Study of multi-electron Kaon decays at the CERN NA62 experiment and measurement of the pi0 Dalitz decay branching ratio and pi0 electromagnetic transition form factor slope

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Universit`

a degli Studi di Pisa

FACOLT `A DI SCIENZE MATEMATICHE, FISICHE E NATURALI Corso di Laurea in Fisica delle Interazioni Fondamentali

TESI DI LAUREA MAGISTRALE

Study of multi-electron Kaon decays at the CERN NA62

experiment and measurement of the BR(π

0

_{→ e}

+

e

−

γ) and π

0

electromagnetic transition form factor slope

Candidato: Enrico Lari Relatore: Prof. M.Sozzi, Dott. G.Lamanna Anno Accademico 2017/2018

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3.3 Perspectives on TFF slope and BR(K+ _{→ π}+_π0 D) mea-surements . . . 57 3.4 Measurements procedures . . . 60 3.4.1 TFF slope . . . 60 3.4.2 BR(K+ _{→ π}+_π0 D) . . . 62 3.5 Event selection . . . 65 3.5.1 K+ → π+_π0 D Selection . . . 68 3.5.2 Normalization (K3π) . . . 82 3.6 TFF slope measurement . . . 85 3.7 BR(K+ _{→ π}+_π0 D) . . . 92 3.8 Improvements . . . 95 3.9 Conclusions . . . 96 i

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ii CONTENTS

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Introduction

The present work has been carried on within the NA62 experiment, the current CERN research program for testing the Standard Model (SM) through the study of the rare kaon decays.

Two kaon decays are discussed:

K+ _{→ π}+π0e+e− K+ → π+_π0

D

where D in the latter stands for Dalitz decay mode, i.e. π0_{→ e}+_e−_γ_{. Since}

the former is a rare kaon decay channel, first detected in recent years, it was studied in terms of its perspectives in the NA62 experiment, i.e. estimating the upper limit on the total number of events that can be collected, using the NA62 beam line and detector capabilities.

The latter was studied in a deeper way with particular interest towards its second step in the decay chain, i.e. the π0 _{→ e}+_e−_γ _{decay. Two}

measure-ments were discussed on this second decay: the branching ratio (BR) of K+ _{→ π}+π_D0, useful to extract the BR(π0 _{→ e}+e−γ), and the π0

transi-tion form factor (TFF). Their interest is due to the fact that the present BR(π0 _{→ e}+_e−_γ) _{uncertainty represents, in other branching ratio}

computa-tions and measurements, a relevant source of error (BR(K+ _{→ π}+_π0_e+_e−₎

is an example) while the value of the TFF enters as a parameter in the computation of important observables of the SM, like the computation of the magnetic moment of the muon, today experimentally tested through the (g − 2) experiment at Fermilab. The large statistics of kaon decays (≈ O(1013_{)), which will be collected in three years of running, could bring}

a sufficient statistics exceeding that of previous experiments, leading to a more precise measurements for both these quantities.

The first chapter gives a general introduction to the NA62 experiment and, for this reason, it contains a brief description of the main kaon decay studied, the ultra-rare K+ _{→ π}+_ν_ν_¯ _{process. This will be useful to understand the}

reason why specific sub-detectors have been integrated and describe their characteristics. A brief description of the NA62 reconstructed data, both for real and simulated events, is also given.

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iv CONTENTS The K+_{→ π}+_π0_e+_e−_{decay is discussed in chapter two. The theory and the}

previous studies are summarized and the approach used to tune the selection of signal events is described. After a first selection proposal, problems linked to it are shown and some possible improvements introduced. The chapter ends giving some perspectives for the study of this decay in NA62.

Chapter three is dedicated to the analysis of the π0

D decay. After describing

the theoretical framework, the measurable physical quantities are presented, together with the current knowledge. The signal event selection is then dis-cussed and the computation of BR(K+_{→ π}+_π0

D)and of the π0TFF, with a

first estimate of their errors, is given. Finally a study of possible systematic uncertainties is given.

This final chapter summarizes the results of the work and presents future perspectives.

