\documentclass[fleqn,twoside]{article}
\usepackage[headings]{espcrc2}
\usepackage{graphicx}
\usepackage[figuresright]{rotating}
\usepackage{amsmath}

% put your own definitions here:

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

% Some useful journal names
\def\NCA{\rm Nuovo Cimento}
\def\NIM{\rm Nucl. Instrum. Methods}
\def\NIMA{{\rm Nucl. Instrum. Methods} A}
\def\NPB{{\rm Nucl. Phys.} B}
\def\PLB{{\rm Phys. Lett.}  B}
\def\PRL{\rm Phys. Rev. Lett.}
\def\PRD{{\rm Phys. Rev.} D}
\def\ZPC{{\rm Z. Phys.} C}
\def\EPJ{{\rm Eur. Phys. J.} C}
\def\IJMP{{\rm Int. Journ. of Mod. Phys.} A} 

% 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\vp{{\bf p}}
\def\al{\alpha}
\def\ab{\bar{\alpha}}
\def\be{\begin{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\CPbar{\hbox{{\rm CP}\hskip-1.80em{/}}}

\def\ko{K^0}
\def\kb{\bar{K^0}}
\def\K0{\mbox{$\ko$~}}
\def\KB{\mbox{$\kb$~}}

\def\pipi{${\pi\pi}$}
\def\mpipi{{\pi\pi}}
\def\Cpipi{${\pi^+\pi^-}$}
\def\Npipi{${\pi^0\pi^0}$}

\def\real{${Re}$}
\def\mdecNN{ N^{\pi^0\pi^0}}
\def\mdecNC{ N^{\pi^+\pi^-}}
\def\mdecNNS{ N^{\pi^0\pi^0}_S}
\def\mdecNCS{ N^{\pi^+\pi^-}_S}
\def\mdecNNL{ N^{\pi^0\pi^0}_L}
\def\mdecNCL{ N^{\pi^+\pi^-}_L}
\def\lifetime{lifetime}
\def\lifetimes{lifetimes}
\def\propertime{proper time}
\def\propertimes{proper times}
\def\beamline{beamline}
\def\beamlines{beamlines}
\def\beampipe{beampipe}
\def\readout{read-out}
\def\deadtime{deadtime}
\def\spacepoint{space-point}
\def\spacepoints{space-points}
\def\afterpulse{after-pulse}
\def\afterpulses{after-pulses}
\def\downscaling{down-scaling}
\def\downscalings{down-scalings}
\def\prescaling{pre-scaling}
\def\prescalings{pre-scalings}
\def\datataking{data-taking}
\def\crosscheck{cross-check}

\def\ev{\,\mathrm{eV}}
\def\Kev{\,\mathrm{keV}}
\def\Mev{\,\mathrm{MeV}}
\def\Gev{\,\mathrm{GeV}}
\def\Gevc{\,\mathrm{GeV/}{c}}
\def\Mevc{\,\mathrm{MeV/}{c}}
\def\Kevc{\,\mathrm{keV/}{c}}
\def\ucm{\,\mathrm{cm}}
\def\um{\,\mathrm{m}}
\def\umm{\,\mathrm{mm}}
\def\unm{\,\mathrm{nm}}
\def\ukm{\,\mathrm{km}}
\def\uton{\,\mathrm{ton}}
\def\umicron{\,\mathrm{\mu m}}
\def\uT{\,\mathrm{T}}
\def\uK{\,\mathrm{K}}
\def\uns{\,\mathrm{ns}}
\def\ums{\,\mathrm{ms}}
\def\ups{\,\mathrm{ps}}
\def\umicros{\,\mathrm{\mu s}}
\def\us{\,\mathrm{s}}
\def\uKamp{\,\mathrm{KA}}
\def\umamp{\,\mathrm{mA}}
\def\ugradiC{^{\circ}\mathrm{C}}
\def\umrad{\,\mathrm{mrad}}
\def\umicrosr{\,\mu \mathrm{sterad}}
\def\umsr{\,\mathrm{msterad}}
\def\uTorr{\,\mathrm{Torr}}
\def\umbar{\,\mathrm{mbar}}
\def\uHz{\,\mathrm{Hz}}
\def\uKHz{\,\mathrm{kHz}}
\def\ukHz{\,\mathrm{kHz}}
\def\uMHz{\,\mathrm{MHz}}
\def\uGHz{\,\mathrm{GHz}}

\def\CHISQ{$\chi^2$}
\def\mCHISQ{$\chi^2$}
\def\CHISQR{$\chi^2_{\mathrm{relli}}$}

\def\mCHISQR{\chi^2_{\mathrm{relli}}}
\def\Kmu{${K_{\mu 3}}$} 
\def\Kel{${K_{e 3}}$} 

