IMPROVED MEASUREMENT OF \boldmath $CP$ ASYMMETRY\\IN THE NEUTRAL $B$ MESON SYSTEM
T. Higuchi \footnote{The author is a Research Fellow of the Japan Society for the Promotion of Science.}
(for the Belle collaboration)
We present an improved measurement of the standard model $CP$ violation parameter $\sinbb$ (also known as $\sin2\beta$) based on a sample of $45\times10^6$ $B\overline{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. One neutral $B$ meson is reconstructed in the $\jpsi\ks$, $\psi(2S)\ks$, $\chi_{c1}\ks$, $\eta_c\ks$, $\jpsi K^{*0}$, or $\jpsi\kl$ $CP$-eigenstate decay channel and the flavor of accompanying $B$ meson is identified from its decay products. From the asymmetry in the distribution of the time intervals between the two $B$ meson decay points, we obtain $\sinbb=0.82\pm0.12\mbox{(stat)}\pm0.05\mbox{(syst)}$. The result is preliminary.
defs-blife.tex
%======================= The results ==========================================
\def\tbzresultmean{1.554}
\def\tbzresultstat{\pm 0.030}
\def\tbzresultsyst{\pm0.019}

\def\tbmresultmean{1.695}
\def\tbmresultstat{\pm 0.026}
\def\tbmresultsyst{\pm 0.015}

\def\rbmresultmean{1.091}
\def\rbmresultstat{\pm 0.023}
\def\rbmresultsyst{\pm 0.014}

\def\yresultmean{0.114}
\def\yresultstat{{_{-0.064}^{+0.060}}}
\def\yresultsyst{{_{-0.011}^{+0.012}}}

\def\yinterval{-0.013 < y_{CP} < 0.234}

\def\tbzresult{\tbzresultmean \tbzresultstat\;\mbox{(stat)} \; \tbzresultsyst\;\mbox{(syst)}}
\def\tbmresult{\tbmresultmean \tbmresultstat\;\mbox{(stat)} \tbmresultsyst\;\mbox{(syst)}}
\def\rbmresult{\rbmresultmean \rbmresultstat\;\mbox{(stat)} \rbmresultsyst\;\mbox{(syst)}}
\def\yresult{\yresultmean \; \yresultstat \; \yresultsyst}

%%%

\def\rtau{r_\tau}

\def\yllimit{-0.36}
\def\yulimit{0.35}
\def\tbzdstlnu{1.50\pm0.06^{+0.06}_{-0.04}}
\def\tbmdstlnu{1.54\pm0.10^{+0.14}_{-0.07}}
\def\tbzdstpm{1.55^{+0.18}_{-0.17}{}^{+0.10}_{-0.07}}
\def\tbzdppm{1.41^{+0.13}_{-0.12}\pm0.07}
\def\tbmdzpm{1.73\pm0.10\pm0.09}
\def\tbmpsikm{1.87^{+0.13}_{-0.12}{}^{+0.07}_{-0.14}}
\def\tbzpsiks{1.54^{+0.28}_{-0.24}{}^{+0.11}_{-0.19}}
\def\tbzpsikst{1.56^{+0.22}_{-0.19}{}^{+0.09}_{-0.15}}
\def\Tbzdstlnu{$\taubz=(\tbzdstlnu)$~ps}
\def\Tbmdstlnu{$\taubm=(\tbmdstlnu)$~ps}
\def\Tbzdstpm{$\taubz=(\tbzdstpm)$~ps}
\def\Tbzdppm{$\taubz=(\tbzdppm)$~ps}
\def\Tbmdzpm{$\taubm=(\tbmdzpm)$~ps}
\def\Tbmpsikm{$\taubm=(\tbmpsikm)$~ps}
\def\Tbzpsiks{$\taubz=(\tbzpsiks)$~ps}
\def\Tbzpsikst{$\taubz=(\tbzpsikst)$~ps}
\def\Tbzresult{$\taubz=(\tbzresult)$~ps}
\def\Tbmresult{$\taubm=(\tbmresult)$~ps}
\def\Rbmresult{$\rbm=\rbmresult$}
\def\Yresult{$\ycp=\yresult$}
\def\Ylimit{$\yllimit<\ycp<\yulimit$}
\def\intl{5.1}

%========================= Commands ===========================================

\newcommand{\nim}[3]{Nucl. Inst. and Meth. {\bf #1} #2 (#3)}
\newcommand{\prld}[3]{Phys. Rev. Lett. {\bf #1} #2 (#3)}
\newcommand{\prdd}[3]{Phys. Rev. D {\bf #1} #2 (#3)}
\newcommand{\prxd}[3]{Phys. Rev. {\bf #1} #2 (#3)}
\newcommand{\plb}[3]{Phys. Lett. B {\bf #1} #2 (#3)}
\newcommand{\npa}[3]{Nucl. Phys. A {\bf #1} #2 (#3)}
\newcommand{\apphyslet}[3]{App. Phys. Lett. {\bf #1} #2 (#3)}
\newcommand{\zphysa}[3]{Z. Phys. A. {\bf #1} #2 (#3)}
\newcommand{\zpc}[3]{Z. Phys. C {\bf #1} #2 (#3)}
\newcommand{\jphys}[3]{J. Phys. {\bf #1} #2 (#3)}

