch-buchalla}
In addition to Ref.~\cite{bib:ali-parkhomenko}, for example,
S.~Bosch and G.~Buchalla, \Journal{\NPB}{621}{459}{2002};
T.~Huang, Z.~Li and H.~Zhang, \Journal{\JPG}{25}{1179}{1999}.

\bibitem{bib:kekb}
S.~Kurokawa and E.~Kikutani, \Journal{\NIMA}{499}{1}{2003}.

\bibitem{bib:belle-detector}
Belle Collaboration, A.~Abashian \etal, \Journal{\NIMA}{479}{117}{2002}.

\bibitem{bib:svd2}
Y. Ushiroda, \Journal{\NIMA}{511}{6}{2003}.
% The BELLE silicon vertex detector
% Y. Ushiroda (KEK, Tsukuba) [Nucl.Instrum.Meth.A511:6-10,September 2003]

\bibitem{bib:fisher}
R. A. Fisher, \Journal{Ann. Eugen.}{7}{179}{1936}.

\bibitem{bib:belle-pi0pi0} % for kSFW
Belle Collaboration, S.H.~Lee \etal, \Journal{\PRL}{91}{261801}{2003}.

\bibitem{bib:fox-wolfram}
G. C. Fox and S. Wolfram, \Journal{\PRL}{41}{1581}{1978}.

\bibitem{bib:hamlet}
H.~Kakuno \etal, \Journal{\NIMA}{533}{516}{2004}.

\bibitem{bib:cbls}
Crystal Ball Collaboration, J.~E.~Gaiser \etal, \Journal{\PRD}{34}{711}{1986}.

\bibitem{bib:argus-function}
ARGUS Collaboration, H.~Albrecht \etal, \Journal{\PLB}{241}{278}{1990}.

\bibitem{bib:ali-1994} % text right after eq.14
A.~Ali, V. M.~Braun and H.~Simma, \Journal{\ZPC}{6}{437}{1994}.

\bibitem{bib:pdg2004}
Particle Data Group, S. Eidelman \etal, \Journal{\PLB}{592}{1}{2004}.

\bibitem{bib:ali-2004}
A.~Ali, E.~Lunghi and A.~Parkhomenko, \Journal{\PLB}{595}{323}{2004}.


\end{thebibliography}