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$Id: espcrc2.tex,v 1.2 2004/02/24 11:22:11 spepping Exp $
\ProvidesFile{espcrc2.tex}[\filedate \space v\fileversion
     \space Elsevier 2-column CRC Author Instructions]

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% \documentstyle[twoside,fleqn,espcrc2]{article}

% if you want to include PostScript figures
\usepackage{graphicx}
% if you have landscape tables
\usepackage[figuresright]{rotating}

% put your own definitions here:
%   \newcommand{\cZ}{\cal{Z}}
%   \newtheorem{def}{Definition}[section]
%   ...
\newcommand{\ttbs}{\char'134}
\newcommand{\AmS}{{\protect\the\textfont2
  A\kern-.1667em\lower.5ex\hbox{M}\kern-.125emS}}
% my def
\def \daf{DA$\Phi$NE}
\def \ff{${\it \phi - factory}$}
\def \ee{$e^+ e^- $~}
\def \Ko        {${\rm K^o}$}
\def \KoE       {{\rm K^o}}
\def \Kobar     {$\bar{{\rm K^o}}$~}
\def \KobarE    {\bar{{\rm K^o}}~}
\def \KKbar     {${\rm K} \bar{{\rm K}}$~}
\def \KKbarE    {{\rm K} \bar{{\rm K}}~}
\def \KKobar{${\rm K}^o \bar{{\rm K}^o}$}
\def \KKsis{${\rm K}^o - \bar{{\rm K}^o}$}
\def \Kl     {${\rm K_L }$~}
\def \Ks     {${\rm K_S }$~}
\def \Kpm    {${\rm K^{\pm} }$~}
\def \Kls    {${\rm K_{L,S} }$~}
\def \KLKS {${\rm K_L}-{\rm K_S }$~}
\def \Kpipi  {${\rm K^{\pm}} \rightarrow \pi^{\pm}\pi^o$~}
\def \Kmunu  {${\rm K^{\pm}} \rightarrow \mu^{\pm}\bar{\nu}(\nu)$~}
\def \Kmunup {${\rm K^+} \rightarrow \mu^+\bar{\nu}(\gamma)$~}
\def \Kmunum {${\rm K^-} \rightarrow \mu^-\nu$~}
\def \KmunupE {{\rm K^+} \rightarrow \mu^+\bar{\nu}(\gamma)~}
\def \KLKSff {${\rm K_L}{\rm K_S}\rightarrow {\rm f_1 f_2} $}
\def \twopi{$\pi\pi$~}
\def \epsb{$\bar\varepsilon$~}
\def \eps     {$\varepsilon ' /\varepsilon$~}
\def \epsE    {\varepsilon ' /\varepsilon~}
\def \Reeps  {$\Re e(\varepsilon ' /\varepsilon)$}
\def \ReepsE {\Re e(\varepsilon ' /\varepsilon)}
\def \Imeps  {$\Im m(\varepsilon ' /\varepsilon)$}
\def \ImepsE {\Im m(\varepsilon ' /\varepsilon)}
\def \rlh{$\rightleftharpoons$}
%\def \deltas{$\mid~{\Delta}S~\mid$}
\def \phiKK{${\rm \phi} \rightarrow {\rm K_L}{\rm K_S}$}
\def \deltas{$\mid{\Delta}S\mid$}
\def \Klc{${\rm K_L} \rightarrow \pi^+\pi^-$}
\def \KlcE{{\rm K_L} \rightarrow \pi^+\pi^-}
\def \Kln{${\rm K_L} \rightarrow \pi^o\pi^o$}
\def \KlnE{{\rm K_L} \rightarrow \pi^o\pi^o}
\def \Klppp{${\rm K_L} \rightarrow \pi^{\pm}\pi^{\mp}\pi^o$}
\def \Ksc  {${\rm K_S} \rightarrow \pi^+\pi^-$}
\def \KscE  {{\rm K_S} \rightarrow \pi^+\pi^-}
\def \Ksn{${\rm K_S} \rightarrow \pi^o\pi^o$}
\def \KsnE{{\rm K_S} \rightarrow \pi^o\pi^o}
\def \semiKs {${\rm K_S} \rightarrow \pi^{\pm}e^{\mp}\bar{\nu}(\nu)$}
\def \semiKsp {${\rm K_S} \rightarrow \pi^+e^-\bar{\nu}$}
\def \semiKsm {${\rm K_S} \rightarrow \pi^-e^+\nu$}
\def \semiKsg {${\rm K_S} \rightarrow \pi e \nu (\gamma)$}