\newcommand{\DEF}[1]{{#1}\index{#1}}
\newcommand{\D}[1]{\mbox{$ \Delta\! {\rm #1}$~}}
\newcommand{\KL}{\mbox{$\kl$~}}
\newcommand{\KS}{\mbox{$\ks$~}}
\newcommand{\bKS}{$\mathrm \mathbf K_{\mathrm \mathbf S}$~}
\newcommand{\N}[1]{\mbox{${\cal N}_{#1}$}}
\newcommand{\R}{\mbox{$\cal R$~}}
\newcommand{\TAMcons}[3]{{#1}({\rm TAM}_{\rm n}#2\; \& \;{\rm TAM}_{\rm n+1}#3)} 
\newcommand{\aGT}{\gtrsim}
\newcommand{\aLT}{\lesssim}
\newcommand{\alias}[1]{~\mbox{({\em #1})}\index{#1}~}
\newcommand{\bbb}{\mbox{$\rm \bz\bzb$~}}
\newcommand{\boh}{}
\newcommand{\bzb}{\mbox{$\rm \bar{B}^{0}$}~}
\newcommand{\bz}{\mbox{$\rm B^{0}$}~}
\newcommand{\cfr}[1]{~(\S~\ref{sec:#1})}
\newcommand{\chiq}{\chi^{2}}
\newcommand{\comm}[1]{}
\newcommand{\colla}{\vspace*{10cm}}
\newcommand{\ddb}{\mbox{$\rm \dz\dzb$~}}
\newcommand{\dr}[1]{\mbox{${\cal R}_{#1}$}}
\newcommand{\dtarg}{\mbox{$d_{\rm targ}$}~}
\newcommand{\dzb}{\mbox{$\rm \bar{D}^{0}$}~}
\newcommand{\dz}{\mbox{$\rm D^{0}$}~}
\newcommand{\ek}{\mbox{$E_{\rm K}$}~}
\newcommand{\eoe}{\mbox{${\rm Re}(\epsi'/\epsi)$}~}
\newcommand{\epsi}{\varepsilon}
\newcommand{\eqz}[1]{~(Eq.~\ref{eq:#1})}
\newcommand{\fez}{f_{\rm TAM=0}}
\newcommand{\fig}[1]{~(Fig.~\ref{fig:#1})}
\newcommand{\ket}{\mbox{$\mathrm K_{e3}$}~}
\newcommand{\kkb}{\mbox{$\rm \kz\kzb$~}}
\newcommand{\kl}{{\rm K_{L}}}
\newcommand{\kmut}{\mbox{$\mathrm K_{\mu3}$}~}
\newcommand{\kpit}{\mbox{$\mathrm K_{\pi3}$}~}
\newcommand{\ks}{{\rm K_{S}}}
\newcommand{\kto}[1]{\mbox{$\rm \kz\rightarrow{#1}$~}}
%\newcommand{\kzb}{\mbox{$\rm \bar{K}^{0}$}~}
\newcommand{\kz}{\mbox{$\rm K^{0}$}~}
\newcommand{\mini}{\mbox{\rm MINI-DST}~}
\newcommand{\pauli}[1]{\mbox{\large \boldmath $\sigma_{#1}$}}
\newcommand{\pmi}{{\rm\pi^{-}}}
\newcommand{\ppl}{{\rm\pi^{+}}}
\newcommand{\pz}{{\rm\pi^{o}}}
\newcommand{\rell}{\mbox{$\mathrm R_{\mathrm ell}$}~}
\newcommand{\res}[1]{~(\ref{res:#1})}
\newcommand{\state}[1]{\left|{#1}\right>}
\newcommand{\tab}[1]{~(Tab.~\ref{tab:#1})}
\newcommand{\teq}[1]{{\rm TAM\!\!=\!\!#1}}
\newcommand{\tez}{$\teq{0}$~}
\newcommand{\tgt}[1]{{\rm TAM\!\!>\!\!#1}}
\newcommand{\tgz}{$\tgt{0}$~}
\newcommand{\tz}{\mbox{$t_0$}~}
\newcommand{\zv}{\mbox{$z_v$}~}
\newcommand{\piee} {\mathrm{\pi ^0 e^+ e^-}}
\newcommand{\ppee} {\mathrm{\pi^+ \pi^- e^+ e^-}}
\newcommand{\pimumu} {\mathrm{\pi ^0 \mu ^+ \mu ^-}}
\newcommand{\gee} {\mathrm{\gamma e^+ e^-}}
\newcommand{\gmumu} {\mathrm{\gamma \mu ^+ \mu ^-}}
\newcommand{\gaga} {\mathrm{\gamma \gamma}}
\newcommand{\pigg} {\mathrm{\pi ^0 \gamma \gamma}}
\newcommand{\threepio} {\mathrm{\pi ^0 \pi ^0 \pi ^0}}
\newcommand{\pipigg} {\mathrm{\pi ^0 \pi ^0 \gamma \gamma}}
\newcommand{\pipig} {\mathrm{\pi ^0 \pi ^0 \gamma}}
\newcommand{\ppg} {\mathrm{\pi ^+ \pi ^- \gamma}}
\newcommand{\threepi} {\mathrm{\pi ^+ \pi ^- \pi ^0}}
\newcommand{\mumu} {\mathrm{\mu ^+ \mu ^-}}
\newcommand{\ee} {\mathrm{e^+ e^-}}
%
\newcommand{\KLGG} {\kl \rightarrow \gaga}
\newcommand{\KSLGG} {K_{S,L} \rightarrow \gaga}
\newcommand{\KLPGG} {\kl \rightarrow \pigg}
\newcommand{\KLPPG} {\kl \rightarrow \pipig}
\newcommand{\KLPPGG} {\kl \rightarrow \pipigg}
\newcommand{\KSLPGG} {K_{S,L} \rightarrow \pigg}
\newcommand{\KSLPPGG} {K_{S,L} \rightarrow \pipigg}
\newcommand{\KSEEGG} {\ks \rightarrow \ee \gaga}
\newcommand{\KSEEMM} {\ks \rightarrow \ee \mumu}
\newcommand{\KLPEE} {\kl \rightarrow \piee}
\newcommand{\KLPPEE} {\kl \rightarrow \ppee}
\newcommand{\KLEEGG} {\kl \rightarrow \ee \gaga}
\newcommand{\KLMMGG} {\kl \rightarrow \mumu \gaga}
\newcommand{\KLPMM} {\kl \rightarrow \pimumu}
\newcommand{\KLPP} {\kl \rightarrow \pi^0 \pi^0}
\newcommand{\KLPPP} {\kl \rightarrow \threepio}
\newcommand{\KLPPPC} {\kl \rightarrow \threepi}
%
