$B,~D,~K$ decays and CKM matrix from lattice QCD
Masataka Okamoto %(for the Fermilab Lattice
MILC
and HPQCD Collaborations)
%We show that it is now possible to fully determine %the CKM matrix, for the first time, using lattice QCD. We use lattice QCD to fully determine the CKM matrix. $|V_{cd}|$, $|V_{cs}|$, $|V_{ub}|$, $|V_{cb}|$ and $|V_{us}|$ are, respectively, directly determined with recent lattice results for form factors of semileptonic $D\to \pi l\nu$, $D\to K l\nu$, $B\to \pi l\nu$, $B\to D l\nu$ and $K\to \pi l\nu$ decays obtained by the Fermilab Lattice, MILC, and HPQCD Collaborations. %The error from the quenched approximation is removed by %using the MILC unquenched lattice gauge configurations, %where the effect of $u,d$ and $s$ quarks is included. %The error from the ``chiral'' extrapolation ($m_l\to m_{ud}$) %is greatly reduced by using improved staggered quarks. %The accuracy is comparable to %that of the Particle Data Group averages. In addition, $|V_{ud}|$, $|V_{tb}|$, $|V_{ts}|$ and $|V_{td}|$ are determined by using unitarity of the CKM matrix and the experimental result for $\sin{(2\beta)}$. %In this way, we obtain all 9 CKM matrix elements, where %the only theoretical input is lattice QCD.
moriond_okamoto.tex


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% CKM matrix with 2-column errors
\def\Vud{0.9744(5)(3)}
\def\Vus{~~~0.225(2)(1)~~~}
\def\Vub{3.5(5)(5)\!\times\! 10^{-3}}
\def\Vcd{~~~0.24(3)(2)~~~}
\def\Vcs{~~~~0.97(10)(2)~~~~}
\def\Vcb{3.9(1)(3)\!\times\! 10^{-2}}
\def\Vtd{8.1(2.7)\!\times\! 10^{-3}}
\def\Vts{3.8(4)(3)\!\times\! 10^{-2}}
\def\Vtb{0.9992(0)(1)}
% Wolfenstein paramenters
\def\Wlambda{\Vus}
\def\WA{0.77(2)(7)}
\def\WR{0.40(6)(6)}
\def\Wrho{0.16(28)}
\def\Weta{0.36(11)}
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\begin{document}
%\vspace*{4cm}
\title{$B,~D,~K$ decays and CKM matrix from lattice QCD}

\author{Masataka Okamoto
%(for the Fermilab Lattice, MILC, and HPQCD Collaborations)
}

\address{Fermi National Accelerator Laboratory, 
Batavia, Illinois 60510, USA
}

\maketitle\abstracts{
%We show that it is now possible to fully determine
%the CKM matrix, for the first time, using lattice QCD.
We use lattice QCD to fully determine the CKM matrix.
$|V_{cd}|$, $|V_{cs}|$, $|V_{ub}|$, $|V_{cb}|$ and $|V_{us}|$
are, respectively, directly determined
with recent lattice results 
for form factors of
semileptonic $D\to \pi l\nu$,
             $D\to K l\nu$,
             $B\to \pi l\nu$,
             $B\to D l\nu$
         and $K\to \pi l\nu$ decays
obtained by the Fermilab Lattice, MILC, and HPQCD Collaborations.
%The error from the quenched approximation is removed by
%using the MILC unquenched lattice gauge configurations,
%where the effect of $u,d$ and $s$ quarks is included.
%The error from the ``chiral'' extrapolation ($m_l\to m_{ud}$) 
%is greatly reduced by using improved staggered quarks.
%The accuracy is comparable to 
%that of the Particle Data Group averages. 
In addition,
$|V_{ud}|$, $|V_{tb}|$, $|V_{ts}|$ and $|V_{td}|$ are determined
by using unitarity of the CKM matrix and the experimental result
for $\sin{(2\beta)}$.
%In this way, we obtain all 9 CKM matrix elements, where 
%the only theoretical input is lattice QCD. 
}

\section{Introduction}

The Cabibbo-Kobayashi-Maskawa (CKM) matrix,
which relates the mass eigenstates and the weak eigenstates
in the Standard Model electroweak theory, is a set of parameters.
To determine each CKM matrix element, one requires both
theoretical and experimental inputs.
On the theoretical side, one needs to know relevant hadronic
amplitudes, which often contain nonperturbative QCD effects.
A major role of lattice QCD is to calculate such hadronic
amplitudes reliably and accurately, from first principles.
One can then extract the CKM matrix elements by combining 
lattice QCD as the theoretical input
with the experimental input such as decay rates.
In this paper, we show that it is now possible to {\it fully} determine
the CKM matrix, for the first time, using lattice QCD.
The result for the full CKM matrix with lattice QCD is:
        \bea V_{\rm CKM} ~=~
        \left(
        \begin{array}{ccc}
        {{|V_{ud}|}}   & {|V_{us}|}   & {|V_{ub}|} \\
            \Vud       &    \Vus      &    \Vub    \\
        { |V_{cd}| }   & {|V_{cs}|}   & {|V_{cb}|} \\
            \Vcd       &    \Vcs      &    \Vcb    \\
        { |V_{td}| }   & {|V_{ts}|}   & {|V_{tb}|} \\
            \Vtd       &    \Vts      &    \Vtb    \\
        \end{array}
        \right) \label{ckm}
        \eea
where the first errors are from lattice calculations
and the second are experimental, except the one for 
$|V_{td}|$ which is a combined lattice and experimental error.
The results for the Wolfenstein parameters with lattice QCD are:
\bea
\lambda = \!\!\!\!\Wlambda\!\!\!\!\!\!,~~~~
A = \WA ,~~~~
\rho = \Wrho ,~~~~
\eta = \Weta.
\label{Wolf}
\eea