%========================= deffinitions =======================================
\def\etal{{\it et al.}}
\def\chisqndf{{\chi}^2/n}
\def\chisq{\chi^2}
\def\Chisqndf{$\chisqndf$}
\def\Chisq{$\chisq$}
\def\NDF{$N.D.F.$}
\def\degree{{}^{\circ}}
\def\dG{\Delta\Gamma}
\def\dM{\Delta M}
\def\rmix{R_{\rm mix}}
\def\amix{A_{\rm mix}}
\def\re{{\cal R}e}
\def\im{{\cal I}m}
% \def\bzb{{\overline{B{}^0}}}
% \def\bb{{\overline{B{}^0}}}
\def\bzb{{\overline{B}{}^0}}
\def\bb{{\overline{B}{}^0}}
\def\kz{{K{}^0}}
\def\kzb{{\overline{K}{}^0}}
\def\kb{{\overline{K}{}^0}}
\def\bz{{B^0}}
\def\bh{{B_H}}
\def\bl{{B_L}}
\def\bm{{B^-}}
\def\bp{{B^+}}
\def\taubz{\tau(\bzb)}
\def\taubm{\tau(\bm)}
\def\rbm{\taubm/\taubz}
\def\Bzb{$\bzb$}
\def\Bm{$\bm$}
\def\Fb{fb$^{-1}$}
\def\ycp{y_{CP}}
\def\piz{\pi^0}
\def\pip{\pi^+}
\def\pim{\pi^-}
\def\kz{K^0}
\def\kp{K^+}
\def\km{K^-}
\def\ks{K_S^0}
\def\kl{K_L^0}
\def\kb{\overline{K}}
\def\rhom{\rho^-}
\def\bbar{\overline{B}}
\def\bbbar{B\bbar}
\def\bzbzbar{\bz\bzb}
\def\BBbar{$\bbbar$}
\def\BzBzbar{$\bzbzbar$}
\def\ccbar{c\overline{c}}
\def\CCbar{$\ccbar$}
\def\dstar{D^{*}}
\def\dstarz{{D^{*0}}}
\def\dstarp{D^{*+}}
\def\dstarzb{\overline{D}^{*0}}
\def\dstarm{D^{*-}}
\def\dmdstp{\Delta M_{\dstarp}}
\def\dmdstz{\Delta M_{\dstarz}}
\def\dmdst{\Delta M_{\dstar}}
\def\DM{$\Delta M$}
\def\Dstar{$\dstar$}
\def\Dstarz{$\dstarz$}
\def\Dstarp{$\dstarp$}
\def\Dstarzb{$\dstarzb$}
\def\Dstarm{$\dstarm$}
\def\nub{\overline{\nu}}
\def\jpsi{{J/\psi}}
\def\dz{D^0}
\def\Dz{$\dz$}
\def\Dt{\Delta t}
\def\Dz{\Delta z}
\def\dplus{D^+}
\def\Dp{$\dplus$}
\def\dzb{\overline{D}{}^0}
\def\Dzb{$\dzb$}
\def\dstl{\dstar\ell}
\def\dstpl{\dstarp\ell}
\def\dstzl{\dstarz\ell}
\def\dstml{\dstarm\ell}
\def\dstzbl{\dstarzb\ell}
\def\bdstlnu{\overline{B}\to\dstar\ell^-\nub}
\def\bdstxlnu{\overline{B}\to\dstar X\ell^-\nub}
\def\bzdstlnu{\bzb\to\dstarp\ell^-\nub}
\def\bzdstxlnu{\bzb\to\dstarp X\ell^-\nub}
\def\bmdstlnu{\bm\to\dstarz\ell^-\nub}
\def\bmdstxlnu{\bm\to\dstarz X\ell^-\nub}
\def\bmdstpxlnu{\bm\to\dstarp X\ell^-\nub}
\def\bpsik{\overline{B}\to\jpsi\kb}
\def\bdpi{\bbar\to D\pi}
\def\bzdstpm{\bzb\to\dstarp\pim}
\def\bzdstrhom{\bzb\to\dstarp\rhom}
\def\bzdppm{\bzb\to\dplus\pim}
\def\bmdzpm{\bm\to\dz\pim}
\def\bpsiks{B\to\jpsi\ks}
\def\bzbpsiks{\bzb\to\jpsi\ks}
\def\bzpsiks{\bz\to\jpsi\ks}
\def\bzbpsikst{\bzb\to\jpsi\kstarzb}
\def\bmpsikm{\bm\to\jpsi\km}
\def\nbdstlnu{N_{\bdstlnu}}
\def\nbdstxlnu{N_{\bdstxlnu}}
\def\nbb{N_{\bbbar}}
\def\ncc{N_{\ccbar}}
\def\kpi{K^-\pi^+}
\def\kpipiz{\km\pip\piz}
\def\kpipipi{\km\pip\pip\pim}
\def\kstarzb{\overline{K}{}^{*0}}
\def\Kstarzb{$\kstarzb$}