\newcommand{\KSGG} {\ks \rightarrow \gaga}
\newcommand{\KSPPGG} {\ks \rightarrow \pipigg}
\newcommand{\KSPGG} {\ks \rightarrow \pigg}
\newcommand{\KSPPG} {\ks \rightarrow \pipig}
\newcommand{\KSPEE} {\ks \rightarrow \piee}
\newcommand{\KSPPEE} {\ks \rightarrow \ppee}
\newcommand{\KSPMM} {\ks \rightarrow \pimumu}
\newcommand{\KSPP} {\ks \rightarrow \pi \pi}
\newcommand{\KSPZPZ} {\ks \rightarrow \pi^0 \pi^0}
\newcommand{\KSPPP} {\ks \rightarrow \threepio}
%
\newcommand{\kzz} {\mathrm{K^{o}}}
\newcommand{\kzb} {\mathrm{\overline{K^{o}}}}
\newcommand{\kp} {\mathrm{K^{+}}}
\newcommand{\km} {\mathrm{K^{-}}}
\newcommand{\kpm} {\mathrm{K^{\pm}}}
\newcommand{\tpipmp} {\mathrm{\pi ^+ \pi ^- \pi ^+}}
\newcommand{\tpipmm} {\mathrm{\pi ^+ \pi ^- \pi ^-}}
\newcommand{\tpipm} {\mathrm{\pi ^+ \pi ^- \pi ^{\pm}}}
\newcommand{\tpizzp} {\mathrm{\pi ^o \pi ^o \pi ^+}}
\newcommand{\tpizzm} {\mathrm{\pi ^o \pi ^o \pi ^-}}
\newcommand{\tpizz} {\mathrm{\pi ^o \pi ^o \pi ^{\pm}}}
\newcommand{\pppzg} {\mathrm{\pi^+ \pi^o \gamma}}
\newcommand{\pmpzg} {\mathrm{\pi^m \pi^o \gamma}}
\newcommand{\ppmpzg} {\mathrm{\pi^\pm \pi^o \gamma}}
\newcommand{\tpip} {\mathrm{(3\pi) ^+ }}
\newcommand{\tpim} {\mathrm{(3\pi) ^- }}
\newcommand{\ktpppzg} {\kp \rightarrow \pppzg}
\newcommand{\ktpmpzg} {\km \rightarrow \pmpzg}
\newcommand{\ktppmpzg} {\kpm \rightarrow \ppmpzg}
\newcommand{\ktpipmp} {\kp \rightarrow \tpipmp}
\newcommand{\ktpipmm} {\km \rightarrow \tpipmm}
\newcommand{\ktpipm} {\kpm \rightarrow \tpipm}
\newcommand{\ktpizzp} {\kp \rightarrow \tpizzp}
\newcommand{\ktpizzm} {\km \rightarrow \tpizzm}
\newcommand{\ktpizz} {\kpm \rightarrow \tpizz}
\newcommand{\ktpip} {\kp \rightarrow \tpip}
\newcommand{\ktpim} {\km \rightarrow \tpim}
\newcommand{\KZZ}{\mbox{$\kzz$~}}
\newcommand{\KZB}{\mbox{$\kzb$~}}
\newcommand{\KP}{\mbox{$\kp$~}}
\newcommand{\KM}{\mbox{$\km$~}}
\newcommand{\KPM}{\mbox{$\kpm$~}}
\newcommand{\TPIPMP} {\mbox{$\tpipmp$~}}
\newcommand{\TPIPMM} {\mbox{$\tpipmm$~}}
\newcommand{\TPIZZP} {\mbox{$\tpizzp$~}}
\newcommand{\TPIZZM} {\mbox{$\tpizzm$~}}
\newcommand{\TPIP} {\mbox{$\tpip$~}}
\newcommand{\TPIM} {\mbox{$\tpim$~}}
\newcommand{\KTPIPMP} {\mbox{$\ktpipmp$~}}
\newcommand{\KTPIPMM} {\mbox{$\ktpipmm$~}}
\newcommand{\KTPIZZP} {\mbox{$\ktpizzp$~}}
\newcommand{\KTPIZZM} {\mbox{$\ktpizzm$~}}
\newcommand{\KTPIP} {\mbox{$\ktpip$~}}
\newcommand{\KTPIM} {\mbox{$\ktpim$~}}
\newcommand{\KTPIPM} {\mbox{$\ktpipm$~}}
\newcommand{\KTPIZZ} {\mbox{$\ktpizz$~}}
%
\newcommand{\aj} {A_{R}}
\newcommand{\as} {A_{L}}
\newcommand{\ap} {A_{+}}
\newcommand{\am} {A_{-}}
\newcommand{\AJ} {\mbox{$\aj$~}}
\newcommand{\AS} {\mbox{$\as$~}}
\newcommand{\AP} {\mbox{$\ap$~}}
\newcommand{\AM} {\mbox{$\am$~}}
\newcommand{\ahp} {A^{\uparrow}}
\newcommand{\ahm} {A^{\downarrow}}
\newcommand{\bp} {B^{\uparrow}}
\newcommand{\bm} {B^{\downarrow}}
\newcommand{\BP} {\mbox{$\bp$~}}
\newcommand{\BM} {\mbox{$\bm$~}}
\newcommand{\AHP} {\mbox{$\ahp$~}}
\newcommand{\AHM} {\mbox{$\ahm$~}}
\newcommand{\rj} {R_{R}}
\newcommand{\rs} {R_{L}}
\newcommand{\RJ} {\mbox{$\rj$~}}
\newcommand{\RS} {\mbox{$\rs$~}}
%
\newcommand{\CP} {\mathrm{\hspace{-1.5mm} \diagup \hspace{-4.5mm} C\!P}}
\newcommand{\BR} {\mathrm{BR}}
\newcommand{\Imm} {\frak{Im}}
\newcommand{\Ree} {\frak{Re}}
\newcommand{\kbar} {\mathrm{\overline{K}^{_{\scriptstyle 0}}}}
%
\newcommand{\pim}{{\rm\pi^{-}}}
\newcommand{\pip}{{\rm\pi^{+}}}
\newcommand{\piz}{{\rm\pi^{o}}}
%
\newcommand{\E}[1] {\mathrm{\times 10^{#1}}}
\newcommand{\definmath}[2] {\def#1{\ifmmode#2\else\ensuremath{\mathrm{#2}} \fi}}
\newcommand{\epe} {\mathrm{\epsilon'/\epsilon}}
\newcommand{\delp} {\mathrm{\Delta p}}
\newcommand{\ddpk} {\mathrm{\Delta p_K}}
\newcommand{\mrm}{\mathrm}