To directly determine 5 CKM matrix elements 
($|V_{cd}|$, $|V_{cs}|$, $|V_{ub}|$, $|V_{cb}|$ and $|V_{us}|$),
we use 5 semileptonic decays 
($D\to \pi l\nu$,
 $D\to K l\nu$,
 $B\to \pi l\nu$,
 $B\to D l\nu$ and
 $K\to \pi l\nu$),
for which the techniques for lattice calculations are well
established, and thus reliable calculations are possible.
The accuracy of previous lattice calculations
was limited
by two large systematic uncertainties ---
the error from the ``quenched'' approximation (neglect of
virtual quark loop effects)
and the error from the ``chiral'' 
extrapolation in light quark mass ($m_l\to m_{ud}$).
Both led to effects of around 10--20\%.
Recent work by the Fermilab Lattice, MILC, and HPQCD 
Collaborations~\cite{Aubin:2004ej,Okamoto:2004xg} 
successfully reduces these two dominant uncertainties.
The error from the quenched approximation is removed by
using the MILC unquenched gauge configurations~\cite{milc},
where the effect of $u,d$ and $s$ quarks is included ($n_f=2+1$).
The error from the chiral extrapolation is greatly 
reduced by using improved staggered quarks. 
With this improved approach, the accuracy of the 5 CKM matrix elements
is comparable to that of the Particle Data Group~\cite{Eidelman:wy}. 
The results for $|V_{ub}|$, $|V_{cb}|$ and $|V_{us}|$ are preliminary.
%
%Since we determine all 3 elements in the charm row of the CKM matrix,
%$|V_{cq}|~(q=d,s,b)$, we can check   
%a unitarity condition on the CKM matrix using only 
%our results from lattice QCD. 
%Adding in $|V_{us}|$ and $|V_{ub}|$, we 
We then use CKM unitarity
to determine the other
4 CKM matrix elements ($|V_{ud}|$, $|V_{tb}|$, $|V_{ts}|$ and $|V_{td}|$).
In this way, we obtain all 9 CKM matrix elements 
and all the Wolfenstein parameters.
%where the only theoretical input (for nonperturbative QCD effects) 
%is lattice QCD.
%(assuming that the Standard Model is correct).
%.\footnote{We assume here that 
%the Standard Model is correct. 
%}
%
%This paper is organized as follows.
%In Sec.~\ref{sec:SLdecay} we present our results
%for the 5 semileptonic decays and the 5 CKM matrix elements.
%In Sec.~\ref{sec:unitary} we first check unitarity
%of the charm row of the CKM matrix,
%and then give the results for the other 4 CKM matrix elements from  
%unitarity, as well as the Wolfenstein parameters.
%In Sec.~\ref{sec:summary} we give a summary. %and discuss future plans.
The results for the $D$ and $B$ decays have been presented in 
Refs.~\cite{Aubin:2004ej,Okamoto:2004xg}.
This work is a part of ongoing project 
of flavor physics with lattice QCD
by the Fermilab Lattice, MILC, and HPQCD Collaborations;
see also
\cite{Simone:2004fr,diPierro:2003iw,Okamoto:2004df}.


\section{5 CKM matrix elements from 5 semileptonic decays}
\label{sec:SLdecay}

\subsection{$D\to\pi(K)l\nu$, $|V_{cd(s)}|$ and $B\to\pi l\nu$, $|V_{ub}|$}
The differential decay rate $d\Gamma/dq^2$ for 
the heavy-to-light semileptonic decay $H\to Pl\nu$
is proportional to $|V_{ij}|^2 |f_+(q^2)|^2$,
where $f_+$ is a form factor of the relevant hadronic amplitude
defined through
\bea
\< P | V^\mu | H \>
 &=& 
f_+(q^2) (p_H+p_P-\Delta)^\mu + f_0(q^2) \Delta^\mu \label{eq:HLff}\\
&=& 
\sqrt{2m_H} \, \left[v^\mu \, f_\parallel(E) +
p^\mu_\perp \, f_\perp(E) \right]. \nn
\eea
Here $q = p_H - p_P$, $\Delta^\mu=(m_H^2-m_P^2)\, q^\mu / q^2$,
$v=p_H/m_H$, $p_\perp=p_P-Ev$ and $E=E_P$.
To determine the CKM matrix element $|V_{ij}|$ with the
experimental rate
$\int^{q^2_{\rm max}}_{q^2_{\rm min}}dq^2\ (d\Gamma/dq^2)$,
we calculate $f_{+,0}$ as a function of $q^2$.
Below we briefly describe the analysis 
procedure in Refs.~\cite{Aubin:2004ej,Okamoto:2004xg}.