\newcommand{\pemiss}{\ensuremath{|\vec{p}_{\rmk miss}|-E_{\rmk miss}}}
\newcommand{\dmp}{\ensuremath{\Delta_{\mu \pi}}}
\newcommand{\dep}{\ensuremath{\Delta_{e \pi}}}
\newcommand{\pmiss}{\ensuremath{\vec{p}_{\rmk miss}}}
\newcommand{\emiss}{\ensuremath{E_{\rmk miss}}}
\newcommand{\LK}{\ensuremath{L_{K}}}
\newcommand{\DKSeIII}{\ensuremath{K_S\rightarrow\pi e \nu}}
\newcommand{\DKSpippim}{\ensuremath{K_S\rightarrow\pi^+\pi^-}}
%
\newcommand{\Pe}{\ensuremath{e}}
\newcommand{\Pem}{\ensuremath{e^-}}
\newcommand{\Pep}{\ensuremath{e^+}}
\newcommand{\Pemp}{\ensuremath{e^\mp}}
\newcommand{\Pmump}{\ensuremath{\mu^\mp}}
\newcommand{\Pnu}{\ensuremath{\nu}}
\newcommand{\Pnubar}{\ensuremath{\bar{\nu}}}
\newcommand{\Pphi}{\ensuremath{\phi}}
\newcommand{\Ppi}{\ensuremath{\pi}}
\newcommand{\Ppim}{\ensuremath{\pi^-}}
\newcommand{\Ppip}{\ensuremath{\pi^+}}
\newcommand{\Ppio}{\ensuremath{\pi^0}}
\newcommand{\Ppipm}{\ensuremath{\pi^\pm}}
\newcommand{\BR}[1]{\ensuremath{\mathrm{BR}(#1)}}
\newcommand{\Emiss}{\ensuremath{E_\mathrm{miss}}}
\newcommand{\Pmiss}{\ensuremath{p_\mathrm{miss}}}
\newcommand{\DKPeIII}{\ensuremath{K^+\rightarrow\pi^0 e^{+}\nu}}
\newcommand{\DKP}{\ensuremath{K^+\rightarrow\pi^0 \pi^+}}
\newcommand{\DKPme}{\ensuremath{K\rightarrow\pi e\mu}}

%
\def\lifet#1{\ifm{\tau_{\mathrm{K}_{#1}}}}
\def\pienu{\ifm{\pi^\pm e^\mp\bar\nu(\nu)}}
\def\pimunu{\ifm{\pi^\pm \mu^\mp\bar\nu(\nu)}}
\def\toP{\ifm{\rightarrow}}
\def\ifm#1{\relax\ifmmode#1\else$#1$\fi}  \def\DAF{DA\char8NE}
\def\x{\ifm{\times}}  \def\pt#1,#2,{\ifm{#1\x10^{#2}}}
\def\up#1{\ifm{^{#1}}}  \def\dn#1{\ifm{_{#1}}}
\def\ab{\ifm{\sim}}  \def\deg{\ifm{^\circ}}  \def\gam{\ifm{\gamma}} 
\def\to{\ifm{\rightarrow}} \def\kl{\ifm{K_L}}   \def\ks{\ifm{K_S}}
\def\eiii{\ifm{\pi^\pm e^\mp\nu}}  \def\keiii{\ifm{K_{e3}}}
\def\muiii{\ifm{\pi^\pm \mu^\mp\nu}}   \def\kmuiii{\ifm{K_{\mu3}}}
\def\pio{\ifm{\pi^0\pi^0}} \def\po{\ifm{\pi^0}}
\def\pic{\ifm{\pi^+\pi^-}}  \def\K{\ifm{K}}
\def\xc{\ifm{\vec x_{\rmk c}}}   \def\pc{\ifm{\vec p_{\rmk c}}}
\def\lc{\ifm{l_{\rmk c}}}   \def\dc{\ifm{d_{\rmk c}}}
\def\rmk{\rm\kern.5mm }   \def\f{\ifm{\phi}}  
\def\Vus{\ifm{|V_{us}|}}
\def\Vud{\ifm{|V_{ud}|}}