\def\UPS{$\Upsilon(4S)$}
\def\bgu{(\beta\gamma)_\Upsilon}
\def\pdstl{\mathbf{p}_{\dstar\ell}}
\def\pb{\mathbf{p}_{B}}
\def\Gevc{GeV/$c$}
\def\Gevcsq{GeV/$c^2$}
\def\Mevc{MeV/$c$}
\def\Mevcsq{MeV/$c^2$}
\def\degree{{}^{\rm o}}
\def\Degree{${}^{\rm o}$}
\def\dE{\Delta E}
\def\DE{$\dE$}
\def\mb{M_{\rm bc}}
\def\Mb{$\mb$}
\def\micron{$\mu$m}
\def\delz{\Delta z}
\def\delt{\Delta z}
\def\dt{\Delta t}
\def\dzb{\delz_B}
\def\dtb{\dt_B}
\def\dtp{\dt'}
\def\DTb{$\dtb$}
\def\dtrec{\dt_{rec}}
\def\dtgen{\dt_{gen}}
\def\dzrec{\delz_{rec}}
\def\dzgen{\delz_{gen}}
\def\sigdt{\sigma_{\dt}}
\def\sigpdt{\sigma'_{\dt}}
\def\sigmisdt{\sigma_{tail}^{\dt}}
\def\sigdz{\sigma_{\delz}}
\def\sigtdz{\tilde{\sigma}_{\delz}}
\def\sigtmisdz{\tilde{\sigma}_{tail}^{\delz}}
\def\arec{\alpha_{rec}}
\def\aasc{\alpha_{asc}}
\def\sigzrec{\sigma_{z}^{rec}}
\def\sigzasc{\sigma_{z}^{asc}}
\def\sigtzrec{\tilde{\sigma}_{z}^{rec}}
\def\sigtzasc{\tilde{\sigma}_{z}^{asc}}
\def\sigk{\sigma_{K}}
\def\sigmisk{\sigma_{tail}^{K}}
\def\smis{S_{tail}}
\def\scharm{S_{charm}}
\def\sdet{S_{det}}
% \def\sdata{S_{det}}
\def\sdata{s_{\rm data}}
\def\scmis{S_{tail}^{charm}}
\def\sdmis{S_{tail}^{det}}
\def\smisbg{S_{tail}^{\rm bkg}}
\def\sbg{S_{\rm bkg}}
\def\mudz{\mu_{\delz}}
\def\mumisdz{\mu_{tail}^{\delz}}
\def\mumisbg{\mu_{tail}^{\rm bkg}}
\def\muz{\mu_0}
\def\mumisz{\mu_{tail}^0}
\def\mudt{\mu_{\dt}}
\def\mumisdt{\mu_{tail}^{\dt}}
\def\amu{\alpha_\mu}
\def\amismu{\alpha_{tail}^{\mu}}
\def\mubg{\mu_{\rm bkg}}
\def\fmis{f_{tail}}
\def\fmisbg{f_{tail}^{\rm bkg}}
\def\flmbg{f_{\lambda \rm bkg}}
\def\fsig{f_{\rm sig}}
\def\fbkg{f_{\rm bkg}}
\def\fbg{f_{\rm bkg}}
\def\Fbg{F_{\rm bkg}}
\def\Fsig{F_{\rm sig}}
\def\lmbg{\lambda_{\rm bkg}}
\def\pbg{p_{\rm bkg}}
\def\fm{f_-}
\def\fz{f_0}
\def\ffdst{f_{f \dstar}}
\def\pfdst{p_{f \dstar}}
\def\lfdst{\lambda_{f \dstar}}
\def\ffl{f_{f \ell}}
\def\fbb{f_{\bbbar}}
\def\fcc{f_{\ccbar}}
\def\ftbg{f_{\tau {\rm bkg}}}
\def\frdstl{f_{R(\dstar\ell)}}
\def\fbgde{F_{\rm bkg}^{\dE}}
\def\fsigde{F_{\rm sig}^{\dE}}
\def\fbgmb{F_{\rm bkg}^{\mb}}
\def\fsigmb{F_{\rm sig}^{\mb}}
\def\rsig{R_{\rm sig}}
\def\rfdst{R_{f \dstar}}
\def\pfl{p_{f \ell}}
\def\pbb{p_{\bbbar}}
\def\pcc{p_{c\overline{c}}}
\def\Rsig{$\rsig$}
\def\rdz{R_{\delz}}
\def\rbg{R_{\rm bkg}}
\def\Rdz{$\rdz$}
\def\tbm{\tau_-}
\def\tbz{\tau_0}
\def\tsig{\tau_{\rm sig}}
\def\tbg{\tau_{\rm bkg}}
%\def\lfdst{{\cal L}_{f \dstar}}
\def\BF{{\cal B}}
\def\cosb{\cos\theta_B}
\def\ie{{\it i.e.}}
\def\psig{{{\cal P}_{\rm sig}}}
\def\pbkg{{{\cal P}_{\rm bkg}}}
\def\pasym{{{\cal P}_{\rm asym}}}
\def\rdet{{{R}_{\rm det}}}
\def\rnp{{{R}_{\rm np}}}
\def\rk{{{R}_{\rm k}}}