\newcommand{\hugepage}{\enlargethispage{9.0\baselineskip}}
\newcommand{\verylongpage}{\enlargethispage{2.0\baselineskip}}
\newcommand{\longpage}{\enlargethispage{\baselineskip}}
\newcommand{\shortpage}{\enlargethispage{-\baselineskip}}
\newcommand{\shorterpage}{\enlargethispage{-2\baselineskip}}
\newcommand{\veryshortpage}{\enlargethispage{-5.0\baselineskip}}
\newcommand{\tinypage}{\enlargethispage{-9.0\baselineskip}}

% add words to TeX's hyphenation exception list
\hyphenation{author another Post-Script stu-dies co-axial}

% set the starting page if not 1
% \setcounter{page}{17}

% declarations for front matter
\title{Status report on CP violation with charge kaons}       

\author{G. Collazuol, on behalf of the NA48/2 Collaboration
\\Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa Italy \\ E-mail: gianmaria.collazuol@pi.infn.it}
      
% If you use the option headings,
% the title is also used as the running title,
% and the authors are also used as the running authors.
% You can change that by using \runtitle and \runauthor.

\runtitle{Status report on CP violation with charge kaons}
\runauthor{G. Collazuol}

\begin{document}

\begin{abstract}
The NA48/2 experiment at CERN performed a high precision study of
direct CP-violation in charged kaon decays into three pions, 
using an upgraded NA48 setup and a novel design for simultaneous 
unseparated \KPM beams. The asymmetry in the Dalitz plot linear 
slopes $A_g=(g_+ - g_-)/(g_+ + g_-)$ is measured to be
$A^c_g=(-1.3\pm2.3)\cdot10^{-4}$ by studying $3.1\cdot10^{9}$ \KTPIPM
decays and $A^n_g=(2.1\pm1.9)\cdot10^{-4}$ by studying $91\cdot10^{6}$ 
\KTPIZZ decays. The unique \KPM simultaneuos beam system, the design of the detectors 
and the method of analysis provide good control of the instrumental charge
asymmetries and allow to keep the precision of the result limited by statistics, 
reaching accuracy one order of magnitude better than in previous experiments.
The large amount of charged kaon decays collected 
allow also precision measurements of several rare decay processes.
\end{abstract}

% typeset front matter (including abstract)
\maketitle

\section{Introduction}
More than 40 years after its discovery in
the mixing of neutral kaons, the full under-standing of CP violation is far from being
reached. Two recent breakthroughs spread light over this puzzling phenomenon: in the
late 90s the experiments NA48 and KTeV confirmed the earlier indication from NA31
experiment for direct CP-violation in the neutral kaon system. Secondly 
the CP-violating processes were recently found in B mesons by the experiments 
Belle and Babar.

In order to explore possible non-Standard Model (SM) enhancements to 
heavy-quark loops which are at the core of direct CP-violating processes various systems
must be studied. In kaons, besides the $\epsilon'/\epsilon$ parameter in \KZZ decays, 
promising complementary observables are the rates of GIM-suppressed rare kaon decays 
proceeding through neutral currents, and an asymmetry between K + and K decays 
to three pions.

Direct CP violation in $\KPM$ is expected to induce different decay amplitudes: \\
$|A(\kp \rightarrow (3\pi)^+)| \neq |A(\km \rightarrow (3\pi)^-)|$.
The three-body decay has a low Q value, which allows for the following 
parametrization in terms of the two Dalitz variables $u=(s_3-s_0)/m_{\pi}^2$
(odd pion coordinate) and $v=(s_1-s_2)/m_{\pi}^2$ (even pion coordinate): 
$|A(\mathrm{K} \rightarrow (3\pi))| = a + b\times u + \mathcal{O}(u^2,v^2)$, 
where $a$ and $b$ are two $\Delta I=1/2$ interfering amplitudes.
If $a$ and $b$ have different weak and strong phases, the transitions to
the two charge conjugate states $(3\pi)^\pm$ are not equally affected 
by the interference, resulting in different distributions of final 
state momentum for \KP and \KM decays.
If the matrix element
is parametrized as $|M(u,v)|^2  \propto 1 + g \times u + \mathcal{O}(u^2,v^2) $, 
the asymmetry $$A_{g} = \frac{g^+ - g^-}{g^+ + g^-} \neq 0$$
of the slope parameter $g$ would be a signal of direct CP violation.