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Chapter 1

The NA62 Experiment

Contents

1.1 Physics Motivations . . . 1

1.2 The NA62 experiment . . . 2

1.2.1 Tracking system . . . 5

1.2.2 Veto system . . . 6

1.2.3 Particle identification system (PID) . . . 13

1.3 NA62 Trigger and Data Acquisition System (TDAQ) 16 1.4 NA62 reconstructed data structure and analysis framework . . . 19

1.5 NA62 MC package . . . 21

1.1 Physics Motivations

The NA62 experiment aims to detect ∼ 100 ultra rare kaon decays K+→ π+_ν_ν_¯ _{to measure its BR with a 10% precision. The K}+_{→ πν ¯ν is a}

Flavour Changing Neutral Current process and so, in the Standard Model, is forbidden at tree level and proceeds trough box or penguin diagrams (Figure 1.1). The matrix element could be determined from the semileptonic de-cay K+_{→ π}0_e+_ν

e, which is well measured [1]. The electroweak amplitude is

dominated by top-quarks loops, resulting in a theoretically clean dependence on the product of CKM matrix elements V∗

tsVtd. The most updated

theoret-ical predictions and experimental measurements of this decay are shown in Table 1.1.

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2 THE NA62 EXPERIMENT

Figure 1.1: Feynman diagrams for the K+ _{→ π}+_ν_ν_¯ _{process. The Box}

diagram on the left and Penguin on the center-right part.

Theory Experiment

(9.11± 0.72) × 10−11 _(17.3+11.5

−10.5)×10−11

Table 1.1: Most recent values of the K+_{→ π}+_ν_¯_ν_{branching ratio taken from}

[2] and [3].

1.2 The NA62 experiment

According to the SM prediction of the BR(K+ _{→ π}+_ν_¯_{ν) (}_{∼ O(10}−10₎₎_,

a way to accomplish the main purpose of the experiment is to have a detector acceptance of 10%, a background rejection factor of 1012_{for other kaon decay}

modes, and an integrated flux of O(1013₎ _{kaon decays. These requirements}

are reached with a experimental setup based on: • the use of a higher energetic proton beam; • the exploit of a decay in flight technique.

Both represent an innovation among the experiments which have measured the BR of K+_{→ π}+_ν_ν_¯_{decay so far, exploiting protons with lower}

momen-tum and kaon decays at rest [4]. The use of a high energetic proton beam (400 GeV/c) from the CERN SPS accelerator, enables the production of the required number of kaon decays in a few years of data taking [5]. This occurs because the kaon production cross section increases at increasing values of the proton energy. The proton beam produces a 75 GeV/c secondary beam, after impinging on a beryllium target. The disadvantage of using a high energetic beam is represented by the impossibility of separating the pion

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3

Figure 1.2: Sketch of the NA62 detector in the Y Z plane [5]. The Z co-ordinate follows the beam propagation and the origin is at the position of the beryllium target. The Y axis is vertical and points upwards. The X axis is oriented to form a right-handed coordinate system. The decay region, starting from 102.4 m, is indicated. Some of the sub-detectors are shown. and protons from the kaons. The particle rate of 750 MHz, composing the secondary hadron beam, contains a 6% (45 MHz) kaon composition. Among the produced kaons, only ∼ 10% (Table 2 in [5]) decay in the 65 m fiducial decay volume (Figure 1.2), for a total of ∼ 5%[5] MHz kaon decays.

The decay in flight technique takes profit of the Lorentz boost of 75 GeV/c allowing to concentrate all the detectors in the forward region. Moreover the detection of some backgrounds is made simpler, especially for those contain-ing photons in the final state.

The signal decay contains only two detectable particles: the incoming K+ and the outgoing π+.

The rejection of the most abundant kaon decay modes is performed through the quantity

m2_miss = (PK− Pπ)2 (1.1)

(PK is the 4-momentum of the parent particle, assumed to be a kaon, and

Pπ is the 4-momentum of the decay particle, assumed to be a charged pion):

two different Signal Regions (SR1 and SR2) are defined by looking at the distribution of (1.1) for background and signal events, plotted in Figure 1.3. The same plot is shown in Figure 1.4 but with the finite width of the K+ _{→ π}+_π0 _{peak due to the resolution. The choice of (1.1) as the}

discriminating variable determined part of the structure of the detector, since simulations show that to have a kinematic rejection factor of O(104_{− 10}5₎_,

a control on the K2π peak at a level of 0.001 (GeV/c2) is needed and, to

accomplish this result, a precise tracking system was inserted in the detector, measuring the momentum and angle of the kaon with a precision of ∼ 0.2% and 0.016 mrad respectively, and 1% and 0.06 mrad for the downstream track [5].

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Figure 1.3: Distribution of m2

miss for some background kaon decay modes

(K+ _{→ µ}+_ν _(K

µ2), K+ → π+π0 (K2π), K+ → π+π+π− (K3π)) and signal

(red line). The two signal regions are indicated. Negative values of the variable are present because we are imposing the mass of π+ _{to an outgoing}

track to build Pπ; if the mass assignment is wrong, the computed missing

mass can be negative [6].