\newcommand{\Bcp}{B_{CP}}
\newcommand{\Btag}{B_{\rm tag}}
\newcommand{\zcp}{z_{CP}}
\newcommand{\ztag}{z_{\rm tag}}

\newcommand{\Brec}{B_{\rm rec}}
\newcommand{\Basc}{B_{\rm asc}}
\newcommand{\trec}{t_{\rm rec}}
\newcommand{\tasc}{t_{\rm asc}}
\newcommand{\zrec}{z_{\rm rec}}
\newcommand{\zasc}{z_{\rm asc}}
\newcommand{\Rrec}{R_{\rm rec}}
\newcommand{\Rasc}{R_{\rm asc}}
\newcommand{\Srec}{\sigma_{\rm rec}}
\newcommand{\Sasc}{\sigma_{\rm asc}}
\newcommand{\Scp}{\sigma_{CP}}
\newcommand{\Stag}{\sigma_{\rm tag}}
\newcommand{\Sdz}{\sigma_{\Dz}}
\newcommand{\Sdt}{\sigma_{\Dt}}

\newcommand{\tSdt}{\tilde{\sigma}_{\Dt}}
\newcommand{\tSdtm}{\tilde{\sigma}^{\Dt}_{\rm main}}
\newcommand{\tSdtt}{\tilde{\sigma}^{\Dt}_{\rm tail}}

\newcommand{\Sdtm}{\sigma^{\Dt}_{\rm main}}
\newcommand{\Mdtm}{\mu^{\Dt}_{\rm main}}
\newcommand{\Sdtt}{\sigma^{\Dt}_{\rm tail}}
\newcommand{\Mdtt}{\mu^{\Dt}_{\rm tail}}

\newcommand{\tScp}{\tilde{\sigma}_{CP}}
\newcommand{\tStag}{\tilde{\sigma}_{\rm tag}}
\newcommand{\tSdz}{\tilde{\sigma}_{\Dz}}
\newcommand{\tSdzm}{\tilde{\sigma}^{\Dz}_{\rm main}}
\newcommand{\tSdzt}{\tilde{\sigma}^{\Dz}_{\rm tail}}

\newcommand{\Sdzm}{\sigma^{\Dz}_{\rm main}}
\newcommand{\Mdzm}{\mu^{\Dz}_{\rm main}}
\newcommand{\Sdzt}{\sigma^{\Dz}_{\rm tail}}
\newcommand{\Mdzt}{\mu^{\Dz}_{\rm tail}}

\newcommand{\srec}{s_{\rm rec}}
\newcommand{\sasc}{s_{\rm asc}}

\newcommand{\sk}{\sigma_{\rm k}}
\newcommand{\snpm}{s_{\rm main}^{\rm NP}}
\newcommand{\snpt}{s_{\rm tail}^{\rm NP}}
\newcommand{\smain}{s_{\rm main}}
\newcommand{\stail}{s_{\rm tail}}
\newcommand{\ftail}{f_{\rm tail}}

% \newcommand{\bra}[1]{\left<#1\right|}
% \newcommand{\ket}[1]{\left|#1\right>}
\newcommand{\bra}[1]{\langle#1|}
\newcommand{\ket}[1]{|#1\rangle}
\newcommand{\braket}[2]{\langle#1|#2\rangle}
\newcommand{\rexp}[1]{{\rm e}^{#1}}
\newcommand{\ri}{{\rm i}}
\newcommand{\lcp}{{\lambda_{CP}}}
\newcommand{\dedx}{{\rm d}E/{\rm d}x}
\newcommand{\sinbb}{{\sin2\phi_1}}

\newcommand{\bcdot}{\!\cdot\!}

\def\dzp{\delz^\prime}
\def\fdelbg{f_\delta^{\rm bkg}}
\def\mudelbg{\mu_\delta^{\rm bkg}}
\def\mutaubg{\mu_\tau^{\rm bkg}}

\def\pol{p_{\rm ol}}
\def\fol{f_{\rm ol}}
\def\sigol{\sigma_{\rm ol}}



moriond.tex
%====================================================================%
%                  MORIOND.TEX     2-Feb-1995                        %
% This latex file rewritten from various sources for use in the      %
% preparation of the standard proceedings Volume, latest version     %
% for the Neutrino'96 Helsinki conference proceedings                %
% by Susan Hezlet with acknowledgments to Lukas Nellen.              %
% Some changes are due to David Cassel.                              %
%                                                                    %
% Updated to LaTeX2e and adapted to Moriond 2001 conditions          %
%                     by F.Montanet 24/04/2001                       %
%====================================================================%

\documentclass[11pt]{article}
\usepackage{moriond,epsfig,graphics}
%\documentstyle[11pt,moriond,epsfig]{article}


\bibliographystyle{unsrt}
% for BibTeX - sorted numerical labels by order of
% first citation.

% A useful Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)}

% Some useful journal names
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
\def\NIMA{{\em Nucl. Instrum. Methods} A}
\def\NPB{{\em Nucl. Phys.} B}
\def\PLB{{\em Phys. Lett.}  B}
\def\PRL{\em Phys. Rev. Lett.}
\def\PRD{{\em Phys. Rev.} D}
\def\ZPC{{\em Z. Phys.} C}

% Some other macros used in the sample text
\def\st{\scriptstyle}
\def\sst{\scriptscriptstyle}
\def\mco{\multicolumn}
\def\epp{\epsilon^{\prime}}
\def\vep{\varepsilon}
\def\ra{\rightarrow}
\def\ppg{\pi^+\pi^-\gamma}
\def\vp{{\bf p}}
\def\ko{K^0}
\def\kb{\bar{K^0}}
\def\al{\alpha}
\def\ab{\bar{\alpha}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\CPbar{\hbox{{\rm CP}\hskip-1.80em{/}}}
%temp replacement due to no font

\input{defs-blife}
\def\dM{{\Delta m_d}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                %
%    BEGINNING OF TEXT                           %
%                                                %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\vspace*{4cm}
\title{IMPROVED MEASUREMENT OF \boldmath $CP$ ASYMMETRY\\IN THE NEUTRAL $B$ MESON SYSTEM}

\author{T. Higuchi
 \footnote{The author is a Research Fellow of the Japan Society for the Promotion of Science.}
\\(for the Belle collaboration)}

\address{Department of Physics, Faculty of Science, the University of Tokyo,\\
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan}