We first extract the
form factors $f_\parallel$ and $f_\perp$,
%and carry out the chiral extrapolation in $m_l$
%for them at fixed final-state energy $E$.
%To this end, 
and 
%we 
interpolate and
extrapolate the results for $f_\parallel$ and $f_\perp$ to common values
of $E$ using 
the parametrization of Becirevic and Kaidalov (BK)
\cite{Becirevic:1999kt}. 
We then perform the chiral extrapolation ($m_l\to m_{ud}$) at each $E$
using the NLO correction
in staggered chiral perturbation theory~\cite{Aubin:2004xd}.
%We try various fit forms for the extrapolation, 
%and the differences between the fits, 2--4\%, are taken as 
%associated systematic errors. 
%
Finally we convert 
the results for $f_{\perp}$ and $f_{\parallel}$ at $m_l=m_{ud}$,
to $f_+$ and $f_0$.
%To extend
%$f_+$ and $f_0$ to functions of $q^2$,
%we again make a fit using the BK parameterization \cite{Becirevic:1999kt},
The results for $f_+$ and $f_0$ are parameterized with the 
BK form~\cite{Becirevic:1999kt},
\bea\label{eq:BK}
f_+(q^2) = \frac{f_+}{(1-\tilde{q}^2)(1-\alpha\tilde{q}^2)},~~~
f_0(q^2) = \frac{f_+}{1-\tilde{q}^2/\beta},
\eea
where $\tilde{q}^2=q^2/m_{H^{*}}^2$.
We obtain~\cite{Aubin:2004ej,Okamoto:2004xg}
%\bea
$
f_+^{D\to \pi}=0.64(3),~
\alpha^{D\to  \pi}=0.44(4),~ \beta^{D\to \pi}=1.41(6)$ and
$f_+^{D\to  K}=0.73(3),~  
\alpha^{D\to  K}=0.50(4),~  \beta^{D\to  K}=1.31(7)
$
%\eea
for the $D$ decays, and 
%\bea
$
f_+^{B\to\pi}=0.23(2),~ \alpha^{B\to\pi}=0.63(5),~ \beta^{B\to\pi}=1.18(5)
$
%\eea
for the $B$ decay, where the errors are statistical only. 
To estimate the error from the BK parameterization, {\it i.e.,}
the error for $q^2$ dependence,
we also make an alternative analysis, where we perform a 2-dimensional 
polynomial fit in $\left(m_l,E(q^2)\right).$ 
A comparison between two analyses is shown in Fig.~\ref{fig:B2pi}.
The results for $D$ decays agree well with recent experimental 
results \cite{unknown:2004nn}.
%
\begin{figure}[tb]
\begin{center}
\centerline{
\epsfig{file=f0+.D2pi.BK-noBK.eps,height=37mm}
\epsfig{file=f0+.B2pi.BK-noBK.eps,height=37mm}}
\vspace{-.3cm}
\caption{Form factors from 
BK-based (filled symbols and curves) and non-BK-based (open symbols) analyses
for $D\to\pi l\nu$ (left panel) and $B\to\pi l\nu$ (right) decays.}
\label{fig:B2pi}
\vspace{-1cm}
\end{center}
\end{figure}
%
%
We then determine the CKM matrix elements 
by integrating $|f_+(q^2)|^2$ over $q^2$ and 
using experimental decay rates~\cite{Eidelman:wy,Athar:2003yg,Belle:B2pi}.
For $|V_{ub}|$ we use a combined average of 
the decay rate for $q^2 \ge 16$ GeV$^2$
in Refs.~\cite{Athar:2003yg} and \cite{Belle:B2pi}.
We obtain
\bea
~~~|V_{cd}| = 0.239(10)(24)(20) \,\,\,\,\, ,\,\,\,\,\,
   |V_{cs}| = 0.969(39)(94)(24)
\label{eq:VcdVcs}
\eea
from the $D$ decay, and 
\bea
~~~|V_{ub}|\times 10^{3} = 3.48(29)(38)(47) 
\label{eq:Vub}
\eea
from the $B$ decays, where the first errors are statistical,
the second systematic, and the third are experimental errors from
the decay rates.
The systematic errors 
are dominated by the finite lattice spacing effects,
{\it i.e.,} the lattice discretization effects; 
see Table~\ref{tab:error}.
The results for the CKM matrix elements agree with the 
Particle Data Group averages~\cite{Eidelman:wy} with a comparable accuracy.

\begin{table}[b]
\begin{center}
\caption{Systematic errors in lattice calculations. 
For comparison, the error for each CKM matrix element by the
Particle Data Group~\protect\cite{Eidelman:wy} is shown in the last row.}
%\label{tab:error}
{\begin{tabular}{l|rrrr}
\hline
semileptonic decay  &$D\to \pi(K)l\nu$ & $B\to \pi l\nu$ & $B\to D l\nu$ & 
$K\to \pi l\nu $\\
CKM matrix element  &$|V_{cd(s)}|$  &$|V_{ub}|$   &$|V_{cb}|$ & $|V_{us}|$\\
\hline
%3-pt function fit& 3\% & 3\% & 1\% & $<$1\%\\
$q^2$ dependence & 2\% & 4\% &  & $<$1\%\\
$m_l\!\to\! m_{ud}$ extrapolation& 3\%(2\%) &4\% & 1\% & 1\%\\
operator matching & $<$1\% & 1\% &  1\%  & $<$1\%\\
%$a$ uncertainty  & 1\% & 1\% &   &  \\
{discretization effects} & { 9\%}& { 9\%} &  $<$1\%  & \\
\hline
total systematic error   & { 10\%} & { 11\%} &  { 2\%}  & {1\%}\\
\hline
\hline
\vspace{-.4cm}\\
error in PDG average%~\cite{Eidelman:wy} 
& 5\%(1\%)       & 13\%       &  4\%    & 1\%\\
\hline
\end{tabular}\label{tab:error}}
\end{center}
\end{table}