The missing rejection factor of ∼ O(107₎_−O(108₎_{, to reach the desired level}

Figure 1.4: Distribution of m2

miss for some background kaon decay modes

(K+ _{→ µ}+_ν _(K

µ2), K+ → π+π0 (K2π), K+ → π+π+π0 (K3π)) and signal

(red line). The left plot is in linear scale. On the right a logarithmic scale is used to emphasize to relative contribution of each decay mode [5].

of background suppression (O(1012₎_{), is obtained through the inclusion of a}

veto and a Particle IDentification (PID) system. The former to veto muons or photons (coming both from π0 _{decays or radiative processeses), and the}

latter to distinguish between muons and pions.

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5

Figure 1.5: GTK layout in two different planes. The magnet structure com-posing the achromat is drawn in green. The beam is represented by the brown line and propagates along the Z direction [5].

reject accidental events, given the high particle rate. In the following a description of each sub-system is given.

1.2.1 Tracking system

The tracking system is composed by two sub-detectors: the beam spec-trometer (GTK) and the STRAW specspec-trometer (STRAW).

The former provides precise measurements of momentum, time and direction of the incoming beam particle. The GTK is located inside the beam pipe im-mediately upstream of the K+_{decay region and is composed by three similar}

silicon detector stations, installed around four dipole magnets arranged as an achromat [5] . The particle momentum can be derived from the particle displacement of the trajectory in the second station, as shown in Figure 1.5. Besides the momentum resolution, an important quality of the GTK is the time resolution, better than 200 ps. Each station is a hybrid silicon detector consisting of 18000 pixels of 300 × 300 µm2 _{size, arranged in a matrix of}

200× 90 elements, read out by dedicated electronics. The total amount of material is ≈ 0.5%X0 per station (≈ 500 µm of silicon) . The detector is

cooled to reduce problems due to the radiation, operating at a temperature of ≈ −15◦_C _[5].

The STRAW spectrometer measures the trajectories of the particles down-stream of the decay region, starting from ∼ 20 m after it and covering a length of 35 m in the longitudinal direction. The guidelines used in its con-struction were to minimize multiple scattering and to give a uniform space resolution over the full active area. The former is accomplished using light material for the straws (36 µm thick polyethylene terphthalate, coated with 50 nmof copper and 20 nm of gold on the inside and gold-plated tungsten anode wires of 30 µm in diameter) and placing them into vacuum. The total amount of material corresponds to 1.8% X0.

The straws are arranged into four chambers, two before and two after a dipole magnet (MNP33), with an integrated field of ≈ 0.9 Tm. Each chamber is

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6 THE NA62 EXPERIMENT Decay BR µ+ν _{∼ 63%} π0µ+ν _{∼ 3%} π+π0 _{∼ 21%} π+π0π0 _{∼ 2%}

Table 1.2: Branching ratios of the main kaon decay channels with a π0 _{or a}

µ+ _{in the final state [1].}

composed by two modules and each module by two views (or planes) (Fig-ures 1.6 (a)). The views in the first module measure X and Y coordinates, while the others in second module measure the U and V orientations, angled to −45 ◦_C _{and 45} ◦_C _{respectively (Figure 1.6 (b)). The resulting circular}

shape has a diameter of 2.1 m. In the middle of each view a gap, 12 cm in diameter, is present, forming a free passage for the beam. Overlaying the four views an octagon shaped central hole with 6 cm apothem is formed. Since the beam comes out the GTK with a displacement towards positive X values and receives a kick in the middle of the MNP33 magnet, bringing it towards the detector longitudinal axis, the hole of each chamber is displaced with respect to each others (Figure 1.7). To reconstruct a track, hits in all but one modules are required. The track reconstruction efficiency is reduced if the track is close to the beam line. The overall momentum resolution is [5]:

σ(p)

p = 0.30%⊕ 0.005% ∗ p (1.2)

with p in GeV/c.

The MNP33 magnet is the same of the previous NA48 experiment. The magnetic field points in the negative Y direction and the integral of the other components is smaller by a factor of 10−3_{. The momentum kick is}

270 MeV/c. A sketch of the tracking system is shown in Figure 1.8.

1.2.2 Veto system

Among the common kaon decay modes, the ones containing a π0 _{or a}

muon represent the ≈ 89% of the kaon total branching ratio. These are shown in Table 1.2. These decays are the main background sources to the signal when the two photons of the π0 _{escape the detector geometric}

accep-tance and the µ+ _{is misidentified as a π}+_{. Two veto systems are used to}

rejects these decays.