Theoretical predictions based on the Standard Model
cover the range $\sim 10^{-6}-10^{-3}$ for $A^c_{g}$~\cite{theory_1,theory_2}, 
relative to the ``charged $3\pi$ channel'' \KTPIPM. 
The asymmetry $A^n_{g}$ for the ``neutral $3\pi$ channel'' 
\KTPIZZ, which is dominated by NLO counterterms in the chiral 
perturbation theory ($\chi PT$), is expected to be of the same order of 
magnitude of $A_{g}$, due to the suppression of the $\Delta I=3/2$ 
transition observed in $\epp/\epsilon$.
Values of $A_{g}$ above the level of $5 \times 10^{-5}$ would 
imply physics beyond the 
standard model~\cite{weinberg} and would strengthen the still open question 
about non-standard contributions to $\epp/\epsilon$. 
%The value of $2\times 10^{-4}$ is, for example, predicted by the 
%three Higgs doublet model of Weinberg~\cite{weinberg}.

In the past no slope asymmetries were found at a level of $10^{-3}$.
The BNL experiment~\cite{FORD} studied $A^c_{g}$
with a total of $3\times 10^{6}$ decays and 
measured a slope asymmetry $A^c_{g} = (-7\pm5) \times 10^{-3}$ and 
a total decay rate asymmetry $\Delta\Gamma/2\Gamma = (5\pm7)\times 10^{-4}$.
Recently HyperCP~\cite{HYPERCP} at FNAL measured \\ 
$A_{g} = (2.2\pm1.5\pm3.7) \times 10^{-3}$.

\begin{figure*}[tb]
\vspace{-3mm}
\begin{center}
{\resizebox*{0.82\textwidth}{!}{\includegraphics{na48_2_beam.eps}}}
\end{center}
\vspace{-11mm} \caption{A view of NA48/2 beam line (TAX17,18: motorized beam dump selecting
momentum of $K^+/K^-$ beams; DFDF: focusing quadrupoles, KABES1--3: beam spectrometer) and
detector (DCH1--4: drift chambers, Hodo: hodoscope, LKr: EM
calorimeter, HAC: hadron calorimeter, MUV: muon veto). Vertical
scale differs in two parts of the figure.}
\vspace{-5mm}
\label{fig:beams}
\end{figure*}

An experiment~\cite{SMITH} at the CERN-PS measured 
a slope asymmetry at a level of $A^n_{g} = (0.2\pm1.2) \times 10^{-2}$ and 
$\Delta\Gamma/2\Gamma = (4\pm3)\times 10^{-4}$ in the ``neutral channel''. 
Recently experiment ISTRA+~\cite{ISTRA} at TNF-IHEP found 
$A^b_{g} = (0.2\pm1.9) \times 10^{-3}$.

The aim of NA48/2 is to measure $A^c_{g}$ and $A^n_{g}$ 
with an accuracy of $10^{-4}$ (statistically dominated).

\section{Beams and detectors}
The novel design of the K12 beam line (Fig.~\ref{fig:beams})
allows the transport simultaneously of positive and negative particles.
A $400 \Gevc$ primary proton beam    
with an intensity of $7 \times 10^{11}$ protons per spill
impinge the Be target located 
$\sim 200\um$ upstream from the central detector. The particles of 
opposite charge produced at $0^{o}$ are split, selected in a 
narrow momentum band ($p_{\mathrm{K}} = 60 \pm 2.5 \Gevc$) 
and recombined by passing through an achromatic dipole magnet system. 
A quadruplet of quadrupoles focuses the beams so that they overlap
with an accuracy of better than $1 \umm$ at the beginning of
the central detector. 
A second ``achromat'' houses a collimator to absorb neutrons, 
and two stations of Micromegas type TPC detector (KAon-BEam-Spectrometer). 
In combination with a third chamber, located downstream, 
the KABES chambers provide tagging and momentum measurement 
of individual kaons. 
The particle rate at the KABES position is $\sim 40 \uMHz$. 
The final collimator, placed $\sim 100\um$ downstream of the target, 
is followed by a decay volume of $\sim 115\um$ length.

The NA48 central detector described elsewhere~\cite{epsi97} had 
a new drift chamber \readout\ capable of withstanding high rates without
introducing \deadtime. The spectrometer magnet
was operated to give a $p_T = 120 \Mevc$ kick,
and the resolution in momentum (GeV/c) was $ \sigma_p/p = 1.0\% + 0.044\% p$.
The Liquid Krypton calorimeter, which has been very stable across years of running,
provides an energy resolution of 
$\sigma_E/E = 3.2\%/\sqrt{E} + 9\%/E + 0.42\%$ where $E$ is in $\Gev$.

Kaon masses from three-pion decay are reconstructed with 
very good resolution ($1.7\Mev$ for \KTPIPM decays 
and $0.9\Mev$ for \KTPIZZ decays), allow 
for precise calibration and monitoring of the 
spectrometer performance.

The trigger is based on a low level (L1) fast pre-selection 
(hodoscope multiplicity and cluster number counting in the calorimeter)
and a high level (L2) selection (on-line processing of the information 
from calorimeter and drift chambers). 
From an input rate of $1\uMHz$, an output rate of $~10\ukHz$ triggers
the \readout\ with negligible dead time.