\subsection{$B\to D l\nu$, $|V_{cb}|$ and $K\to \pi l\nu$, $|V_{us}|$}
%
%The form factors of $B\to D l\nu$ and $K\to \pi l\nu$ decays
%can be calculated more accurately than those of 
%heavy-to-light ($H\to P l\nu$) decays, due to the symmetry
%between the initial and final states.
The differential decay rate of $B\rightarrow D l\nu$ is
proportional to the square of $|V_{cb}| {\cal{F}}(w)$, 
where ${\cal{F}}(w)$ is 
the relevant form factor and 
%a linear combination of $h_+(w)$ and $h_-(w)$ defined through
%\begin{eqnarray}\label{eq:definition_of_the_form_factors}
%\langle D| V^{\mu}|{{B}}\rangle ~=~ \sqrt{m_B m_D} \times 
%[h_+(w) (v+v')^{\mu} + h_-(w) (v-v')^{\mu}],
%\end{eqnarray}
%with $v=p_B/m_B$, $v'=p_D/m_D$ and
%$w=v\cdot v'$.
$w=v\cdot v'$ with $v=p_B/m_B$, $v'=p_D/m_D$.
To extract $|V_{cb}|$,
we calculate the form factor at $w=1$, ${\cal{F}}(1)$,
by employing the double ratio method \cite{Hashimoto:1999yp}.
The light quark mass dependence of ${\cal{F}}(1)$ is 
mild, and by
extrapolating the result linearly to $m_l\to 0$ 
we obtain~\cite{Okamoto:2004xg}
%\bea
$
{\cal{F}}^{B\rightarrow D}(1)=1.074(18)(16),
%\label{b2dFF}
%\eea
$
where the first error is statistical, and the second is systematic.
%, as %summarized in Table~\ref{tab:error}.
Combining with the experimental result for 
$|V_{cb}{|\cal{F}}(1)$~\cite{HFAG}, we obtain 
\bea
   |V_{cb}|\times 10^{2} = 3.91(07)(06)(34),
\label{eq:Vcb}
\eea
%where the errors from the lattice calculation (first two)
%are smaller than the experimental one (third).
where the first two errors from lattice calculation are smaller than
the experimental one (third).

\begin{figure}[tb]
\begin{center}
\epsfig{file=am-df.k2p.eps,height=40mm}
\vspace{-.5cm}
\caption{$m_l$-dependence of $\Delta f$ for $K\to\pi l\nu$ decay,
together with results from Refs.~\protect\cite{Becirevic:2004ya,Leutwyler:1984je}.}
\label{fig:K2pi}
\vspace{-.6cm}
\end{center}
\end{figure}

Finally we study the $K\to\pi l\nu$ decay to determine $|V_{us}|$.
The expression for the $K\to\pi$ decay amplitude is given in an
analogous way to Eq.~(\ref{eq:HLff}).
We calculate the $K^0\to\pi^-$ form factor at $q^2=0$, $f_+(0)=f_0(0)$,
by employing the three-steps method, as in 
Ref.~\cite{Becirevic:2004ya}.
%\begin{enumerate}
%\item Extract the $f_0$ form factor at $q^2=q^2_{\rm max}$
%by applying the double ratio method similar to the $B\to D$ 
%case~\cite{Hashimoto:1999yp}.
%\item Extrapolate $f_0$ at $q^2=q^2_{\rm max}$ to $q^2=0$
%by using the experimental result~\cite{Alexopoulos:2004sw}
%for the slope parameter
%$\lambda_0$ defined by $f_0(q^2)\!=\!f_0(0)/(1-\lambda_0 q^2)$.\footnote{
%An unquenched lattice calculation of 
%$\lambda_0$ should be done in the future.}
%This gives $f_0(0)\!=\!f_+(0)$ for each $m_l$.
%\item Perform the $m_l\!\to\! m_{ud}$ extrapolation for $f_+(0)$.
%To this end, we subtract the leading logarithmic correction $f_2$
To perform the $m_l\!\to\! m_{ud}$ extrapolation for $f_+(0)$,
we subtract the leading logarithmic correction $f_2$
in chiral perturbation theory,
{\it i.e.,} define $\Delta f\equiv 1+f_2-f_+(0)$.
We make a fit to $\Delta f$ adopting an ansatz,
$\Delta f = (A +B m_l)(m_s-m_l)^2$, where $A,B$ are fit parameters.
%The $(m_s-m_l)^2$ dependence is expected due to the Ademollo-Gatto theorem.
%\end{enumerate}
%As an exploratory study of ${f}_{+}^{K\to\pi}$, 
%we use an improved staggered action
%for $u,s$ quarks and an improved Wilson action for the $d$ quark.
The $m_l$-dependence of $\Delta f$ and the extrapolated result
are shown in Fig.~\ref{fig:K2pi}, together with 
a recent quenched lattice result~\cite{Becirevic:2004ya}
and an earlier result by 
Leutwyler and Roos~\cite{Leutwyler:1984je}.
Our preliminary result~\cite{Okamoto:2004df}
is $\Delta f = 0.015(6)(9)$, giving
%\bea
$
{f}_{+}^{K^0\to\pi^-}(0) = 0.962(6)(9),
%\label{eq:f0K2pi}
%\eea
$
which agrees well with those of  
Refs.~\cite{Becirevic:2004ya,Leutwyler:1984je}.
Combining with a recent experimental result for 
$|V_{us}|{f}_{+}(0)$~\cite{Alexopoulos:2004sw},
we obtain
\bea
|V_{us}| = 0.2250(14)(20)(12).
\label{eq:Vus}
\eea


\section{Other 4 CKM matrix elements using unitarity and 
Wolfenstein parameters}\label{sec:unitary}

Having the 5 CKM matrix elements directly determined from
the 5 semileptonic decays, we can check unitarity
of the second row of the CKM matrix. Using 
Eqs.~(\ref{eq:VcdVcs}) and (\ref{eq:Vcb}), we get
\bea
({|V_{cd}|^2+|V_{cs}|^2+|V_{cb}|^2})^{1/2}={ 1.00(10)(2)},
\eea
which is consistent with unitarity.
Hereafter the first error is from the lattice calculation and the second
is experimental, unless otherwise stated.