The Photon Veto (PV) is composed by the NA48 Liquid Kripton calorime-ter (LKr), the Large Angle Veto (LAV) detector, the Incalorime-termediate Ring

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7

(a)

(b)

Figure 1.6: Details of the STRAW spectrometer [5]. In (a) a single chamber with two modules is shown. In (b), on the left, the arrangement of the straw tubes in the different views of a chamber is shown. On the right the overlap of the two double layers per view is sketched. This arrangement is required to have at least two straw crossing per view per track, to solve the left-right ambiguity.

Calorimeter (IRC) and Small-Angle Calorimeter (SAC). The system is per-formed to suppress the kaon decays with a π0 _{in the final states, the most}

abundant of which is K+ _{→ π}+_π0 _(K

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Figure 1.7: The displacement of the STRAW chamber centers in the X direction [5] is visible in this schematic drawing of the XZ plane of the detector. Note that the scale is different on the two axes.

Figure 1.8: Sketch of the NA62 detector. The hadronic beam propa-gates along the Z direction. The GTK and the STRAW spectrometers are highlighted in green with respect to the other sub-detectors (in pur-ple). The GTK stations (GTK1, GTK2, GTK3) and STRAW chambers (CH1,CH2,CH3,CH4), with the MNP33 magnet are shown. The slanted dashed line is a charged particle receiving the kick of the downstream spec-trometer magnet.

factor, the π+ _{momentum of a signal decay is required to lie in the}

inter-val 15 − 35 GeV/c. With this requirement the π0 _{of K}

2π, with an energy

at least of 40 GeV, cannot escape the angular coverage of the PV because of the anti-correlation between energies and emission angles [5]. The polar angular range is subdivided as follows:

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9

Figure 1.9: Sketch of the photon veto system (in blue). The beam propagates along the Z direction. The three intervals of angular coverage are shown from 0 mrad (the beam line) to 50 mrad (just at the beginning of the decay region).

• from 8.5 mrad to 50 mrad by the LAV detector; • from 1 mrad to 8.5 mrad by LKr;

• from 0 mrad to 1 mrad by the IRC an SAC;

These sub-detectors are highlighted in Figure 1.9 together with the angular coverage.

The LAV detector is composed by 12 ring-shaped stations (Figure 1.10 (a)), 11 installed in vacuum tank and the last one in air just 3 m upstream the LKr front (Figure 1.9). Each station is an arrangement of 4 − 5 layers of the lead-glass blocks from the OPAL experiment, shown in Figure 1.10 (b), with a 75% composition of lead oxide. Layers are separated by 1 cm and are staggered in the XY plane (see Figure 1.10 (a)). In this way, particles cross-ing the detector intercept an average of three blocks, with a total effective material depth of 21X0. The overall inefficiency of the LAV detector must

be less than 10−4 _{to reach the required 10}8 _{rejection power.}

The LKr electromagnetic calorimeter is the one used in the NA48 exper-iment. The only change has been applied to the read out system to satisfy the demanding rate requirements of NA62 [7]. It is a quasi-homogeneous ion-ization chamber, filled by 9000 [5] litres of liquid krypton at 120 K, housed in a cryostat. Geometrically it has a octagonal shape and extends from the beam pipe, with a inner radius of ≈ 8 cm, to an outer one of 128 cm. The total length along the beam direction is 127 cm, corresponding to 27X0.

The active area is divided in 13248 longitudinal cells with a cross section of 2×2 cm2_{. A drawing of the LKr is shown in Figure 1.11. A cluster is formed}

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(a)

(b)

Figure 1.10: (a) Drawing of one LAV station with 4 layers of lead-glass blocks. In (b) one of the blocks composing the LAV station with its measures is shown [5].

by looking for a cell with a energy > 250 MeV and larger than the sum of the energies in the 8 neighboring cells. All the energies measured from cells within 11 cm from the cluster center are summed to build the total energy of the cluster. The energy resolution of the LKr is [5]:

σ(E) E = 4.8% √ E ⊕ 11% E ⊕ 0.9% (1.3)

with E in GeV. The position is an energy weighted average of the X and Y coordinates of all the cells partecipating in the cluster.

The LKr is also exploited to make particle identification together with the STRAW spectrometer information on the track momentum, by computing the "energy over momentum ratio" (E/p).

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11

Figure 1.11: Representation of a quarter of the LKr and of its inner side with the cells arrangement [5].

(a) (b)

Figure 1.12: Pictures of the two detectors composing the SAV system. (a) The IRC. (b) The SAC. The WLS fibers are visible [5].