\maketitle\abstracts{
We present an improved measurement of the standard model $CP$ violation
parameter $\sinbb$ (also known as $\sin2\beta$) based on a sample of $45\times10^6$
$B\overline{B}$ pairs collected at the $\Upsilon(4S)$ resonance
with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.
One neutral $B$ meson is reconstructed in the $\jpsi\ks$, $\psi(2S)\ks$,
$\chi_{c1}\ks$, $\eta_c\ks$, $\jpsi K^{*0}$, or $\jpsi\kl$ $CP$-eigenstate
decay channel and the flavor of accompanying $B$ meson is identified from its
decay products.  From the asymmetry in the distribution of the time intervals
between the two $B$ meson decay points, we obtain
$\sinbb=0.82\pm0.12\mbox{(stat)}\pm0.05\mbox{(syst)}$.
The result is preliminary.
}

In the Standard Model (SM), $CP$ violation arises from an
irreducible complex phase in the weak interaction quark mixing matrix
(CKM matrix)\cite{bib:ckm}.
In particular, the SM predicts a $CP$ violating asymmetry
in the time-dependent rates for $\bz$ and $\bb$ decays to a common
$CP$ eigenstate, $f_{CP}$,
with negligible corrections from strong interactions\cite{bib:sanda}:
\be
A(t) \equiv \frac{\Gamma(\bb\to f_{CP}) - \Gamma(\bz\to f_{CP})}
{\Gamma(\bb\to f_{CP}) + \Gamma(\bz\to f_{CP})} = -\xi_f \sinbb \sin\dM t,
\ee
where $\Gamma(\bz,\bb \to f_{CP})$ is the decay rate for a $\bz$ or $\bb$
to $f_{CP}$ dominated by $b\to c\overline{c}s$ transition
at a proper time $t$ after production, $\xi_f$ is the $CP$ eigenvalue of
$f_{CP}$, $\dM$ is the mass difference between the two $\bz$ mass eigenstates,
and $\phi_1$ is one of the three interior angles of the CKM unitarity triangle,
defined as $\phi_1 \equiv \pi-\arg(-V_{tb}^*V_{td}/-V_{cb}^*V_{cd})$.

In this paper, we report an improved measurement of $\sinbb$ using
$45\times 10^6$ $B\overline{B}$ pairs (42~fb$^{-1}$) collected with the Belle detector\cite{bib:belle} at the $\Upsilon(4S)$ resonance in collisions of 8.0~GeV $e^-$ to
3.5~GeV $e^+$ at KEKB\cite{bib:kekb}, where two $B$ mesons reside in a coherent
$p$-wave state until one of
them decays.  The decay of one of the $B$ mesons to a self-tagging state,
$f_{\rm tag}$, {\it i.e.}, a final state that distinguishes $\bz$ and
$\bb$, at a time $t_{\rm tag}$ projects the accompanying meson onto the
opposite $b$-flavor at that time; this meson decays to $f_{CP}$ at time
$t_{CP}$.  The $CP$ violation manifests itself as an asymmetry $A(\Dt)$,
where $\Dt$ is the proper time interval $\Dt \equiv t_{CP}-t_{\rm tag}$.
At KEKB, the $\Upsilon(4S)$ resonance is produced with a boost of $\beta\gamma=0.425$
along the electron beam direction ($z$ direction).  Because
the $\bz$ and $\bb$ mesons are nearly at rest in the $\Upsilon(4S)$ center
of mass system (cms), $\Dt$ can be determined as $\Dt \simeq \Dz/(\beta\gamma)c$,
where $\Dz$ is the $z$ distance
between the $f_{CP}$ and $f_{\rm tag}$ decay vertices, $\Dz \equiv \zcp-\ztag$.
The average value for $\Dz$ is approximately 200 $\mu$m.