The full on-line kinematics reconstruction at L2 and the narrow range of 
beam momenta allow for triggering on both three-track events 
and (two or) one-track events (with some $\pi^{o}$ or photons
in the LKr calorimeter) with adequate missing mass in order 
to reject the main background from $\pi^{\pm}\pi^{o}$.

Data were taken in the years 2003 and 2004 for a total of more than 100 days 
of effective running, providing more than 4 billion \KTPIPM and 
more than 100 million \KTPIZZ. In total $18 \times 10^9$ triggers were collected.
In the following we report the preliminary analysis 2003 and 2004 data.

\section{Experimental method}

The asymmetry measurement method is based on comparing the reconstructed $u$
spectra of $K^+$ and $K^-$ decays $N^+(u)$ and $N^-(u)$. The possible
presence of a direct CP violating difference between the linear slopes
of $K^+$ and $K^-$, i.e. $\Delta g=g^{+}-g^{-}$, can be extracted from
a fit to the ratio:
\begin{equation}
R(u)=\frac{N^+(u)}{N^-(u)}\propto\frac{1+(g+\Delta g)u+hu^2}{1+gu+hu^2}
\label{ratio}
\end{equation}
where $g$ and $h$ are the actual of the Dalitz slope parameters.
The measured asymmetry is then given by $A_g=\Delta g/2g$.

Charge symmetrization of experimental conditions is to a large
extent achieved by using simultaneous collinear $K^+/K^-$
beams of similar momentum spectra. However, the presence of
magnetic fields in both the beam line (achromats,
quadrupoles) and the spectrometer, combined with some
asymmetries in detector performance, introduces residual charge
asymmetries. To equalize local effects on the
acceptance, polarities of all the magnets in the beam line were
reversed during the data taking on an approximately weekly basis
(corresponding to the periodicity of SPS technical stops), while the
polarity of the spectrometer magnet was alternated on a more
frequent basis.

Data collected over a period with all the four possible setup
configurations (i.e. combinations of beam line and spectrometer
magnet polarities) spanning about two weeks of data taking
represent a ``supersample'', which is treated as an independent
self-consistent set of data for asymmetry measurement. Nine
supersamples numbered 0 to 8 were collected in two years of running.

Each supersample contains eight distinct data samples
corresponding to various combinations of setup configurations
and kaon sign. In order to minimize the effects of beam and detector
asymmetries, the following
``quadruple ratio'' involving the eight $u$ spectra,
composed as a product of four $R(u)=N^+(u)/N^-(u)$ ratios with
opposite kaon sign, and deliberately chosen setup configurations in
numerator and denominator, is considered:
$$
R_4(u) = R_{US}(u)\cdot R_{UJ}(u)\cdot R_{DS}(u)\cdot R_{DJ}(u)
$$
Here the indices $U$ ($D$) denote
beam line polarities corresponding to $K^+$ passing along the
upper (lower) path in the achromats, and the indices
$S$ ($J$) represent spectrometer magnet polarities (opposite for
$K^+$ and $K^-$) corresponding to the ``even''
 pions deflection to negative (positive) $x$, i.e.
towards the Sal\`eve (Jura) mountains. Fitting
the ratio $R_4(u)$ with $f(u)=n\cdot(1+\Delta
g\cdot u)^4$ results in two parameters: the normalization $n$ and
the slope difference $\Delta g$.

The quadruple ratio technique completes the procedure of
polarity reversals, and allows a three-fold cancellation of
systematic biases: 1) beam line biases cancel between $K^+/K^-$ samples
with the beams following the same path; 2) local detector
biases cancel between $K^+/K^-$ samples with decay products
illuminating the same parts of the detector;
3) due to simultaneous $K^+/K^-$ beams,
global time-variable biases and rate dependent effects cancel
between $K^+/K^-$ samples.

The method is independent of the $K^+/K^-$ flux ratio and the
relative sizes of the samples collected with different setup
configurations. The result remains sensitive only
to time variations of asymmetries in the experimental conditions
with characteristic times smaller than corresponding field
alternation period, and in principle should be free of systematic
biases. In addition only charge-asymmetric effects dependent on
$u$ can bias the measurement.

With the above method, no Monte Carlo (MC) corrections
to the acceptance are required. Nevertheless, a detailed GEANT-based
MC simulation was developed as a tool for systematic studies,
including full geometry and material description,
simulation of time variations of local DCH inefficiencies,
beam geometry and DCH alignment. A large MC
production was made, providing a sample of a size comparable
to that of the data.

\section{Evaluation of the CPV asymmetry in the ``charge'' mode} 

The absence of background in the \KTPIPM channel allows very simple 
on-line and off-line selection.
Only information from the spectrometer and the hodoscope are used:
tracks and vertex topology are reconstructed using the measured
magnetic field map of the spectrometer analyzing magnet rescaled
according to the recorded current and taking into account the stray
magnetic fields in the decay volume. 

The most relevant systematic effects that need carefull
investigation are the following:\\
\\
(i) time variations of the detector response,
mainly due to
variations of the transverse alignment of the chambers, which are measured 
to drift by small but relevant amounts (below $70 \umicron$) and to trigger
inefficiencies.

The right-left accuracy of the relative transverse DCH alignment 
is obtained by by imposing that \KP and \KM three-pion decays have the same
reconstructed invariant mass averaged over periods of $\sim 1$ hour.
The sensitivity of $m_{\mathrm{K}}$  is  $\sim 150 \Kev/c^2$ for $100 \umm$  
displacement along the horizontal direction.
Also the absolute momentum scale is tuned so that 
the reconstructed invariant mass of \KTPIPM decays equals
the PDG value for the kaon mass.