Finally the two sub-detectors IRC and SAC compose the small angle veto (SAV) system, deputed to detect photons not hitting the previous PV detectors, due to their proximity to the beam pipe. In Figure 1.9 the angular coverage of the SAV system is in yellow. Both IRC and SAC, respectively shown in Figure 1.12 (a) and (b), are shashlyk calorimeters, with lead and plastic scintillator plates traversed by wavelength-shifting (WLS) fibers. Be-cause of their position close to the beam pipe, these detectors sustain a photon rate of 1 MHz. Moreover, the total rate on the IRC is increased by muons, coming from the decays of the beam particles, up to values of 10 MHz. The same rate is not present in the SAC because a magnet, placed just before it, deflects the charged beam.

The muon veto (MUV) system is used to discriminate between π+_{and µ}+

and is composed by three sub-detectors: two hadron calorimeters, MUV1 and MUV2, and, after a 80 cm thick iron wall, a fast muon veto detector (MUV3). The former are square-shaped sampling calorimeters placed one in front of

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12 THE NA62 EXPERIMENT the other, perpendicular respect to the beam pipe, which crosses them at the center. Both are built with alternate layers of iron plates and plastic scintillators. MUV1 was designed for the NA62 experiment and contains 24 layers of iron, with the first and the last one higher than the innermost 22 to support the whole structure. The distance between layers is 12 mm. They are interleaved by 23 layers of scintillator strips, along the horizontal and vertical direction. The MUV2 is an heredity of the NA48 experiment. It is quite similar to the MUV1 in its structure of alternating layers of iron and scintillating material.

The MUV3 is used for muon identification, as only muons can reach the detector after passing the LKr, MUV1/2 and iron wall, for a total of 14 interaction lengths [5]. It is composed by 140 plastic scintillator tiles, 50 mm thick, with an area of 220 × 220 mm2_{, and 8 smaller ones in the region close}

to the beam pipe because of the high rate of particles in this inner region. The MUV3 is crossed by an average of 13 MHz muons at nominal beam intensity.

The whole MUV veto system is sketched in Figure 1.13.

Figure 1.13: Sketch of the MUV system and other veto sub-detectors (in red): CHANTI, MUV0, HASC. The beam is propagating along the Z direction.

Three other veto sub-detectors belong neither to the PV nor to the MUV system. These are:

• the CHarged ANTI (CHANTI) detector is a hodoscope used to veto events in which the beam has inelastically interacted with the last GTK station (GTK 3), creating a signal similar to the K+ _{→ π}+_ν_ν_¯_{. It is}

composed by 6 hodoscope stations of 300 × 300 mm2 _{in cross section}

with a 95 × 65 mm2 _{hole in the center to leave the space to the beam.}

The first station is placed just after GTK 3 and the distance between each station and the next one approximately doubles for successive sta-tions. A final angular hermetic coverage in the polar angle of 49 mrad and 1.34 rad is reached with this arrangement.

• The MUV0 sub-detector is a hodoscope placed just downstream the RICH detector to detect π− _{deflected by the MNP33 magnet towards}

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13

Figure 1.14: The PID system (highlighted in blue and green) with respect to the other sub-detectors which are in purple.

two layers of 48 plastic scintillator tiles with dimensions of 200 × 200 × 10 mm2_.

• The HAdronic Sampling Calorimeter (HASC) is placed at the end of the NA62 experimental apparatus and is employed to detect π+_coming

from K+ _{→ π}+_π+_π− _{with momentum > 50 GeV/c which generally}

travel through the beam holes in the center of the STRAW chambers. A dipole magnet is placed before the MUV3 and is used to deflect the charged beam towards the HASC. The sub-detector is a sandwich of 60 lead plates 16 mm thick, interleaved with 60 plates of plastic scintillator of 100×100 mm2 _{in the transverse direction, (4 mm) thick.}

1.2.3 Particle identification system (PID)

The PID system is composed by two detectors, both exploiting the Cherenkov radiation: the Ring Image CHerenkov counter (RICH) and the CEDAR (coupled with the Kaon TAGger or KTAG). The position of each detector is shown in Figure 1.14

The CEDAR, or KTAG, is used to identify kaons among the beam par-ticles. The CEDAR is a differential Cherenkov counter filled with nitrogen (N2)at 1.75 bar at room pressure[5]. This represent a total of 3.5×10−2X0in

the path of the beam. The pressure of the radiator is chosen so that only the light coming from the desired particle passes through an annular diaphragm. The CEDAR gas volume and optics are suitable for use in NA62, but the original photodetectors and readout electronics are not capable of sustaining the nominal 45 MHz kaon rate of the NA62 beam line and of reaching the de-sired 100 ps time resolution. Then the new KTAG was developed. The light reflected back by the CEDAR passes through eight quartz windows and is focused onto eight spherical mirrors. The mirrors reflect the light outwards, in the radial direction, which is collected by a light guide and driven into eight light boxes (or sectors) containing PMTs (Figure 1.15). Requiring a timing coincidence in at least 5 sectors, gives an overall kaon tag efficiency

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Figure 1.15: On the left 3D representation of the KTAG detector with its main parts highlighted. On the right a picture of the system CEDAR + KTAG as is installed in the NA62 experimental hall. To have a reference, the direction of the beam is indicated [5].

of 98% [5].