We reconstruct $\bz$ decays to the following $CP$ eigenstates
\footnote{Throughout this paper, when a decay mode is quoted,
the inclusion of the charge conjugation mode is implied.}:
$\jpsi\ks$, $\psi(2S)\ks$, $\chi_{c1}\ks$, $\eta_c\ks$ for $\xi_f = -1$ and
$\jpsi\kl$ for $\xi_f$ = +1.  We also use $\bz\to\jpsi K^{*0}$ decays where
$K^{*0} \to \ks\piz$.  Here the final state is a mixture of even and odd
$CP$, depending on the relative orbital angular momentum of the $\jpsi$
and $K^{*0}$.  We find that the final state is primarily $\xi_f$; the
$\xi_f=-1$ fraction is $0.19\pm0.04\mbox{(stat)}\pm0.04\mbox{(syst)}$\cite{bib:itoh}.
For reconstructed $B$ candidates except $\jpsi\kl$,
we identify $B$ decays using the
energy difference $\dE\equiv E_B^{\rm cms}-E_{\rm beam}^{\rm cms}$ and the
beam-energy constrained mass
$\mb \equiv \sqrt{(E_{\rm beam}^{\rm cms})^2-(p_B^{\rm cms})^2}$, where
$E_{\rm beam}^{\rm cms}$, $E_B^{\rm cms}$, and $p_B^{\rm cms}$ are the beam
energy, the energy, and the momentum of the reconstructed $B$ candidate in the
cms, respectively.
Figure \ref{fig:mbc} (top) shows the $\mb$ distributions for all
$\bz$ candidates except for $\bz\to\jpsi\kl$ that are found in the $\dE$ signal
region.
\begin{figure}[t]
\hspace{0.1cm}
\begin{minipage}{7.8cm}
\begin{center}
\hspace{0.008cm}
\psfig{figure=mbc.eps,width=6.9cm,height=2.8cm}
\\
\psfig{figure=pbs.eps,width=6.7cm,height=2.7cm}
\\
\vspace*{-0.1cm}
\caption{(Top) the beam-energy constrained mass distribution for all decay modes
combined other than $\jpsi\kl$.
(Bottom) the $p_B^{\rm cms}$ distribution for $\bz\to\jpsi\kl$ candidates with the results of the fit.
}
\label{fig:mbc}
\end{center}
\end{minipage}
\hspace*{0.1cm}
\begin{minipage}{7.6cm}
\hspace{0.3cm}
\begin{center}
\begin{minipage}{7.6cm}
\footnotesize
Table 1: The numbers of observed candidates ($N_{\rm ev}$) and the estimated
background ($N_{\rm bkg}$) in the signal region for each $f_{CP}$ mode.
\vspace*{0.3cm}
\end{minipage}
\label{tab:number}
\vspace{0.4cm}
\begin{tabular}{|l|r|r|}
\hline
Mode & $N_{\rm ev}$ & $N_{\rm bkg}$ \\
\hline
$\jpsi(\ell^+\ell^-)\ks(\pi^+\pi^-)$       & 636 & 31.2 \\
$\jpsi(\ell^+\ell^-)\ks(\pi^0\pi^0)$       & 102 & 20.8 \\
$\psi(2S)(\ell^+\ell^-)\ks(\pi^+\pi^-)$    &  49 &  2.4 \\
$\psi(2S)(\jpsi\pi^+\pi^-)\ks(\pi^+\pi^-)$ &  57 &  4.3 \\
$\chi_{c1}(\jpsi\gamma)\ks(\pi^+\pi^-)$    &  34 &  2.3 \\
$\eta_c(K^+K^-\pi^0)\ks(\pi^+\pi^-)$       &  39 & 11.1 \\
$\eta_c(\ks K^-\pi^+)\ks(\pi^+\pi^-)$      &  33 &  8.9 \\
\hline
$\jpsi(\ell^+\ell^-) K^{*0}(\ks\pi^0)$     &  55 &  6.0 \\
\hline
$\jpsi(\ell^+\ell^-) \kl$                  & 767 & 307 \\
\hline
\end{tabular}
\end{center}
\end{minipage}
\vspace*{-.5cm}
\end{figure}
Table 1 lists the
numbers of observed candidates ($N_{\rm ev}$) and the background ($N_{\rm bkg}$)
estimated by extrapolating the rate in the non-signal $\dE$ vs $\mb$ region
into the signal region.
Candidate $\bz\to\jpsi\kl$ decays are selected by requiring
electromagnetic calorimeter
(ECL) and/or $\kl$ and muon detector
(KLM) hit patterns that are consistent with the presence of a shower
induced by a neutral hadron.
The centroid of the shower is required to be
in a $45^\circ$ cone centered on the $\kl$ direction that is inferred from
two-body decay kinematics and the measured four-momentum of the $\jpsi$.
Figure \ref{fig:mbc} (bottom) shows the $p_B^{\rm cms}$ distribution,
calculated with the $\bz\to\jpsi\kl$ two-body decay hypothesis.  The histograms
are the results of a fit to the signal and background distributions.
There are 767 entries in total in the region $0.20\le p_B^{\rm cms}\le0.40$~GeV/$c$ with KLM clusters and in $0.20\le p_B^{\rm cms}\le0.40$~GeV/$c$ with
clusters in the ECL only.
The fit finds a signal purity of 60\%.
The reconstruction and selection criteria for used channels
are described elsewhere\cite{bib:cpv}.

Leptons, charged pions, kaons, and $\Lambda$ baryons that are not associated
with a reconstructed $CP$ eigenstate decay are used to identify the $b$-flavor
of the accompanying $B$ meson;
high momentum leptons from $b\to c\ell^-\overline{\nu}$,
lower momentum leptons from $c\to s\ell^-\overline{\nu}$,
charged kaons and $\Lambda$ baryons from $b\to c \to s$,
fast pions from $\bz\to D^{(*)-}$($\pi^+,\rho^+,a_1^+$, etc.), and
slow pions from $D^{*-}\to \overline{D}{}^0\pi^-$.
Using those tracks, two parameters, $q$ and $r$, are assigned to an event.
The first, $q$, has the discrete values $q=\pm1$ that is $+1(-1)$
when $\Btag$ is likely to be a $\bz$($\bb$), and the parameter $r$ is an
event-by-event flavor-tagging dilution factor ranging from $r=0$ for no flavor
discrimination to $r=1$ for unambiguous flavor assignment.  It is used only
to sort data into six intervals of $r$, according to flavor purity;
the wrong-tag probabilities, $w_l~(l=1,6)$, for the final fit are determined
directly from data.
The decay to exclusively reconstructed self-tagged channels
are utilized to obtain $w_l$ using time-dependent $\bz$-$\bb$ mixing
oscillation: $(N_{\rm OF}-N_{\rm SF})/(N_{\rm OF}+N_{\rm SF}) = (1-2w_l)\cos(\dM\Dt)$.  Here $N_{\rm OF}$ and $N_{\rm SF}$ are the numbers of opposite
and same flavor events.
The total effective tagging efficiency is $\sum_{l=1}^6f_l(1-2w_l)^2 = 0.270\pm0.008\mbox{(stat)}^{+0.006}_{-0.009}\mbox{(syst)}$,
where $f_l$ is the event fraction for each $r$ interval.