Concerning inefficiencies of trigger components, they are measured 
as functions of $u$ using control data samples from low bias triggers 
collected along with the main triggers, which allows to account for 
their time variations, and propagate their statistical errors into 
the result. Among the different components only corrections for 
the L2 trigger were applied, as the others were stable in time and
independent of $u$.\\
\\
(ii) time variations of the \KP vs \KM beam geometries:  
the systematic biases related to beam movements in short
term (beam spill) and long term (hours) and to the imperfect
overlap and coaxiality of the two beams are minimized by applying
a the radial selection around the average measured beam position.
In additon, being this selection azimuthally symmetric it   
also reduces also possible systematic biases due to the presence
of stray permanent magnetic elds (Earth eld, vacuum tank magnetization).\\

In order to cross-check the effects from various systematics some
``fake asymmetries'' are studied, which should be zero 
from first principles, but can differ from zero due to detector/beam effects. 
For instance the slope asymmetries extracted 
from the ratios $R_J(u)/R_S(u)$
are good indicators of the degree of left-right symmetry
of the setup after the above-mentioned analysis procedure. 

With a total of $3.1 \times 10^9$ selected \KTPIPM events
(collected in 2003 and 2004 years) 
the difference in Dalitz plot slope parameter is found to be:
$$\Delta g^c = g^{c+}-g^{c-} =$$
$$=(0.6 \pm 0.7_{stat.} \pm 0.4_{trig.(stat.)} \pm 0.6_{syst.})\times 10^{-4}$$
leading to a CPV charge asymmetry of:
$$ A^c_g = (-1.3 \pm 1.5_{stat.} \pm 0.9_{trig.(stat.)} \pm 1.4_{syst.})\times 10^{-4}=$$ 
$$= (-1.3\pm2.3)\times 10^{-4}$$

\begin{figure*}[tb]
\vspace{-3mm}
\begin{center}
%{\resizebox*{0.82\textwidth}{!}{\includegraphics{stability.ps}}}
{\includegraphics[height=5cm]{stability.ps}}
\end{center}
\vspace{-11mm} \caption{Time stability of the results (``charged'' asymmetry on the left
and `neutral'' asymmetry on the right) and ``fake'' L-R and U-D asymmetries.}
\vspace{-5mm}
\label{fig:beams}
\end{figure*}

\section{Evaluation of the CPV asymmetry in the ``neutral'' mode} 

The event reconstruction in the ``neutral'' mode exploits only the spectrometer
and the LKr calorimeter. 
The spectrometer inner radial selection is chosen according to the 
measured average beam position, as described before. 
The decay vertex is recostructed from the photon impact positions on the LKr,: 
by imposing for each $\pi^o$ the relation $Z_{ij}=1/m_{\pi^o}\sqrt{E_{i} E_{j} d^2_{ij}}$.
This allows for the best resolution especially in the low $u$ region,
where the fit is most sensitive to the asymmetry. 

The ``neutral'' mode is in general less sensitive to biases due to beam geometry 
and detector acceptance (DCH vs LKr) than the ``charged'' mode is.
The most relevant potential source of systematic bias is the L1 component
of the trigger generated by the number of x and y 1D projections of the 
clusters as they were counted on-line by the calorimeter (NTPEAK). 

With a total of $91 \times 10^6$ selected \KTPIZZ events (collected in 2003 and 2004 years) 
the difference in Dalitz plot slope parameter is found to be:
$$\Delta g^n = g^{n+}-g^{n-} = $$
$$=(2.7 \pm 2.0_{stat.} \pm 1.3_{syst.} \pm 0.3_{ext.})\times 10^{-4}$$
where the uncertainty related to the trigger is included in the systematic error and the ``external''
error comes from the uncertainty on the $g$ and $h$ dalitz plot parameters\cite{pdg}
The resulting CPV charge asymmetry is:
$$ A^n_g = (2.1 \pm 1.6_{stat.} \pm 1.0_{syst.} \pm 0.2_{ext.})\times 10^{-4}=$$
$$= (2.1\pm1.9)\times 10^{-4}$$

The reason for a similar precision of the results given ``neutral'' and ``charged''
asymmetry measurements, despite a factor of  30 in the collected statistics, is the fact that 
the population density of the Dalitz plot is more favourable in 
the ``neutral'' mode.

\section{Conclusions}
The largest samples ever of \KTPIPM and \KTPIZZ 
were recently analyzed by NA48/2 and null CP violating 
asymmetries were found. The results, respectively 
$A^c_g = (-1.3\pm2.3)\times 10^{-4}$ 
and $A^n_g = (2.1\pm1.9)\times 10^{-4}$ are one order 
of magnitude more precise than previous measurements 
and does not contradict the SM.
Due to the high precision they can be used to constrain
SM extensions predicting enhancements of the
charge asymmetry.