We now use unitarity of the CKM matrix to determine
the other 4 CKM matrix elements.
$|V_{ud}|$, $|V_{tb}|$ and $|V_{ts}|$ are easily determined:
\bea
|V_{ud}| &=& (1 - |V_{us}|^2 - |V_{ub}|^2)^{1/2} ~=~ \Vud, \\
|V_{tb}| &=& (1 - |V_{ub}|^2 - |V_{cb}|^2)^{1/2} ~=~ \Vtb, \\
|V_{ts}| &=& |V_{us}^{*}V_{ub} + V_{cs}^{*}V_{cb}|\ /\ |V_{tb}|
~\simeq~ |V_{cs}^{*}V_{cb}|\ /\ |V_{tb}| ~=~ \Vts. 
\eea
%Before proceeding to extract $|V_{td}|$, let us give 
%some of the Wolfenstein parameters.
%Using Eqs.~(\ref{eq:Vus}), (\ref{eq:Vcb}) and (\ref{eq:Vub}),
%we get
Eqs.~(\ref{eq:Vus}), (\ref{eq:Vcb}) and (\ref{eq:Vub}) 
give some of the Wolfenstein parameters,
\bea
\lambda &=& |V_{us}| ~~~~~~~~~~=\!\!\!\! \Wlambda\!\!\!\!\!\!, \\
A &=& |V_{cb}|/\lambda^2 ~~~~~~=~ \WA, \\
(\rho^2 + \eta^2)^{1/2} &=& |V_{ub}| / (A\lambda^3) ~=~ \WR. 
\label{eq:WR}
\eea
%
%It is difficult to extract $|V_{td}|$ accurately using unitarity 
%alone,
%because $V_{td}$ ($=A\lambda^3(1\!-\!\rho\!-\!i\eta)$
%in Wolfenstein parameterization) contains a large 
%CP-violating phase and its magnitude is small.
To extract $|V_{td}|$ and $(\rho,\eta)$,
we use the experimental result for $\sin(2\beta)$
from $B\to (c\bar{c}) K^{(*)}$ decays. 
From a unitary triangle analysis with 
$\sin(2\beta)=0.726(37)$~\cite{HFAG}
and Eq.~(\ref{eq:WR}),
we obtain
\bea
\rho ~=~ \Wrho, &&~ \eta ~=~ \Weta, \\
|V_{td}| &=& \Vtd    
\eea
with a combined lattice and experimental error,
completing the {full} CKM matrix. 
%The accuracy of $(\rho,\eta)$ is dominated by that of $|V_{ub}|$.


\section*{Acknowledgments}

We thank 
all members of the Fermilab Lattice, MILC and HPQCD Collaborations,
in particular, 
the authors in Ref.~\cite{Aubin:2004ej}.
%%%% AUTHOR LIST HERE %%%%%%
%C.~Aubin,
%C.~Bernard,
%C.~DeTar,
%M.~Di Pierro,
%A.~El-Khadra,
%Steven~Gottlieb,
%E.~B.~Gregory,
%U.~M.~Heller,
%J.~Hetrick,
%A.~S.~Kronfeld,
%P.~B.~Mackenzie,
%D.~Menscher,
%M.~Nobes,
%M.~Okamoto,
%M.~B.~Oktay,
%J.~Osborn,
%J.~Simone,
%R.~Sugar,
%D.~Toussaint, and 
%H.~D.~Trottier.
%
%We thank Andreas~S.~Kronfeld, Jack~Laiho, and Robert~Sugar
%for valuable comments on the manuscript.
This work is supported by
the Fermilab Computing Division, the SciDAC program, and
FermiQCD~\cite{DiPierro:2003sz}.
%the Theoretical High Energy Physics Programs at the DOE and NSF, 
%and URA.
Fermilab is operated by Universities Research Association Inc., under
contract with the U.S. Department of Energy.


\begin{thebibliography}{99}

%%
%%  bibliographic items can be constructed using the LaTeX format in SPIRES:
%%    see    http://www.slac.stanford.edu/spires/hep/latex.html
%%  SPIRES will also supply the CITATION line information; please include it.
%%
%\cite{Aubin:2004ej}
\bibitem{Aubin:2004ej}
  C.~Aubin {\it et al.},
%[Fermilab Lattice Collaboration],
  %``Semileptonic decays of D mesons in three-flavor lattice QCD,''
  Phys.\ Rev.\ Lett.\  {\bf 94}, 011601 (2005)
  [arXiv:hep-ph/0408306].
  %%CITATION = HEP-PH 0408306;%%

%\cite{Okamoto:2004xg}
\bibitem{Okamoto:2004xg}
M.~Okamoto {\it et al.},
%``Semileptonic D $\to$ pi / K and B $\to$ pi / D decays in 2+1 flavor lattice
%QCD,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 140}, 461 (2005)
  [arXiv:hep-lat/0409116].
  %%CITATION = HEP-LAT 0409116;%%

\bibitem{milc} C. Bernard {\it et al.},
%[MILC collaboration],
Phys.\ Rev.\ D {\bf 64}, 054506 (2001);
%
%\cite{Aubin:2004wf}
%\bibitem{Aubin:2004wf}
C.~Aubin {\it et al.},
%``Light hadrons with improved staggered quarks: Approaching the continuum
%limit,''
%Phys.\ Rev.\ D 
{\bf 70}, 094505 (2004).
%[arXiv:hep-lat/0402030].
%%CITATION = HEP-LAT 0402030;%%

