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\title{Highlights on Rare Charged Kaon Decays}
\author{V.A. Duk \address[INR]{Institute for Nuclear Research of RAS\\
117312 Moscow 60-th Anniversary pr. 7a}%
\thanks{Viacheslav.Duk@cern.ch},
}
\runtitle{Highlights on Rare Charged Kaon Decays}
\runauthor{V.A. Duk}
\begin{document}
\begin{abstract}
We review recent experimental results on radiative rare charged
kaon decays. The results from ISTRA+ and KEK E-460 experiments
are considered. The obtained branching fractions are compared
with theoretical predictions. For K$l3\gamma$ decays the estimations of T-odd
asymmetry are given.
\vspace{1pc}
\end{abstract}
\maketitle
\section{Introduction}
Radiative kaon decays are dominated by long distance (low energy) physics. For low energy
processes we don't have predictions from SM and use effective theories such
as Chiral pertubation theory (ChPT). ChPT gives decay rates for most decay
modes. That's why radiative kaon decays provide a testing ground for ChPT.
Moreover these decays are sensitive to New Physics, e.g. one can study T-odd
asymmetries in radiative K$l3$ decays.
\section{ISTRA+ recent results}
\subsection{Experimental setup}
The experiment has been performed at the IHEP 70 GeV proton synchrotron U-70.
The experimental setup "ISTRA+" (Fig.~\ref{fistra})has been described in some details
elsewhere\cite{ISTRA}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{figure}[h]
\includegraphics[scale=.25 , angle=90]{duk-fig1.eps}
\caption{\em Elevation view of the "ISTRA+" detector}\label{fistra}
\end{figure}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{ K$^-\to\mu^-\nu_{\mu} \gamma$ decay}
The decay K$^-\to\mu^-\nu_{\mu} \gamma$ is sensitive to hadronic weak
currents in low-energy region.
The decay amplitude includes two terms - internal bremsstrahlung
(IB) and structure dependent term (SD). IB contains radiative corrections from
K$^-\to\mu^-\nu_{\mu}$. SD allows to probe electroweak
structure of kaon.
The differential decay rate is calculated within ChPT and can be written
in terms of standard kinematical variables x=2$E^\star_\gamma/M_k$
and $y=2E^\star_\mu /M_k$ (see \cite{mng1},\cite{mng2} for details).
The event selection criteria are: one charged track, ${\mu}$ flag in HCAL;
one shower in ECAL not associated with a charged track; z-coordinate
of the decay vertex within interval 300 $< z_{vertex} < $1650 cm.
Additional cuts are applied to suppress backgrounds:
- missing energy $>$ 1GeV;
- no photons in SP2 calorimeter;
- missing momentum points to ECAL aperture.
Main background comes from 2 decay modes - K$^-\to\mu^-\nu\pi^0$
and K$^-\to\pi^-\pi^0$ with one gamma lost from $\pi^0\to\gamma\gamma$
and $\pi$ misidentified as $\mu$. Distribution over M($\mu\nu\gamma)$ is
used for signal observation.
M$^2(\mu\nu\gamma)=(P_\mu+P_\nu+P_\gamma)^2$ where $P_\mu, P_\nu, P_\gamma$ are 4-momenta
of corresponding particles; missing mass is supposed to be equal to 0 so that
$\overrightarrow p_\nu=\overrightarrow p_K-\overrightarrow p_\mu-\overrightarrow p_\gamma;
E_\nu=|\overrightarrow p_\nu|$. M($\mu\nu\gamma)$ peaks at K$^-$
mass for signal.
To extract signal, the following procedure is applied:
- all kinematical (x,y) region is divided into little bins;
- we look at M($\mu\nu\gamma)$ in each bin;
- bins with signal peak are selected(see fig.~\ref{mng}).The selected kinematical region is
30 $< E^\star_\gamma <120 MeV; 150 < E^\star_\mu < 230 MeV$(fig.3, red);
- Fitting M($\mu\nu\gamma)$ gives the number of K$^-\to\mu^-\nu\gamma$ events
(the shape of background distribution is taken from MC).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h]
\begin{minipage}[t]{0.15\textwidth}
\centering
\includegraphics[scale=.15 , angle=0]{duk-fig2.eps}
\caption{\em M($\mu\nu\gamma)$ for (x,y) bin, real data}\label{mng}
\end{minipage}
\hspace{1cm}
\begin{minipage}[t]{0.15\textwidth}
\centering
\includegraphics[scale=.15 , angle=0]{duk-fig3.eps}
\caption{\em x=2$E^\star_\gamma/M_k$, $y=2E^\star_\mu /M_k$
ISTRA+(red); BNL E787(green);KEK-104(blue)}\label{mng2}
\end{minipage}
\begin{picture}(1,1)
\put(-46,24){\tiny ISTRA+}
\put(-55,46){\tiny KEK-104}
\put(-3,15){\tiny KEK-104}
\put(-3,46){\tiny BNL}
\put(-3,41){\tiny E787}
\put(-72,75){\tiny X}
\put(4,1){\tiny Y}
\put(-140,1){\tiny }
\end{picture}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Total number of K$^-\to\mu^-\nu\gamma$ events is 22472$\pm$465. To measure
BR(K$^-\to\mu^-\nu\gamma$), we normalize on BR( K$^-\to\mu^-\nu\pi^0)$.