\begin{thebibliography}{9}
\bibitem{epsi_NA48}
%%A.~Lai {\it et~al.} {\em Eur. Phys. J.}, C22:231--254, 2001.
A.~Lai {\it et~al.}, \Journal{\EPJ}{22}{231}{2001}.
%\bibitem{epsi_KTEV}
%A.~Glazov, Presentation at KAON2001, Pisa (2001).
\bibitem{epsi97}
%V.~Fanti {\it et~al.}, {\em Phys. Lett.}, B465:335, 1999.
V.~Fanti {\it et~al.}, \Journal{\PLB}{465}{335}{1999}
%\bibitem{na31final}
%%G.~D. Barr {\it et~al.}, {\em Phys. Lett.}, B317:233--242, 1993.
%G.~D. Barr {\it et~al.}, \Journal{\PLB}{317}{233}{1993}.
%\bibitem{na48:prop}
%G.~D. Barr {\it et~al.}, Proposal CERN-SPSC/90-22 (1990).
%\bibitem{NA48II}
%R.~Batley {\it et~al.}, Addendum to proposal CERN-SPSC-2000-003 (2000).
\bibitem{weinberg}
S.~Weinberg,~\Journal{\PRL}{37}{657}{1976}.
\bibitem{cabibbo}
N.~Cabibbo,~\Journal{\PRL}{93}{121801}{2004}.
\bibitem{HYPERCP}
Choong~W-S., PhD Thesis LBNL-47014, Berkeley, 2000.
%\bibitem{TNF}
%V.~Ammosov {\it et~al.}, Protvino proposal (1996).
\bibitem{FORD}
W.~T.~Ford {\it et~al.}, \Journal{\PRL}{25}{1370}{1970}. 
\bibitem{SMITH}
K.~M.~Smith {\it et~al.}, \Journal{\NPB}{60}{411}{1973} and 
\Journal {\NPB}{91}{45}{1975}.
%\bibitem{ISTRA}
%I.~V.~Ajinenko {\it et~al.}, hep-ex/0205027 (2002).
\bibitem{ISTRA}
Akopdzhanov {\it et~al.}, hep-ex/04060008 (2004).
\bibitem{theory_1}
G.~D'Ambrosio and G.~Isidori, \Journal{\IJMP}{13}{}{1998}. 
\bibitem{theory_2}
G.~D'Ambrosio, G.~Isidori and G.~Martinelli, hep-ph/9911522 (1999).
\bibitem{pdg}
W.-M. Yao {\it et al}. (PDG), J. Phys. {\bf G33} (2006) 1.
%\bibitem{ch64}
%J.H. Christenson {\it et al}., Phys. Rev. Lett. {\bf 13} (1964) 138.
%
%\bibitem{ba93}
%H. Burkhardt {\it et al}. (NA31), Phys. Lett. {\bf B206} (1988) 169.\\
%G. Barr {\it et al}. (NA31), Phys. Lett. {\bf B317} (1993) 233.
%
%\bibitem{fa99}
%V. Fanti {\it et al}. (NA48), Phys. Lett. {\bf B465} (1999) 335.\\
%A. Lai {\it et al}. (NA48), Eur. Phys. J. {\bf C22} (2001) 231.\\
%J.R. Batley {\it et al}. (NA48), Phys. Lett. {\bf B544} (2002) 97.
%
%\bibitem{al99}
%A. Alavi-Harati {\it et al}. (KTeV), Phys. Rev. Lett. {\bf 83} (1999) 22.\\
%A. Alavi-Harati {\it et al}. (KTeV), Phys. Rev. {\bf D67} (2003)
%012005.
%
%\bibitem{au01}
%B. Aubert {\it et al}. (Babar), Phys. Rev. Lett. {\bf 87} (2001) 091801.\\
%K. Abe {\it et al}. (Belle), Phys. Rev. Lett. {\bf 87} (2001)
%091802.
%
%\bibitem{ab04}
%K. Abe {\it et al}. (Belle), Phys. Rev. Lett. {\bf 93} (2004) 021601.\\
%B. Aubert {\it et al}. (Babar), Phys. Rev. Lett. {\bf 93} (2004)
%131801.
%
%\bibitem{pdg}
%W.-M. Yao {\it et al}. (PDG), J. Phys. {\bf G33} (2006) 1.
%
%\bibitem{is92}
%G. Isidori, L. Maiani, A. Pugliese, Nucl. Phys. {\bf B381} (1992)
%522.
%
%\bibitem{fo70}
%W.T. Ford {\it et al}., Phys. Rev. Lett. {\bf 25} (1970) 1370.
%
%\bibitem{sm75}
%K.M. Smith {\it et al}., Nucl. Phys. {\bf B91} (1975) 45.\\
%G.A. Akopdzhanov {\it et al}. (TNF--IHEP), Eur. Phys. J. {\bf C40}
%(2005) 343.
%
%\bibitem{ma95}
%G. F\"aldt and E.P. Shabalin, Phys. Lett. {\bf B635} (2006) 295.\\
%A.A. Belkov, A.V. Lanyov, G. Bohm, Czech. J. Phys. {\bf 55B} (2004) 193.\\
%E. Gamiz, J. Prades, I. Scimemi, JHEP {\bf 0310} (2003) 042.\\
%G. D'Ambrosio, G. Isidori, Int. J. Mod. Phys. {\bf A13} (1998) 1.
%
%\bibitem{sh98}
%G. D'Ambrosio, G. Isidori, G. Martinelli, Phys. Lett. {\bf B480}
%(2000) 164.\\
%E.P. Shabalin, ITEP preprint {\bf 8-98} (1998).
%
%\bibitem{ag}
%J.R. Batley {\it et al.} (NA48/2), Phys. Lett. {\bf B634} (2006) 474.
%
%\bibitem{cusp}
%J. R. Batley {\it et al}. (NA48/2), Phys. Lett. {\bf B633} (2006) 173.\\
%M. Pepe, these proceedings.
%
%\bibitem{ca05}
%N. Cabibbo, G. Isidori, JHEP {\bf 503} (2005) 21.
%
\end{thebibliography}
%

\end{document}