\bibitem{Eidelman:wy}
S.~Eidelman {\it et al.}
 [Particle Data Group Collaboration],
%``Review Of Particle Physics,''
Phys.\ Lett.\ B {\bf 592}, 1 (2004).
%%CITATION = PHLTA,B592,1;%%

%\cite{Simone:2004fr}
\bibitem{Simone:2004fr}
  J.~N.~Simone {\it et al.},
%[The Fermilab Lattice, MILC and HPQCD Collaborations],
  %``Leptonic decay constants f(D/s) and f(D) in three flavor lattice QCD,''
  Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 140}, 443 (2005)
  [arXiv:hep-lat/0410030].
  %%CITATION = HEP-LAT 0410030;%%

% correction of earliar result by Fermilab
%\cite{diPierro:2003iw}
\bibitem{diPierro:2003iw}
M.~di Pierro {\it et al.},
%``D/s spectrum and leptonic decays with Fermilab heavy quarks and improved
%staggered light quarks,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 328 (2004);
%[arXiv:hep-lat/0310045].
%%CITATION = HEP-LAT 0310045;%%
%
%\cite{diPierro:2003bu}
%\bibitem{diPierro:2003bu}
%M.~di Pierro {\it et al.},
%``Properties of charmonium in lattice QCD with 2+1 flavors of improved
%staggered sea quarks,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 340 (2004);
%[arXiv:hep-lat/0310042].
%%CITATION = HEP-LAT 0310042;%%
%
%\cite{Okamoto:2003ur}
%\bibitem{Okamoto:2003ur}
M.~Okamoto {\it et al.},
%``Semileptonic decays of D mesons in unquenched lattice QCD,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 334 (2004).
%[arXiv:hep-lat/0309107].
%%CITATION = HEP-LAT 0309107;%%

%\cite{Okamoto:2004df}
\bibitem{Okamoto:2004df}
  M.~Okamoto  [Fermilab Lattice Collaboration],
  %``Full CKM matrix with lattice QCD,''
  arXiv:hep-lat/0412044.
  %%CITATION = HEP-LAT 0412044;%%


%\cite{Becirevic:1999kt}
\bibitem{Becirevic:1999kt}
D.~Becirevic and A.~B.~Kaidalov,
%``Comment on the heavy $\to$ light form factors,''
Phys.\ Lett.\ B {\bf 478}, 417 (2000).
%[arXiv:hep-ph/9904490].
%%CITATION = HEP-PH 9904490;%%


%\cite{Aubin:2004xd}
\bibitem{Aubin:2004xd}
C.~Aubin and C.~Bernard,
%``Staggered chiral perturbation theory with heavy-light mesons,''
arXiv:hep-lat/0409027, and work in progress.
%%CITATION = HEP-LAT 0409027;%%


%\cite{unknown:2004nn}
\bibitem{unknown:2004nn}
M.~Ablikim {\it et al.}
[BES Collab.],
hep-ex/0406028;
%%CITATION = HEP-EX 0406028;%%
%
%\bibitem{Huang:2004fr}
G.~S.~Huang {\it et al.}
[CLEO Collab.],
%``Study of semileptonic charm decays D0 $\to$ pi- l+ nu and D0 $\to$ K- l+
%nu,''
hep-ex/0407035;
%%CITATION = HEP-EX 0407035;%%
%
%\cite{Link:2004dh}
%\bibitem{Link:2004dh}
J.~M.~Link {\it et al.} [FOCUS Collab.],
%``Measurements of the q**2 dependence of the D0 $\to$ K- mu+ nu and D0 $\to$
%pi- mu+ nu form factors,''
hep-ex/0410037.
%%CITATION = HEP-EX 0410037;%%

%\cite{Athar:2003yg}
\bibitem{Athar:2003yg}
S.~B.~Athar {\it et al.} [CLEO Collaboration],
%  [CLEO Collaboration],
%``Study of the q**2 dependence of B $\to$ pi l nu and B $\to$ rho (omega) l  nu
%decay and extraction of $|$V(ub)$|$,''
Phys.\ Rev.\ D {\bf 68}, 072003 (2003).
%[arXiv:hep-ex/0304019].
%%CITATION = HEP-EX 0304019;%%
%(See also K.~Abe {\it et al.}, hep-ex/0408145.)

\bibitem{Belle:B2pi}
K.~Abe {\it et al.} [Belle Collaboration], hep-ex/0408145.

%\cite{Hashimoto:1999yp}
\bibitem{Hashimoto:1999yp}
S.~Hashimoto {\it et al.}, 
%``Lattice {QCD} calculation of anti-B $\to$ D l anti-nu decay form factors  at
%zero recoil,''
Phys.\ Rev.\ D {\bf 61}, 014502 (2000).
%[arXiv:hep-ph/9906376].
%%CITATION = HEP-PH 9906376;%%

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

%\cite{Becirevic:2004ya}
\bibitem{Becirevic:2004ya}
D.~Becirevic {\it et al.},
%``The K $\to$ pi vector form factor at zero momentum transfer on the lattice,''
arXiv:hep-ph/0403217.
%%CITATION = HEP-PH 0403217;%%

%\cite{Leutwyler:1984je}
\bibitem{Leutwyler:1984je}
H.~Leutwyler and M.~Roos,
%``Determination Of The Elements V (Us) And V (Ud) Of The Kobayashi-Maskawa
%Matrix,''
Z.\ Phys.\ C {\bf 25}, 91 (1984).
%%CITATION = ZEPYA,C25,91;%%