\def\costante{\frac{G_F^2 M_K^5}{128\pi^3} C_K^2 S_{EW}}
\def\Vfs{\ifm{|V_{us}|}^2 f_+^{{\rmk K^o}\pi^-}(0)^2}
\def\integrale{I_i(\lambda_+^{\prime},\lambda_+^{\prime\prime},\lambda_o)}
\def\corr{(1 + \delta^i_{SU(2)} + \delta^i_{em})}

\def\Vf{\ifm{|V_{us}|} f_+^{{\rmk K^o}\pi^-}(0)}

\def \dc{${\rm K_{L,S}} \rightarrow \pi^+\pi^-$}
\def \dn{${\rm K_{L,S}} \rightarrow \pi^o\pi^o$}
\def \dpipi{${\rm K_{L,S}} \rightarrow \pi\pi$}
\def \df    {${\rm \phi} \rightarrow {\rm K} \bar{\rm K}$}
\def \dfE   {{\rm \phi} \rightarrow {\rm K} \bar{\rm K}}
\def \burpE {\stackrel{<}{\sim}}
\def \birpE {\stackrel{>}{\sim}}
\def \burp {${\stackrel{<}{\sim}}$}
\def \birp {${\stackrel{>}{\sim}}$}

\def\DAF{DA\char8NE}  \def\epm{\ifm{e^+e^-}}
\def\ifm#1{\relax\ifmmode#1\else$#1$\fi}
\def\pic{\ifm{\pi^+\pi^-}}
\def\to{\ifm{\rightarrow}}
\def\ff{$\phi$--factory}  \def\f{\ifm{\phi}}
\def\K{\ifm{K}}
\def\pienu{\ifm{\pi^\pm e^\mp\bar\nu(\nu)}}
\def\pimunu{\ifm{\pi^\pm \mu^\mp\bar\nu(\nu)}}
\def\ab{\ifm{\sim}}  \def\x{\ifm{\times}}
\def\pt#1,#2,{\ifm{#1\x10^{#2}}}
\def\kneu#1{\ifm{K_{#1}}}
\def\ketre#1{\ifm{\pi e\nu_e}}
\def\kmutre#1{\ifm{\pi\mu\nu_{\mu}}}
\def\pai#1{\ifm{\pi^{#1}}}
\def\lifet#1{\ifm{\tau_{\mathrm{K}_{#1}}}}
\newcommand{\etal}{{\em et al.}}
\newcommand{\SN}[2]{\ensuremath{#1\times10^{#2}}}
\newcommand{\VS}[2]{\ensuremath{#1\pm#2}}
\newcommand{\Fig}[1]{Fig.~#1}


\newcommand{\kp}{\mbox{$K^+$}}





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\title{Semileptonic K decays: recent measurements of \Vus  }

\author{A. Antonelli\address[MCSD]{Laboratori Nazionali di Frascati- INFN, \\ 
        Via E. Fermi 40, 00044 Frascati Rome Italy}}
        
       
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\runtitle{2-column format camera-ready paper in \LaTeX}
\runauthor{A. Antonelli}

\begin{document}

\begin{abstract}
After a long history the kaon system continues to be a laboratory for
 interesting physics,
 from flavour physics to CP violation. Kaon rare decays
are also a powerful tool, complementary to B decays, to probe the physics
beyond the Standard Model. In this paper I will review most of the recent
results from kaon semileptonic decays usefull for the extraction of the CKM matrix element \Vus.

