The KPM stream selection algorithms

Five selection algorithms have been developed for the identification of φ→ K⁺K⁻ events and constitute the official procedure of the Event Classification program for the KPM stream:

1. Alg1, based on the existence of a candidate φ → K⁺K⁻ vertex in the interaction region;

2. Alg2, looking for events with both K^± tracks reconstructed without a φ vertex;

3. Alg3, trying to identify a charged kaon by requiring specific cuts on a fitted track;

4. TOPO, exploiting the typical geometrical configuration of a K⁺K⁻event;

5. TAG, founded on the kinematic reconstruction and identification of a tagging two-body K^± decay.

The first three algorithms listed above [101] have been developed and tested on a Monte Carlo sample of ∼ 60000 events, before the start of KLOE data taking. They are applied in cascade, according to the diagram shown in Fig.

3.9³. Each algorithm analyzes the events by means of suitable selection criteria and a corresponding veto tests them against the background hypothesis: if such conditions are fulfilled, the events are definitively kept and no further requirements are imposed, otherwise the events are left to the analysis of the next algorithm(s).

Figure 3.9Logic scheme applied for the Alg1,Alg2 and Alg3 algorithms in the Event Classification program.

The definition of the selection criteria applied in the first three algorithms and of the corresponding vetoes is given in the following. The motivations that

3 A fourth independent algorithm has been also studied (Alg4) [102], aiming to identify those events in which both K⁺ and K⁻ decay in the µν mode, but it has not been used in the analyses presented in the rest of this thesis.

have brought to these definitions are extensively discussed in [102, 103]. Since the algorithms are applied in cascade, only the efficiency of the first one (Alg1) can be studied, while the efficiencies for the other two procedures cannot be considered independently of it.

In the Alg1 procedure vertices with 2 tracks and total zero charge are required in the fiducial volume defined by rV ≡^qx²_V + y²_V and |zV| < 40 cm.

In addition, the two tracks momenta ~p1 and ~p2 must be such that 180 <

|~p1| + |~p2| < 235 MeV , −20 < p1x+ p_2x < 40 M eV ,|p1y+ p_2y| < 30 MeV and

|p1z+ p2z| < 20 MeV . Veto1 is satisfied if the two tracks are both produced at small polar angle (θ_K < 0.60 rad) or the points of closest approach for the tracks back-extrapolated towards the origin are such that|r^pca1 + r₂^pca| ≥ 16 cm or|z^pca1 + z^pca₂ | ≥ 16 cm.

The Alg2 procedure asks for two tracks whose innermost (outermost) DC layer hit is < 20 (< 35), corresponding to 72.5 cm (117.5 cm) in the xy-plane.

The distance between the last hits of the two tracks has to be at least 88 cm, the distance between the centres of the two helicoidal trajectories in the xy-plane has not to exceed 25 cm. Subsequently, the following cuts are required:

a) 70 <|~p¹| < 170 MeV ; |z^pca1 | < 70 cm; |r^pca1 | < 15 cm;

b) 50 <|~p2| < 200 MeV ; |z^pca2 | < 100 cm; |r2^pca| < 25 cm;

c) 145 < |~p¹+ ~p2| < 260 MeV ; |z^pca1 − z2^pca| < 100 cm; |r1^pca+ r₂^pca| < 16 cm.

The definition of Veto2 coincides with Veto1.

In the Alg3 procedure a single track is searched with innermost (outer-most) DC layer hit < 10 (< 35), which corresponds to 48.5 cm (117.5 cm) in the xy-plane; its length has to be less than 150 cm and the momentum between 85 and 120 M eV , while the point of closest approach to the origin must satisfy r^pca < 10 cm and |z^pca| < 20 cm. In order Veto3 to be satisfied the logical OR of the four conditions is required: |z^pca| > 5 cm, |r^pca| > 5 cm,

|~p| < 80 MeV and |θ^K| < 0.7 rad.

An unexpectedly high background rate in the KPM stream has been ob-served since the starting of the KLOE data taking in 1999, when only these three algorithms had been implemented in the Event Classification program.

Algorithms 4. and 5. have been developed in order to reduce the presence of machine background in the finally streamed data sample and to provide an estimate of the systematics induced by the first three algorithms. Their definitions are given below.

The TOPO algorithm initially requires two tracks of opposite charge in the event which satisfy the following preselection cuts:

a1) point of closest approach to the IP: |z^pca| < 15 cm, |r^pca| < 15 cm;

a2) momentum at the point of closest approach between 70 and 130 M eV ; a3) last hit in a fiducial volume obtained by rotating around the collisionar

axis (z) the isosceles trapezium having parallel sides, 250 cm and 270 cm long, whose distances from the z axis are 40 cm and 150 cm, respectively.

The angle ϕem in the IP between the emission line of the two kaons and the horizontal axis is then considered. The two momenta ~p₁ and ~p₂ have to satisfy these two conditions simultaneously:

While b1) exploits the correlation between the momenta of the two candidate tracks, the condition b2) uses the information of the boost of the φ meson (∼ 13 MeV along the −x direction).^b

The TAG algorithm requires two tracks connected to the same vertex.

The radial distance from the vertex to the beam axis has to be 40 < rV <

150 cm. Out of the two tracks, one (identified as the kaon candidate) must have 70 <|~p1| < 130 cm and a point of closest approach to the beam line with radial (longitudinal) distance from IP smaller than 10 cm (20 cm). Moreover, the candidate daughter track should have the same charge as the parent kaon track and momentum in the laboratory (kaon rest frame - using the π^± mass hypothesis) ranging from 120 and 320 M eV (180 and 270 M eV ).

One peculiar feature of the KPM stream concerns the track fit procedure.

For the particles that cross the various materials or travel through the gas

in the DC, the energy losses between consecutive hits are treated using the Bethe-Bloch formula under the pion mass hypothesis. This is taken into ac-count at the Event Classification level, when no charged kaons have still been identified, because the various cuts applied do not directly depend on the en-ergy/momentum loss of the tracked particles. Nevertheless, once a track has been identified by the streaming algorithms as a K^±, a better estimate of its momentum is obtained by re-tracking it under the charged kaon mass hypoth-esis. The correct knowledge of the kaon momentum allows to re-compute the absolute T 0 of the event − and consequently to improve the quality of the reconstruction − by identifying the EMC cluster connected to the daughter track (and possibly those of the two photons produced by a neutral pion in the case of a K^± → π^±π⁰ decay).