The Ring Image CHerenkov counter (RICH) is designed to separate muons and pions in the 15 − 35 GeV/c momentum interval, providing a factor 100 of rejection for kaon decays with a muon in the final state. It is composed by a 17.5 m long cylindrical vessel, filled with neon gas used as radiator. The Cherenkov light, reflected by the mosaic of 20 spherical mirrors (Figure 1.16 (a)), placed at the end cap of the vessel, is collected by two photomultiplier (PMTs) arrays placed at the upstream of the RICH, on the left and right of the beam pipe crossing the detector. 2000 PMTs are used to reach the required angular resolution. The RICH structure is shown in Figure 1.16 (b).

To get a good discrimination efficiency in the lower part of the momentum range, the minimum pion momentum to generate Čherenkov radiation must be 12.5 GeV/c. This requirement, through the relation

pt=

m √

n2_{− 1} (1.4)

where m is the mass of the particle radiating in the medium, can be used to extract the value of n, the gas refractive index at operating condition. For a pion:

n= 1 + 6.2∗ 10−5 (1.5)

which is quite similar to the gas nominal value at standard temperature and pressure condition [1]:

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15

(a)

(b)

Figure 1.16: The NA62 RICH detector. (a) The mosaic of mirrors with the structure used to sustain its weight. The total budget material is 20% of a radiation length.(b)The whole structure of the sub-detector. The direction of the beam is indicated, as well as the two PMTs spots, and the back plane, housing the spherical mosaic of mirror.

n0 = 1 + 6.7∗ 10−5. (1.6)

Two Charged particle HODoscopes (CHOD) complete the NA62 detec-tor. One is a heredity of the previous NA48 experiment while the other was built specifically for NA62. For this reason they are generally called "Old CHOD", or simply CHOD, and "New CHOD". They are employed especially to generate trigger signals and, in association with the spectrometer and the KTAG, to give precise time measurements of the track and of the matching with the GTK track. They are exposed to a particle flux of 13 MHz [5], mostly kaon decay products and in a little fraction by muon halo and pion decays. The two detectors are separated longitudinally by ≈ 70 cm.

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(a) (b)

Figure 1.17: (a) The NewCHOD with its tile structure. The direction of the beam in this case is perpendicular to the paper. (b) Incident flux of particles in the NewCHOD. The number in each tile is the expected rate in MHz at nominal beam intensity [5]. Due to the presence of the beam, the central tiles receive a higher rate of incident particles [5].

The NewCHOD is placed just after the RICH end cap and is composed by 152 plastic scintillator tiles of 30 mm thickness (0.13X0) covering a disk

surface with inner and outer radius of 140 mm and 1070 mm respectively (Figure 1.17 (a)). The tile structure is used to equalize the hit rate distri-bution, shown in Figure 1.17 (b). The time resolution is O(1 ns).

The CHOD detector (Figure 1.18) is composed by two planes (H and V) of 64 vertical and 64 horizontal plastic scintillator slabs of 20 mm (0.10X0)

thickness. Each slab is read by PMTs through light guides. The 64 slabs are assembled into 4 quadrants with 16 slabs in each one. Two independent time measurements are provided for each charged particle crossing a vertical and a horizontal slab, reducing the possible tails given by out-of-time events, reaching a time resolution of 0.3 ns. The incident flux is greater than the expected 13 MHz and reaches almost 35 MHz for each plane. The difference is due to the activity of the upstream and downstream detectors, such as the LAV12 induced activity or the particle back-scattering from LKr.

1.3 NA62 Trigger and Data Acquisition System (TDAQ)

The high intensity of the NA62 beam requires an high performance trig-ger and data acquisition system, with the main purposes of minimizing the dead time and maximizing the data collection processes, while keeping a time resolution as high as possible. One of the features of the NA62 experiment

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17

Figure 1.18: The CHOD cross section with the two arrangement of slabs in the two planes H, V. At the end of each slab a PMT is present. The hole at the center of the detector houses the beam pipe passage. On the right a side view of the detector [5].

is that the trigger and data acquisition system are unified. This is somewhat different to the most common case in which a restricted sub-set of informa-tions is processed by a dedicated trigger system. Improvements introduced by this approach are the elimination of a specific trigger data path, conse-quently reducing the needed hardware, and the exact offline reproducibility of the trigger algorithms.