\vspace{1pc}
\end{abstract}

% typeset front matter (including abstract)
\maketitle

\section{Unitarity test of CKM matrix.  }
The measurement of the  semileptonic kaon decay widths
allows us to test many fundamental aspects of the Standard Model.

The most precise test of unitarity of the CKM matrix comes from
its first row: $1-\Delta \simeq |V_{\mathrm{ud}}|^{2} + |V_{\mathrm{us}}|^{2}$.
Using $|V_{\mathrm{ud}}|$ as extracted from nuclear beta decays,  
and $|V_{\mathrm{us}}|$ as extracted from the semileptonic decay width
of the kaon, 
a  test for the expectation on $\Delta$=0 with a precision of few parts per mil
can be performed. Using the PDG 2004 values for \Vus\ and \Vud\, one finds a
2 $\sigma$ deviation from unitarity. 
The  value of \Vus\ can be extracted from the measurement of the 
semileptonic kaon decay width using~\cite{CKMWG}:
\begin{eqnarray}
\Vus\ \cdot f_{+}^{K^0 \pi^-} (0) = & \left[ \frac{\Gamma}
{ {\cal N} \, S_{\rm ew} \,  I_{i} (\lambda_+, \lambda_0, 0) }
\right]^{1/2} \\ \nonumber 
& \frac{1}{1 + \delta^{i}_{e^2 p^2} + \frac{1}{2}\Delta I_{i} (\lambda_+,
  \lambda_0) }
\label{vus}
\end{eqnarray}
with
\[
{\cal N} =  \frac{G_{\mu}^2 M_{K_i}^5}{192 \pi^3}
\]
where $f_{+}^{K^0 \pi^-}$(0) is the vector form factor at zero momentum
transfer, $I_{i} (\lambda_+, \lambda_0, 0)$ is the result of the phase
space integration after factoring out $f_{+}^{K^0 \pi^-}$(0), and both are
evaluated in absence of radiative corrections.  The radiative
corrections for the form factor and the phase space integral are
included via $\delta^{i}_{e^2 p^2}$ and $\Delta I_{i} (\lambda_+,
\lambda_0)$ respectively. The parameters  $\lambda_+$ and $\lambda_0$ are 
 describe the momentum transfer  dependence of the
vector and scalar form factor.

 The first new result on kaon semiletonic decays comes in 2003 from E865
experiment\cite{e865}. They measure a BR(\DKPeIII) that is 2.7 $\sigma$ above
the previous measurements but which gives a  value of \Vus\ consistent with
unitarity. The key issue in this measurement is the systematic control of the
branching ratio.  The detector was not optimised for photons, it was
designed to search for \DKPme\ decays, and $\pi^0$ Dalitz decay is required
in both  signal and
in normalisation (\DKP)channels . There was a lot of interest in seeing this
result confirmed.  KLOE, NA48 ,KTEV and ISTRA+ experiments have recently
measured semileptonic kaon branching ratios, lifetime and form factors using
different techniques.




