Event selection

During physics runs in November-December 1999 and March-April 2001, 206M and 363M events were logged on DLT's. This information is supported by about 100M MC events generated with Geant3 [10]. MC generation includes realistic description of the setup: decay volume entrance windows, track chambers windows, gas, sense wires and cathode structure, Cerenkov counters mirrors and gas, shower generation in EM calorimeters etc.

The usual first step of the data processing is the EM calorimeter calibration, using special runs with 10 GeV electrons; track system alignment, HCAL and guard system calibration with muon beam runs. The data processing starts with the beam particle reconstruction in $BPC_{1}\div BPC_{4}$, then the secondary tracks are looked for in $PC_{1} \div PC_{3}$ ; $DC_{1} \div DC_{3}$; $DT_{1} \div DT_{4}$ and events with one good negative track are selected. The decay vertex is searched for, and a cut is introduced on the matching of incoming and decay track. The next step is to look for showers in $SP_{2}$ calorimeter. A method of shower parameters reconstruction based on the MC-generated patterns( $\sim 2000\; 3 \times 3$ patterns) of showers is used. The matching of the charged track and a shower in $SP_{2}$ is done on the basis of the difference between the track extrapolation and the shower coordinates. The electron identification is done using E/P ratio- of the energy of the shower associated with the track and the track momentum, see Fig.2.

Figure 2: The E/p plot- the ratio of the energy of the associated cluster in ECAL to the momentum of the charged track. The arrow shows the cut used for the electron separation.

The selection of events with the two extra showers results in $M_{\gamma \gamma}$ spectrum shown in Fig.3.

Figure 3: The $\gamma \gamma$ mass spectrum for the events with the identified electron and two extra showers.

The $\pi^{0}$ peak has a mass of $M_{\pi0}=134.8 MeV$, and a resolution of 8.6 MeV. Another important variable for the $K^{-} \rightarrow e \nu \pi^{0}$ selection is the missing mass squared- $(P_{K}-P_{e}-P_{\pi ^{0}})^{2}$, where P are the corresponding four-momenta, see Fig.4. The cut is $\pm 0.01$ GeV$^{2}$.

Figure 4: The missing four-momentum squared $(P_{K}-P_{e}-P_{\pi ^{0}})^{2}$ for the selected events for 1999 run (left) and 2001 run (right). The points with errors are the data, the histogram- MC.

The futher selection is done by the requirement that the event passes 2C $K \rightarrow e \nu \pi ^{0}$ fit. At the same time, similar 2C fit $K \rightarrow \pi^{-} \pi$ should fail.. The missing energy $E_{K}-E_{e}-E_{\pi^{0}}$ after this selection is shown in Fig.5 The peak at low $E_{miss}$ corresponds to the remaining $K^{-} \rightarrow \pi^{-} \pi^{0}$ background. The corresponding cut is $E_{miss}>1GeV$. The surviving background is estimated from MC to be less than $3\%$.

Figure 5: The missing energy for the $e \pi ^{0}$ events, for 1999 run (left) and 2001 run (right). The points with errors are the data, the histograms- MC. The dark(blue) peak at zero value corresponds to the MC-predicted $K \rightarrow \pi ^{-} \pi ^{0}$ background. The arrow indicates the cut value.

The detailed data reduction information is shown in Table.1.

Table 1: Event reduction statistics. The main steps are shown for the 1999 and 2001 runs .

Run	1999	2001
$N_{events}$ on tapes	206.544.909	363.002.105
Beam track reconstructed	159.459.629=77$\%$	268.564.958 =74 $\%$
One secondary track found	81.166.929=41$\%$	134.227.095 =37$\%$
Written to DST	70.015.610 =34$\%$	107.215.783 =30 $\%$
$e^{-}$ identified	1.300.958	1.998.719
2 showers reconstructed	252.177	361.621
$\pi^{0}$ identified	186.850	251.489
$\vert M_{miss}^{2}\vert<0.01$	96.652	144.642
$K \rightarrow \pi ^{-} \pi ^{0}$ rejected	79.660	117.566
$K \rightarrow e \nu \pi ^{0}$ accepted	65.208	97.585
$E_{miss} >$ 1 GeV	54.009	79.248