%\cite{Alexopoulos:2004sw}
\bibitem{Alexopoulos:2004sw}
T.~Alexopoulos {\it et al.}  [KTeV Collaboration],
%``A determination of the CKM parameter $|$V(us)$|$,''
Phys.\ Rev.\ Lett.\  {\bf 93}, 181802 (2004).
%[arXiv:hep-ex/0406001].
%%CITATION = HEP-EX 0406001;%%
%
%\cite{Alexopoulos:2004sy}
%\bibitem{Alexopoulos:2004sy}
%T.~Alexopoulos {\it et al.}  [KTeV Collaboration],
%``Measurements of semileptonic K(L) decay form factors,''
%Phys.\ Rev.\ D {\bf 70}, 092007 (2004).
%[arXiv:hep-ex/0406003].
%%CITATION = HEP-EX 0406003;%%


%\cite{AliKhan:2001ek}
%\bibitem{AliKhan:2001ek}
%A.~Ali Khan {\it et al.}  [CP-PACS collaboration],
%``Equation of state in finite-temperature QCD with two flavors of  improved
%Wilson quarks,''
%Phys.\ Rev.\ D {\bf 64}, 074510 (2001)
%[arXiv:hep-lat/0103028].
%%CITATION = HEP-LAT 0103028;%%

%\cite{Okamoto:2001jb}
%\bibitem{Okamoto:2001jb}
%  M.~Okamoto {\it et al.}  [CP-PACS Collaboration],
%``Charmonium spectrum from quenched anisotropic lattice QCD,''
%  Phys.\ Rev.\ D {\bf 65}, 094508 (2002)
%  [arXiv:hep-lat/0112020].
%%CITATION = HEP-LAT 0112020;%%


%\cite{DiPierro:2003sz}
\bibitem{DiPierro:2003sz}
  M.~Di Pierro {\it et al.},
%  [FermiQCD Colaboration Collaboration],
  %``www.fermiqcd.net,''
  Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 832 (2004)
  [arXiv:hep-lat/0311027].
  %%CITATION = HEP-LAT 0311027;%%



\end{thebibliography}




\end{document}




%%%%%%%%%%%%%%%%%%%%%%
% End of moriond.tex  %
%%%%%%%%%%%%%%%%%%%%%%

hep-ph0505190.extracted_bib
\begin{thebibliography}{99}

%%
%%  bibliographic items can be constructed using the LaTeX format in SPIRES:
%%    see    http://www.slac.stanford.edu/spires/hep/latex.html
%%  SPIRES will also supply the CITATION line information; please include it.
%%
%\cite{Aubin:2004ej}
\bibitem{Aubin:2004ej}
  C.~Aubin {\it et al.},
%[Fermilab Lattice Collaboration],
  %``Semileptonic decays of D mesons in three-flavor lattice QCD,''
  Phys.\ Rev.\ Lett.\  {\bf 94}, 011601 (2005)
  [arXiv:hep-ph/0408306].
  %%CITATION = HEP-PH 0408306;%%

%\cite{Okamoto:2004xg}
\bibitem{Okamoto:2004xg}
M.~Okamoto {\it et al.},
%``Semileptonic D $\to$ pi / K and B $\to$ pi / D decays in 2+1 flavor lattice
%QCD,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 140}, 461 (2005)
  [arXiv:hep-lat/0409116].
  %%CITATION = HEP-LAT 0409116;%%

\bibitem{milc} C. Bernard {\it et al.},
%[MILC collaboration],
Phys.\ Rev.\ D {\bf 64}, 054506 (2001);
%
%\cite{Aubin:2004wf}
%\bibitem{Aubin:2004wf}
C.~Aubin {\it et al.},
%``Light hadrons with improved staggered quarks: Approaching the continuum
%limit,''
%Phys.\ Rev.\ D 
{\bf 70}, 094505 (2004).
%[arXiv:hep-lat/0402030].
%%CITATION = HEP-LAT 0402030;%%

\bibitem{Eidelman:wy}
S.~Eidelman {\it et al.}
 [Particle Data Group Collaboration],
%``Review Of Particle Physics,''
Phys.\ Lett.\ B {\bf 592}, 1 (2004).
%%CITATION = PHLTA,B592,1;%%

%\cite{Simone:2004fr}
\bibitem{Simone:2004fr}
  J.~N.~Simone {\it et al.},
%[The Fermilab Lattice, MILC and HPQCD Collaborations],
  %``Leptonic decay constants f(D/s) and f(D) in three flavor lattice QCD,''
  Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 140}, 443 (2005)
  [arXiv:hep-lat/0410030].
  %%CITATION = HEP-LAT 0410030;%%

% correction of earliar result by Fermilab
%\cite{diPierro:2003iw}
\bibitem{diPierro:2003iw}
M.~di Pierro {\it et al.},
%``D/s spectrum and leptonic decays with Fermilab heavy quarks and improved
%staggered light quarks,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 328 (2004);
%[arXiv:hep-lat/0310045].
%%CITATION = HEP-LAT 0310045;%%
%
%\cite{diPierro:2003bu}
%\bibitem{diPierro:2003bu}
%M.~di Pierro {\it et al.},
%``Properties of charmonium in lattice QCD with 2+1 flavors of improved
%staggered sea quarks,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 340 (2004);
%[arXiv:hep-lat/0310042].
%%CITATION = HEP-LAT 0310042;%%
%
%\cite{Okamoto:2003ur}
%\bibitem{Okamoto:2003ur}
M.~Okamoto {\it et al.},
%``Semileptonic decays of D mesons in unquenched lattice QCD,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 334 (2004).
%[arXiv:hep-lat/0309107].
%%CITATION = HEP-LAT 0309107;%%

%\cite{Okamoto:2004df}
\bibitem{Okamoto:2004df}
  M.~Okamoto  [Fermilab Lattice Collaboration],
  %``Full CKM matrix with lattice QCD,''
  arXiv:hep-lat/0412044.
  %%CITATION = HEP-LAT 0412044;%%