\section{ Results on semileptonic neutral kaon decays: KLOE, NA48, KTEV }
  Measurements of the absolute kaon branching ratios are a unique
 possibility of the \f\  factory. In \f\ decays pairs of  monochromatic \ks
 \kl~ are produced  and the \kl (\ks) can be identified looking at the decay
 of 
the companion on the other side (tagging). The \kl~ is
 selected by identification of \ks~ decays while a \ks~
 beam is tagged using the fraction of events in which the \kneu{L}
 interacts in the calorimeter (\kl~ crash).  Absolute branching ratios can be
 determined by counting the fraction of \kl's that decay into each
 channel and correcting for acceptances, reconstruction efficiencies,
 and background.  KLOE has measured the dominant \kneu{L} branching
 ratios using the \kneu{L} beam tagged by \DKSpippim\
 decays~\cite{BrKl}.  In the 2001/2002 data sample, $\sim$13$\times
 10^6$ tagged \kneu{L} decays have been used for the measurement, and
 $\sim$4$\times 10^6$ to evaluate efficiencies.  To measure the BR's
 for decays to charged particles, a \kneu{L} decay vertex is required
 in the DC fiducial volume. 
The number of events of each type is obtained by fitting the distribution
of missing momentum
minus missing energy, in the $\pi\mu$ mass
 assignment,
with the sum of the MC distributions   
for each of the decay channels.
To select \kneu{L}$\to$3\pai{0} events, at least three photons are required 
from the \kneu{L}
decay vertex. The reconstruction efficiency and purity of the selected sample are both about 99\%.
The resulting BR's are: \\
$BR(K_{L}\to\pi e\nu(\gamma))=0.4049 \pm 0.0010 \pm 0.0031$,\\
$BR(K_{L} \to \pi \mu\nu(\gamma))=0.2726 \pm 0.0008 \pm 0.0022$,\\
$BR(K_{L} \to 3\pi^0)=0.2018 \pm 0.0004 \pm 0.0026$ and,\\
$BR(K_{L} \to \pi^{+}\pi^{-}\pi^{0}(\gamma))=0.1276 \pm 0.0006 \pm 0.0016$, \\
where the errors are dominated by the error on \lifet{L} through 
the geometrical acceptance. 
%%{\bf\red If you're looking for space, you could cut the above values.}
Taking the BR's for rare \kneu{L} decays to $\pi^{+}\pi^{-}$, $\pi^{0}\pi^{0}$,
and $\gamma\gamma$ from the
PDG~\cite{PDG} and imposing the constraint $\sum BR(\kneu{L}) = 1$, 
$\lifet{L}$ can
be measured: $\lifet{L} = (50.72 \pm 0.17 \pm 0.33)ns$. 
%{\bf\red  Suggest delete: with a fractional error of about 0.7\%.}
Imposition of this constraint also results in more precise measurements 
of the dominant BR's:\\
$BR(K_{L} \to \pi e\nu(\gamma)) = 0.4007 \pm 0.0006 \pm 0.0014,$ \\
$BR(K_{L} \to \pi \mu\nu(\gamma)) = 0.2698 \pm 0.0006 \pm 0.0014,$ \\
$BR(K_{L} \to 3\pi^0) = 0.1997 \pm 0.0005 \pm 0.0019,$ \\
$BR(K_{L} \to \pi^{+}\pi^{-}\pi^{0}(\gamma))=0.1263 \pm 0.0005 \pm 0.0011$.
The \kneu{L} lifetime has been also measured directly~\cite{TauKl}, 
employing 10$^7$ $K_{L} \to 3\pi^0$ events selected from the 2001/2002 data sample.
The result is $\lifet{L} = (50.92 \pm 0.17 \pm 0.25)$ ns, which together with that from the
\kneu{L} BR measurements gives the KLOE average: $\lifet{L} = (50.84 \pm 0.23)$ ns.
NA48 and KTEV experiments have used a different approach: they have
measured ratios of branching ratios since they do not have an absolute
normalisation.  NA48 has normalised $K_{L} \to \pi e\nu$ events to
$K_{L} \to 2$ tracks. Using for BR($K_{L} \to 3\pi^0$) the average
of the PDG value and the KTEV measurement, they obtain $BR(K_{L} \to \pi
e\nu(\gamma)) = 0.401 \pm 0.004$ \cite{na48kl}.  KTEV measures 5 ratios of  $K_{L}$ BR's
$\Gamma_{e3}$/$\Gamma_{\mu3}$, $\Gamma_{+-0}$/$\Gamma_{e3}$,
$\Gamma_{000}$/$\Gamma_{e3}$, $\Gamma_{+-}$/$\Gamma_{e3}$ and
$\Gamma_{00}$/$\Gamma_{000}$ . The 6 decay modes in the above ratios 
account for 99.93\%
of $K_{L}$ decays and the ratio can be combined to extract the
semileptonic branching ratio \cite{ktevkl}.
 In Fig.~\ref{fig:anton}
values of the branching ratio from
each experiment are reported and compared with values from  PDG.
 The new measurements agrees quite wellwith each other, while they disagree with the
old PDG values   for
the $K_{L} \to \pi e\nu$ and $K_{L} \to 3\pi^0$ decays.
\begin{figure}
  \includegraphics[height=.4\textheight]{mbr.eps}