The vertex position for $f_{CP}$ is reconstructed using leptons from $\jpsi$
decay and that for $f_{\rm tag}$ is obtained with well reconstructed tracks
not assigned to $f_{CP}$.  Tracks that form a $\ks$ invariant mass are not used.
Each vertex position is required to be consistent with the interaction
point profile smeared in the $r$-$\phi$ plane by the $B$ meson decay length.
The requirement enables us to determine a vertex even with a single track.
The fraction of such vertices is about 10\% for $\zcp$ and 30\% for $\ztag$.
A proper-time interval resolution, $R_{\rm sig}(\Dt)$,
consists of a convolution of four components:
detector resolution for $\zcp$ and $\ztag$, shift in the $\ztag$ reconstruction
due to secondary tracks originated from charmed hadrons such as $D^+$ and $D^0$, and
smearing effect due to kinematic approximation in converting
$\Dz$ to $\Dt$.
We find broad outlier components in $\Dz$ distributions due to
mis-reconstruction, which are represented by Gaussian distributions.
We simultaneously
determine ten resolution parameters from data with a fit of neutral
and charged $B$ meson lifetimes\cite{bib:lifetime}
and obtain a $\Dt$ resolution of $\sim1.56$~ps (rms).
The width and the fraction of the outlier component are determined to be
$36^{+5}_{-4}$~ps, and $(0.06^{+0.03}_{-0.02})\%$ or $(3.1\pm0.4)\%$
(multiple- or single-track case).

After vertexing we find 766 events with $q=+1$ flavor tags and 784 events
with $q=-1$.  Figure \ref{fig:cpfit} shows the observed $\Dt$ distributions
for the $q\xi_f=+1$ (solid points) and $q\xi_f=-1$ (open points) event samples.
The asymmetry between two distributions demonstrates the violation of the
$CP$ symmetry.
\begin{figure}[t]
\hspace{0.1cm}
\begin{minipage}{7.4cm}
\begin{center}
\psfig{figure=cpfit.eps,height=4.0cm}
\vspace*{-0.2cm}
\caption{$\Dt$ distributions for the events with $q\xi_f=+1$ (solid points)
and $q\xi_f=-1$ (open points).  The results of the global fit with
$\sinbb=0.82$ are shown as solid and dashed curves, respectively.}
\label{fig:cpfit}
\end{center}
\end{minipage}
\hspace*{0.1cm}
\begin{minipage}{8.0cm}
\hspace{0.3cm}
\begin{center}
\begin{minipage}{8.0cm}
\footnotesize
Table 2: The values of $\sinbb$ for various subsamples (statistical errors only).
\vspace*{0.3cm}
\end{minipage}
\label{tab:check}
\begin{tabular}{|l|c|}
\hline
Sample & $\sinbb$ \\
\hline
$f_{\rm tag}=\bz$ $(q=+1)$                        & $0.60\pm0.19$ \\
$f_{\rm tag}=\bb$ $(q=-1)$                        & $0.99\pm0.16$ \\
$\jpsi\ks(\pip\pim)$                              & $0.67\pm0.18$ \\
$(c\overline{c})\ks$ except $\jpsi\ks(\pip\pim)$  & $0.88\pm0.31$ \\
$\jpsi\kl$                                        & $1.14\pm0.23$ \\
$\jpsi K^{*0}(\ks\pi^0)$                          & $1.62\pm1.10$ \\
\hline
All                                               & $0.82\pm0.12$ \\
\hline
\end{tabular}
\end{center}
\end{minipage}
\end{figure}
We determine $\sinbb$ from an unbinned maximum-likelihood fit to the observed
$\Dt$ distributions.  The probability density function (pdf) expected
for the signal distribution is given by
\be
{\cal P}_{\rm sig}(\Dt,q,w_l,\xi_f) =
\frac{e^{-|\Dt|/\tau_\bz}}{2\tau_\bz}[1-q\xi_f(1-2w_l)\sinbb\sin\dM\Dt],
\ee
where we fix the $\bz$ lifetime and mass difference at their world average
values\cite{bib:pdg}.
Each pdf is convolved with the appropriate $R(\Dt)$
to determine the likelihood value for each event as a function of $\sinbb$:
\begin{eqnarray}
P_i &=& (1-f_{\rm ol})\int \Bigl[ f_{\rm sig}{\cal P}_{\rm sig}(\Dt',q,w_l,\xi_f)R_{\rm sig}(\Dt-\Dt') \nonumber \\
&& +\; (1-f_{\rm sig}){\cal P}_{\rm bkg}(\Dt')R_{\rm bkg}(\Dt-\Dt')\Bigr] d\Dt'
+ f_{\rm ol}P_{\rm ol}(\Dt),
\end{eqnarray}
where $f_{\rm sig}$ is the signal probability calculated
as a function of $p_B^{\rm cms}$ for $\jpsi\kl$ and of $\dE$ and $\mb$ for
other modes.
${\cal P}_{\rm bkg}(\Dt)$ is a pdf for combinatorial background events
that is modeled as a sum of exponential and prompt components.  It is convolved
with a sum of two Gaussians, $R_{\rm bkg}$.
$P_{\rm ol}$ and $f_{\rm ol}$ are the pdf and the fraction for the outlier
component.
The only free parameter in the final fit is $\sinbb$, which is determined by
maximizing the likelihood function $L=\prod_iP_i$, where the product is over
all events.  The preliminary result of the fit is
\[
\sinbb = 0.82\pm 0.12\mbox{(stat)}\pm0.05\mbox{(syst)} .
\]

The systematic error is dominated by uncertainties due to effects of the tails
of the vertex distribution ($\pm$0.030).  Other significant
contributions come from uncertainties
(a) in $w_l$ ($^{+0.024}_{-0.026}$);
(b) in the resolution function parameters ($^{+0.022}_{-0.019}$);
(c) in the $\jpsi\kl$ background fraction ($^{+0.014}_{-0.015}$).
The errors introduced by uncertainties in $\dM$ and $\tau_\bz$ are 0.01 or less.