%\cite{Becirevic:1999kt}
\bibitem{Becirevic:1999kt}
D.~Becirevic and A.~B.~Kaidalov,
%``Comment on the heavy $\to$ light form factors,''
Phys.\ Lett.\ B {\bf 478}, 417 (2000).
%[arXiv:hep-ph/9904490].
%%CITATION = HEP-PH 9904490;%%


%\cite{Aubin:2004xd}
\bibitem{Aubin:2004xd}
C.~Aubin and C.~Bernard,
%``Staggered chiral perturbation theory with heavy-light mesons,''
arXiv:hep-lat/0409027, and work in progress.
%%CITATION = HEP-LAT 0409027;%%


%\cite{unknown:2004nn}
\bibitem{unknown:2004nn}
M.~Ablikim {\it et al.}
[BES Collab.],
hep-ex/0406028;
%%CITATION = HEP-EX 0406028;%%
%
%\bibitem{Huang:2004fr}
G.~S.~Huang {\it et al.}
[CLEO Collab.],
%``Study of semileptonic charm decays D0 $\to$ pi- l+ nu and D0 $\to$ K- l+
%nu,''
hep-ex/0407035;
%%CITATION = HEP-EX 0407035;%%
%
%\cite{Link:2004dh}
%\bibitem{Link:2004dh}
J.~M.~Link {\it et al.} [FOCUS Collab.],
%``Measurements of the q**2 dependence of the D0 $\to$ K- mu+ nu and D0 $\to$
%pi- mu+ nu form factors,''
hep-ex/0410037.
%%CITATION = HEP-EX 0410037;%%

%\cite{Athar:2003yg}
\bibitem{Athar:2003yg}
S.~B.~Athar {\it et al.} [CLEO Collaboration],
%  [CLEO Collaboration],
%``Study of the q**2 dependence of B $\to$ pi l nu and B $\to$ rho (omega) l  nu
%decay and extraction of $|$V(ub)$|$,''
Phys.\ Rev.\ D {\bf 68}, 072003 (2003).
%[arXiv:hep-ex/0304019].
%%CITATION = HEP-EX 0304019;%%
%(See also K.~Abe {\it et al.}, hep-ex/0408145.)

\bibitem{Belle:B2pi}
K.~Abe {\it et al.} [Belle Collaboration], hep-ex/0408145.

%\cite{Hashimoto:1999yp}
\bibitem{Hashimoto:1999yp}
S.~Hashimoto {\it et al.}, 
%``Lattice {QCD} calculation of anti-B $\to$ D l anti-nu decay form factors  at
%zero recoil,''
Phys.\ Rev.\ D {\bf 61}, 014502 (2000).
%[arXiv:hep-ph/9906376].
%%CITATION = HEP-PH 9906376;%%

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

%\cite{Becirevic:2004ya}
\bibitem{Becirevic:2004ya}
D.~Becirevic {\it et al.},
%``The K $\to$ pi vector form factor at zero momentum transfer on the lattice,''
arXiv:hep-ph/0403217.
%%CITATION = HEP-PH 0403217;%%

%\cite{Leutwyler:1984je}
\bibitem{Leutwyler:1984je}
H.~Leutwyler and M.~Roos,
%``Determination Of The Elements V (Us) And V (Ud) Of The Kobayashi-Maskawa
%Matrix,''
Z.\ Phys.\ C {\bf 25}, 91 (1984).
%%CITATION = ZEPYA,C25,91;%%

%\cite{Alexopoulos:2004sw}
\bibitem{Alexopoulos:2004sw}
T.~Alexopoulos {\it et al.}  [KTeV Collaboration],
%``A determination of the CKM parameter $|$V(us)$|$,''
Phys.\ Rev.\ Lett.\  {\bf 93}, 181802 (2004).
%[arXiv:hep-ex/0406001].
%%CITATION = HEP-EX 0406001;%%
%
%\cite{Alexopoulos:2004sy}
%\bibitem{Alexopoulos:2004sy}
%T.~Alexopoulos {\it et al.}  [KTeV Collaboration],
%``Measurements of semileptonic K(L) decay form factors,''
%Phys.\ Rev.\ D {\bf 70}, 092007 (2004).
%[arXiv:hep-ex/0406003].
%%CITATION = HEP-EX 0406003;%%


%\cite{AliKhan:2001ek}
%\bibitem{AliKhan:2001ek}
%A.~Ali Khan {\it et al.}  [CP-PACS collaboration],
%``Equation of state in finite-temperature QCD with two flavors of  improved
%Wilson quarks,''
%Phys.\ Rev.\ D {\bf 64}, 074510 (2001)
%[arXiv:hep-lat/0103028].
%%CITATION = HEP-LAT 0103028;%%

%\cite{Okamoto:2001jb}
%\bibitem{Okamoto:2001jb}
%  M.~Okamoto {\it et al.}  [CP-PACS Collaboration],
%``Charmonium spectrum from quenched anisotropic lattice QCD,''
%  Phys.\ Rev.\ D {\bf 65}, 094508 (2002)
%  [arXiv:hep-lat/0112020].
%%CITATION = HEP-LAT 0112020;%%


%\cite{DiPierro:2003sz}
\bibitem{DiPierro:2003sz}
  M.~Di Pierro {\it et al.},
%  [FermiQCD Colaboration Collaboration],
  %``www.fermiqcd.net,''
  Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 129}, 832 (2004)
  [arXiv:hep-lat/0311027].
  %%CITATION = HEP-LAT 0311027;%%



\end{thebibliography}