  \caption{Branching ratio comparison.}
\label{fig:anton}
\end{figure} 
\par
 A measurement that is unique to KLOE is that of the BR for  $K_S$ semileptonic decays.Using the
2001-2002 data set (410 pb$^{-1}$) we obtain \cite{kloeks}:
\begin{eqnarray}
\nonumber
\BR{\ks\to\pienu}=\\\SN{(\VS{\VS{7.046}{0.077_{\rm stat}}}{0.049_{\rm syst}})}{-4}.
\end{eqnarray}
From the same sample also the charge asymmetry has been mesured for the
first time.The charge asymmetry is found to be:
$$
A_{S}\!=\!\pt(1.5\pm9.6_{\mathrm{stat}}\pm2.9_{\mathrm{syst}}),-3,
$$ 
This result is compatible with that for $\kl$ semileptonic decays and with the
expectation obtained assuming $CPT$ symmetry, $A_{S}=2 Re(\epsilon)$.
\section{ Results on semileptonic charged kaon decays: KLOE, NA48, ISTRA+ }

The measurement of the inclusive in KLOE BR(K$^{\pm}_{l3}$)'s
uses four independent samples tagged by the decays:
$K_{\mu 2}^+$, $K_{\mu 2}^-$, $K_{\pi 2}^+$ and $K_{\mu 2}^-$.  
Two-body decays are rejected applying a cut on the charged decay particle
momentum computed in the kaon rest frame $p^{\ast}$.
The lepton mass, $m_{lept}^2$, is obtained from the velocity of 
the lepton computed from the ToF.
The number of $K_{e3}$ and $K_{\mu 3}$ decays is then obtained by
fitting the $m_{lept}^2$ distribution to a sum of MC distributions for
the signals and various background sources.
The BR is evaluated separately for each tag sample.
The resulting preliminary BR's are \cite{kloekc}:
\begin{center}
$BR(K^{\pm}_{e3})=
0.05047\pm 0.00046_{\rm stat}\pm0.00080_{\rm syst}$, \\
%\vspace{0.5cm}
$BR(K^{\pm}_{\mu3}) =
0.03310\pm0.00040_{\rm stat}\pm0.00070_{\rm syst}$.
\end{center}
NA48  experiment \cite{na48kc} measures $K^{+}_{e3}$ branching ratio normalising to 
the $K_{\pi 2}$ decay taken from PDG04.They obtain: BR(${\rm K^{\pm}} \rightarrow \pi^o e \nu (\gamma)) = 
(5.14\pm0.02_{stat}\pm0.06_{syst})$\%. They also
 measures the $K^{+}_{e3} / K^{+}_{mu3}$ .