The timing to the whole system is given by the Timing, Trigger and Control (TTC) system developed for the LHC experiments. The TTC provides a common free-running synchronous 40.079 MHz [5] clock which is the unity reference for time measurements.

The data-taking unit in NA62 is called "burst" and corresponds to the SPS beam spill, which is a few seconds long. All the elements of the NA62 TDAQ system are synchronously reset by a Start Of Burst (SOB) and stopped at each End Of Burst (EOB) signal.

The trigger system is composed by three levels: the first (L0) is hardware based, the second (L1) and the third (L2) are software based and are imple-mented on dedicated PCs. The whole trigger chain permits to decrease the event rate from 10 MHz to 10 kHz.

Each detector participating to the L0 trigger produces primitives, a 32 bit word containing sub-25 ns time information and an identifier which indicates which conditions are satisfied at that time. If two different primitives are produced with a time difference less than the sub-detector resolution, they are merged into one. In Table 1.3 the detectors participating to the L0

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trig-18 THE NA62 EXPERIMENT ger together with the features used to generate primitives are listed, while in Table 1.4 examples of primitives are shown.

Sub-detector Basic feature required to produce a trigger primitive

CHOD hit multiplicity and pattern in the H and V plane NewCHOD hit multiplicity and position in the quadrant RICH hit multiplicity on the PMTs

MUV3 multiplicity in the tiles

Calorimeters LKr calorimetric cluster multiplicity or total en-ergy deposit

Table 1.3: Sub-detectors producing primitives for the L0 trigger and their informations. "Calorimeters" indicates the whole chain of these type of sub-detectors (LKr,MUV1-2).

Sub-detector Primitives ID

Explanation

CHOD Q1 at least a coincidence in one

of the quadrants of H and V plane

Q2 at least a coincidence in two different quadrants of H and V plane

NewCHOD QX opposite quadrants are hit

Q2 at least two quadrants are hit

RICH RICH at least two in-time hits in

RICH

MUV3 MO1 signal in outer tiles

MO2 coincidence of signals in two outer tiles

MUV3 any MUV3 primitive

Calorimeters LKr(20) at least 20 GeV released in the calorimeters

> 1 cluster more than one cluster is present in the LKr

Table 1.4: Some of the possible primitives a detector participating to the L0 trigger (first column) could produce. "Calorimeters" indicates the whole chain of these type of sub-detectors (LKr,MUV1-2).

The L0 trigger primitives from sub-detectors are managed by the L0 Trigger Processor (L0TP), which combines them in time in programmable time windows, using the CHOD or the RICH as the reference detectors for

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19 the timing. Their hit time is considered as the time of the event (Ttrigger). In

case chosen logic conditions (called Masks) are satisfied, a L0 trigger signal is produced and sent back to the detectors which send their data to the PC Farm. When more than one mask is satisfied, the or logic condition is applied. The informations from L0TP are saved, including trigger time and the satisfied masks plus the type of the trigger: the type is used to distinguish all the enabled masks in a certain event from the firing of a particular mask, called "Control", with no L1 trigger and with a very loose L0 requirement of at least two hits in the CHOD. In this way the "Control" sample is used to study the efficiency of the other L0 trigger masks. The number and types of Masks can be changed during the data taking, following the necessities linked to new possible decay analyses which can be proposed. A downscaling factor (D) is used to reduce the number of events passed to the L1 trigger for some masks. L0 masks are associated to L1 trigger conditions of the remaining detectors: LAV, STRAW, KTAG. The LAV condition introduce a hit multiplicity cut in the 12 LAV stations, the STRAW condition performs a rough momentum estimation in certain interval cut, and finally the KTAG condition is a check on the number of fired sectors. A fraction of events passing L0 trigger masks is directly saved without being processed by the L1 algorithms (autopass events): this is used as a control sample to perform a subsequent offline analysis of the L1 trigger efficiencies (Table 1.5).