Supposing PDG04 value for BR($K\mu$3) we obtain
BR(K$^-\to\mu^-\nu\gamma)=[1.25\pm 0.04(stat)\pm 0.02(norm)]\times10^{-3}$
which is in good agreement with theory: BR$_{th} \sim 1.28* 10^{-3}$. Our kinematical
region is complementary to that of previous experiments\cite{mng1},\cite{mng2} (see fig.~\ref{mng2}).
\subsection{ Radiative Kl3 decays}
Radiative Kl3 decays (K$\mu3\gamma,Ke3\gamma)$ are interesing to test ChPT
and search for New Physics using T-odd kinematical variable
$\xi = \frac{1} {M^{3}_{K}}
\overrightarrow p_{\gamma}\cdot[\overrightarrow p_{\pi}\times
\overrightarrow p_{l}]$.
In SM the expected value for asymmetry $A_\xi= \frac{N(\xi>0)-N(\xi<0)}
{N(\xi>0)+N(\xi<0)}$ is less than that in SM extensions
(K$\mu3\gamma: A_\xi \sim
1.14\times10^{-4}$ for SM, $A_\xi \sim 2.6\times 10^{-4}$ for SM extensions\cite{A_ksi_mu};
$Ke3\gamma: A_\xi \sim
0.6\times10^{-4}$ for SM, $A_\xi \sim 0.8\times 10^{-4}$ for SM extensions\cite{A_ksi_e}).
\paragraph{K$^-\to\mu^-\nu\pi^0\gamma$}
Radiative K$\mu3$ decay was observed in $K_L$-decays. Here we present first
observation of $K^-_{\mu3\gamma}$ mode\cite{chik}.
Standard selection criteria are used:
- 1 charged track;
- 3 showers in ECAL;
- effective mass m$(\gamma\gamma)$ within $\pm 20MeV/c^2$ from $\pi^0$ mass.
Some additional cuts are applied to suppress backgrounds:
- 400 $< z_{vertex} < $1650 cm;
- missing energy $>$ 1GeV;
- no photons in veto system.
Main background comes from $K\mu3, K\pi2, K\pi3$ decays with 1$\gamma$ lost
or accidental $\gamma$. Invariant mass M($\mu\nu\pi^0)$ is used for signal observation
(it peaks at K$^-$ mass for signal). We separated our signal region into 2
parts: $510MeV)}{BR(Ke3)}$ is measured. For
comparison with other experiments additional cut is applied:
0.6$30MeV, \theta_{e\gamma}^\star>20^\circ$. Supposing PDG04
value for BR(Ke3) BR(Ke3$\gamma$,theor.cuts)=$(3.05\pm0.09)\times10^{-4}$.
Theory gives 2.8$\times10^{-4}$ (tree level) and 3.0$\times10^{-4}$
(O$(p^4)$ level).
For T-odd asymmetry, we get $A_\xi=-0.015\pm0.021$. This estimation is
better than that of K$\mu 3\gamma$ but still far from theoretical predicitons.
\section{Recent result from KEK E470 on K$^+\to\pi^+\pi^0\gamma$}
Two terms give contribution to the decay amplitude: IB (inner bremsstrahlung)
and DE (direct emission). For DE component, ChPT gives
BR(DE)=3.5$\times10^{-6}$ while 1/N$_c$ approach gives
BR(DE)=19.4$\times10^{-6}$. Ambiguous situation exists both in theory and
experiment(see \cite{malik} for details).
Average BRs differ: BR($old$ $exp.$)=$(1.8\pm0.4)\times10^{-5};$
BR($new$ $exp.$)=$(0.44\pm0.07)\times10^{-5}$.
Recently an improved KEK E470 result on DE measurement has
appeared\cite{malik}. E470 experimental setup is shown in fig.~\ref{kek}. Signal extraction
procedure includes kaon identification, charged particle separation by TOF
method, analysis of 3 photon events in CsI(Tl) calorimeter and background
suppression. Total number of K$^+\to\pi^+\pi^0\gamma$ events extracted for
115$