ISTRA+\cite{istrakc} has a similar approach, they obtain: 
BR(${\rm K^{\pm}} \rightarrow \pi^o e \nu (\gamma)) = (5.22\pm0.11)$\%.
It should be noticed here that  PDG06 value for the
$BR(K^{\pm} \rightarrow \pi^o  \pi^\pm)$ decreases by
$\approx$ 1 \%  due to the new $K_{e3}$ value from E865 and $K_{\mu2}$ from KLOE.
\par
KLOE has also measured the ~\Kpm~ lifetime. 
We measure the kaon proper time from the kaon momentum and pathe length,
the kaon path is evaluated taking into account the energy losses.
The vertex reconstruction efficiency and the 
resolution functions are measured directly on data by means
of the $\pi^o$ vertex reconstruction using only
calorimetric information.
The preliminary result is:
$\tau({\rmk K}^{\pm})= 12.367 \pm 0.044_{\rmk stat} \pm 0.065_{\rmk syst} {\ \rm ns}$,
in agreement with PDG 2004. 
\section {Form Factor}
The amplitude of $K_{l3}$ decays can be expressed in terms 
of two vector form factors $f_{\pm}$ ; it is also usual to define a scalar
 form factor ,$f_{0}$, as a combination of $f_{+}$ and $f_{-}$. 
In the $K_{l3}$ decays the $f_{-}$ form factor is multiplied by 
 $m^2_l/m^2_K$ and therefore can be neglected for $K_{e3}$ decays. The momentum (t)
 dependence of the form factor, 
which is relevant for the integral over the phase space,
 is often described in terms of $\lambda$ slopes:
\\$f_+(t) = 1 + \lambda_+ t$ (linear) ,
\\$f_+(t) =
 1 + \lambda_+^{\prime} \frac{t}{m^2_{\pi^+}} +
 \frac{1}{2}\lambda_+^{\prime\prime}(\frac{t}{m^2_{\pi^+}})^2$
 (quadratic), 
\\or using the pole model: ~~~~$f_+(t) = M_V^2/(M_V^2 - t)$.
The slopes are obtained fitting the t-spectrum with different hypotheses on form factor.



\par 
KLOE experiment has fitted the $K_{e3}$ spectrum using the linear, the
 quadratic and the pole parametrization.
 A very slight preference for a small quadratic term is obtained
 \cite{kloeslopes}.The rusults are:
\\{\bf quadratic} ~$\lambda_+^{\prime} = (25.5\pm 1.5 \pm 1.0)\times10^{-3}$ and
     $\lambda_+^{\prime\prime} = (1.4\pm 0.7 \pm 0.4)\times10^{-3}$ with $P(\chi^2)=92\% $,
%\item[Pole model]
%~~~~$f_+(t) = M_V^2/(M_V^2 - t)$
\\{\bf pole model} ~$M_V = 870\pm 7$ MeV  with $P(\chi^2)=92.4\%$.
\\KTeV, ISTRA+ and NA48 experiments have fitted both $K_{e3}$ and $K_{\mu3}$ spectra.
KTeV experiment find a quadratic slope term different from zero at 4 $\sigma$ level
and the slopes are consistent for $K_{e3}$ and $K_{\mu3}$ decay modes
\cite{ktevslopes}. 
NA48 find no
evidence of quadratic term in the $K_{e3}$  spectrum, they obtain a $\lambda_0$
consistent with KTeV result in the $K_{\mu3}$ \cite{na48slopes}. ISTRA+ experiment finds a 
 quadratic slope term different from zero at 2 $\sigma$ level and a
$ \lambda_0= (17.11\pm 2.31)\times10^{-3}$ \cite{istraslopes}.
Fig.~\ref{fig:anton1}  shows the comparison of the KLOE, KTeV, NA48,
and ISTRA+ results. 
The values of the pole masses from the
KLOE, KTeV, and NA48 experiments are in agreement, and their
average value is $M_V = 875.3 \pm 5.4 ~~~~(\chi^2=1.8)$
from which
%From this average pole mass 
we derive the slopes:
$\lambda_+^{\prime} = (25.42\pm 0.31)\times10^{-3} $ and
$\lambda_+^{\prime\prime} = (1.29\pm 0.03)\times10^{-3} $.
%that we will use for the $V_{us}$ evaluation.