A number of checks on the measurement are performed.  Table 2
lists the results obtained by applying the same analysis to various subsamples.
All values are statistically consistent with each other.
The result is unchanged
if we use the $w_l$'s determined separately for $f_{\rm tag}=\bz$ and $\bzb$.
A fit to the non-$CP$ eigenstate self-tagged modes $\bz\to D^{(*)-}\pi^+$,
$D^{*-}\rho^+$, and $\jpsi K^{*0}(K^+\pi^-)$, where no asymmetry is expected,
yields $0.05\pm0.04$.
\\

We also measure $CP$ violating asymmetry in $\bz\to\eta'\ks$ decays
based on $45\times10^6$ $B\overline{B}$ pairs.
Numbers of fully reconstructed events
for $\eta(\gamma\gamma)\pi\pi\ks$ and for $\rho\gamma\ks$
are $27.7^{+6.2}_{-5.5}$ and $45.4^{+8.6}_{-7.9}$, respectively.
Flavor of the accompanying $B$ meson is identified from its decay products.
The decay rate has a time dependence given by
\be
{\cal P}_{\rm sig}(\Dt,q,w_l) = \frac{e^{-|\Dt|/\tau_\bz}}{4\tau_\bz}\Bigl\{1+q(1-2w_l)[S\sin(\dM\Dt)+C\cos(\dM\Dt)]\Bigr\}.
\ee
From the asymmetry in the $\Dt$ distribution,
we obtain $S=0.27^{+0.54}_{-0.55}\mbox{(stat)}\pm0.07\mbox{(syst)}$ and
$C=0.12\pm0.32\mbox{(stat)}\pm0.07\mbox{(syst)}$.

\section*{References}
\begin{thebibliography}{99}
\bibitem{bib:ckm} M.~Kobayashi and T.~Maskawa, {\em Prog.\ Theor.\ Phys.}\ {\bf 49},
652 (1973).

\bibitem{bib:sanda} A.~B.~Carter and A.~I.~Sanda, \Journal{\PRD}{23}{1567}{1981}; I.~I.~Bigi and A.~I.~Sanda, Nucl.\ Phys.\ {\bf B193}, 85 (1981).

\bibitem{bib:belle} Belle Collaboration, A.~Abashian {\it et al}., {\em Nucl.\ Instrum.\ Methods Phys.\ Res.}, Sect.\ A {\bf 479}, 117 (2002).

\bibitem{bib:kekb} E.~Kikutani ed., KEK Preprint 2001-157 (2001), to appear in {\NIM}.

\bibitem{bib:itoh} Belle Collaboration, K~Abe {\it et al}., ``{\it Measurement of Polarization and $CP$ Asymmetry in $B\to\jpsi+K^*$ Decays}'' (2001); BELLE-CONF-0105.

\bibitem{bib:cpv} Belle Collaboration, K~Abe {\it et al}., \Journal{\PRL}{87}{091802}{2001}; Belle Collaboration, K~Abe {\it et al}., arXiv:hep-ex/0202027 submitted to {\PRD}.

\bibitem{bib:lifetime} Belle Collaboration, K~Abe {\it et al}., \Journal{\PRL}{88}{171801}{2002}.

\bibitem{bib:pdg} D.~E.~Groom {\it et al}., {\em Eur.\ Phys.\ J.}\ C\ {\bf 15}, 1 (2000).

\end{thebibliography}

\end{document}

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% End of moriond.tex %
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hep-ex0205020.extracted_bib
\begin{thebibliography}{99}
\bibitem{bib:ckm} M.~Kobayashi and T.~Maskawa, {\em Prog.\ Theor.\ Phys.}\ {\bf 49},
652 (1973).

\bibitem{bib:sanda} A.~B.~Carter and A.~I.~Sanda, \Journal{\PRD}{23}{1567}{1981}; I.~I.~Bigi and A.~I.~Sanda, Nucl.\ Phys.\ {\bf B193}, 85 (1981).

\bibitem{bib:belle} Belle Collaboration, A.~Abashian {\it et al}., {\em Nucl.\ Instrum.\ Methods Phys.\ Res.}, Sect.\ A {\bf 479}, 117 (2002).

\bibitem{bib:kekb} E.~Kikutani ed., KEK Preprint 2001-157 (2001), to appear in {\NIM}.

\bibitem{bib:itoh} Belle Collaboration, K~Abe {\it et al}., ``{\it Measurement of Polarization and $CP$ Asymmetry in $B\to\jpsi+K^*$ Decays}'' (2001); BELLE-CONF-0105.

\bibitem{bib:cpv} Belle Collaboration, K~Abe {\it et al}., \Journal{\PRL}{87}{091802}{2001}; Belle Collaboration, K~Abe {\it et al}., arXiv:hep-ex/0202027 submitted to {\PRD}.

\bibitem{bib:lifetime} Belle Collaboration, K~Abe {\it et al}., \Journal{\PRL}{88}{171801}{2002}.

\bibitem{bib:pdg} D.~E.~Groom {\it et al}., {\em Eur.\ Phys.\ J.}\ C\ {\bf 15}, 1 (2000).

\end{thebibliography}