\begin{figure}
  \includegraphics[height=.25\textheight]{lamda.eps}

  \caption{Slopes comparison.}
\label{fig:anton1}
\end{figure} 

\section{V$_{us}$ extraction}

As discussed in section 1, we can extract V$_{us}$ using the master formula
(1),  where branching ratios, lifetimes and slopes are the experimental
input. V$_{us}$ can be extracted using
both charged and neutral modes, allowing for a consistency check between experiment 
and theory: see Fig. 3.
The value used for $\tau({\rmk K_L})$ is the
average between KLOE and PDG values. 
The slopes $\lambda_+^{\prime}$ and $\lambda_+^{\prime\prime}$
are those obtained by averaging
the pole masses from KTeV, NA48, and KLOE, while the slope $\lambda_o$
is the average from KTeV and ISTRA+. 
Leutwyler and Roos gave in 1984 \cite{LetRos} the
estimate $f_+^{{\rmk K^o} \pi^-}(0) = 0.961 \pm 0.008$.
The yellow band in Fig. 3 is the average value for
~$\Vf$~ = 0.2164(4), from which  ~\Vus = 0.2252(18) and it confirms
unitari\-ty within 1$\sigma$. The yellow band is obtained
imposing the unitarity using ~\Vud~=~0.97377(27)\cite{MarS}. The
uncertainty on $f_+^{{\rmk K^o} \pi^-}(0)$ is reflected in the
width of the ``uni\-ta\-rity'' band.

\begin{figure}
  \includegraphics[height=.26\textheight]{vus_all.eps}
  \caption{$\Vf$ ~comparison between all measured semileptonic K decays. The black
           squares are the PDG 2004 values not included in the average.}
\end{figure}
\section{Measurement of the BR(\Kmunup)} 
Combining \cite{kmu2_theo} the experimental value for the ratio of $K_{\mu 2}$
and $\pi_{\mu 2}$ BR's with the ratio $f_K/f_{\pi}$ known at the
1.3 \% level by the theory \cite{kmu2_theo}, we can extract the ratio
$V_{us}/V_{ud}$ at the 1\% level.
KLOE has measured  BR(K$_{\mu 2}$) using 175 $pb^{-1}$ collected in 2002.
\begin{figure}
  \includegraphics[height=.25\textheight]{vusvud.epsi}
  \caption{Comparison between $V_{us}/V_{ud}$ measurement from \Kmunup and
    \Vus~ from $K_{e3}$}
\label{fig:vusvud}
\end{figure}
The number of  decays ~\Kmunup~ is obtained counting
the events in the signal region of the distribution of the charged decay
particle momentum computed in the kaon rest frame assuming the $\pi$ mass
($p^{\ast}$). The background is given by events with a  $\pi^0$ in the
final state and its contribution to the  $p^{\ast}$ distribution is
obtained directly from data. 
The selection efficiency has been determined directly on data 
using a control sample of ~\Kmunup~ events selected exploiting their
signature in the EMC.
%From a sample of \ab\pt 5.2,8, $\phi$-meson decays, 
We find: $BR(\KmunupE) = 0.6366 \pm 0.0009_{\rmk stat} \pm 0.0015_{\rmk
 syst}$ \cite{kmu2}.
From this measurement and using $f_K/f_{\pi}$ from MILC \cite{kmu2_theo}  collaboration
 we derive  $V_{us}/V_{ud} = 0.2294 \pm 0.0026$.
In fig.\ref{fig:vusvud} this result is compared with the one obtained from
 $K_{e3}$ decay and with the unitarity relation. From the fit, assuming unitarity, we obtain:
~\Vus = 0.2264(9).

\section{Conclusions} 
In the last few years we had a lot new results on kaon semileptonic decays
from different experiments. Using this new results the CKM matrix appears to be unitary within
$\simeq 1\sigma$, however ~\Vus~ is still only known to~$\simeq$~1\%.
NA48 collaboration will have soon final results on charged kaon
semileptonic decays braching ratios and slopes. The KLOE collaboration, with the whole data sample of~ 2.5 fb$^{-1}$,
foresees to complete and to improve the measurements
of the form factor slopes, to improve the kaon
lifetime measurements, and to bring the fractional accuracy
to less than 1\% on BR(K$^{\pm}_{l3}$) and BR(K$_{Se3})$.
A similar improvement needs to come from the theoretical estimate of 
$f_+^{{\rmk K^o}\pi^-}(0)$.
\section{ Acknowledgments }
I would like to tanks NA48, KTeV and KLOE collaborations for providing 
material for this presentation.
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