1.4 NA62 reconstructed data structure and

analy-sis framework

Raw data files produced by the TDAQ system are transferred to the CERN Advanced STORage system (CASTOR) by the Central Data Record-ing (CDR) service. Once on CASTOR data are available for processRecord-ing. Through the execution of the NA62Reconstruction software package, raw in-formations are combined in time and space, using specific algorithms for each sub-detector, to build refined quantities stored in so-called Candidates, the basic structure handled by the final user. As an example, if raw informations are isolated energy releases in the cells of the electromagnetic calorimeter, the Candidates are the possible clusters that could be assembled starting from them. In this way each Candidate becomes the best identification of the energy deposit of the interacting particle. Similar considerations on the spectrometer lead to a Spectrometer Candidate, which in this case is a syn-onymous of fitted track in different chambers. A set of standard tools are available to the user in the NA62Analysis package, which contains also all the software functions to access the different Candidates. In practice this package permits to convert a physical selection into a series of instructions, which can be collected in a unified program called analyzer. Each analyzer

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20 THE NA62 EXPERIMENT Mask ID

(name)

Chain L0[downscaling]:

L1[downscaling] detected decayExample of channel L0: RICH*Q1*!MUV3[200] 0 (Not mu) K+_{→ π}+γγ L1: KTAG(>4)[1]→STRAW1Trk[1] L0: RICH*Q1*UTMC*!QX*!MUV3* *!LKR(<1 cluster or E>30)[1] 1 (Pnn) K+_{→ π}+νν¯ L1: KTAG(>4)[1]→!LAV→STRAW[1] L0: RICH*QX*LKr(>20)[8] 4 K+_{→ π}+e+e− (Di-electron) KTAG(>4)[1]→STRAW1exotics[1]L1: L0: RICH*QX[100] 5 K+_{→ π}+π+π− (Multi-track) KTAG(>4)[1]→STRAWexotics[1]L1:

Control L0: Q1 [400] L1: not applied All decay with at least a charged

track

Table 1.5: Some of the trigger masks used during the data acquisition. The first and the second are quoted to show the role of the downscaling factor: lower for rare decays and higher in standard kaon decay modes. Mask 4 and 5 are reported since they are used in the discussed analyses. Note that the downscaling factor of the L1 trigger is always one. The different STRAW algorithms are quite similar; the only changed request is on the number of reconstructed tracks in the event. The KTAG condition includes the requirement that the timing coincidence of the enabled 4 sectors must occur in 5 ns.

can work independently or in a chain. The latter configuration is useful each time the performed analysis can be subdivided into specific parts, permit-ting to reuse some informations also for other purposes. An example this is the case for an analyzer that identifies electrons using a set of sub-detectors. Among the tools the most used are:

• Time alignment: performing part of the automatic time calibration procedure applied on data.

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21 • Pre-Analyzers: typically applying energy and momentum corrections

to raw quantities provided by the reconstruction.

• Association Tools: combining informations from more than one sub-detector, taking known instrumental effects into account .

• Geometry Tools: applying acceptance cuts or vertexing algorithms. • Filters: used to collect events which share similar characteristics. All of these make the implementation of some standard commands (such as geometrical track propagation from a detector to another) easier and guar-antee a uniform system of selection criteria to the users. Moreover, in the case of real data, filters enter in the creation of final files accessible by users for analysis. In this way the user can run only over the events in which the basic features of the signal are present. All the cuts applied by analyzers are documented in [8]. The NA62Reconstruction and NA62Analysis packages are constantly updated and improved. In this work the standard tools are used in the applied selections but they will not be explained in depth, except where this could bring clarity.

1.5 NA62 MC package

The NA62 MC package is based on GEANT4 [9] for the detector de-scription, TURTLE [10] for the beam optics upstream the first detector (CEDAR), and a set of custom decay generators (mostly for kaons) that include form factors and radiative corrections. TURTLE simulates pure op-tics and no particle interaction; it is possible to generate a separate MC sample using as external input the result of Halo simulation, which includes interactions in the material of the beam elements. Halo tracks muons which leave the nominal beam apertures.

In a MC simulation, the interactions of the generated particles with a spe-cific detector are stored as raw data like a real event. Raw data files are processed with the NA62Reconstruction package to produce the Candidates of the various sub-detectors. In this way there is a unique analysis software both for real and simulated data. Generated events include also the cases where the kaon doesn’t enter the fiducial decay volume and disappears be-cause of inelastic interactions with the last stations of the GTK, without producing the wanted particles of the decay channel.

Three main differences exist between MC and real data:

• the trigger informations are only present in real data, and assume de-fault values in MC;

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22 THE NA62 EXPERIMENT • the "truth" quantities, which are present only for MC events.

Among the latter are the position and the four-momentum of a particle, that the user can ask at some fixed checkpoints between the production and end position, and the process through which the particle is disappeared. The generated particles have a "parent" index used to know from which parti-cles they were born. It’s important to underline that not all the generated particles are saved to files and are accessible by the user. The reason is due to the memory required to store events. An example is the electromagnetic shower simulation, during which the number of simulated particles grows by a factor of ∼ 2t_{, where t is the number of decay required to let all the}

par-ticles reach the critical energy. In these cases, only the final position of the primary photon (or positron/electron) is known and its end process name.

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Chapter 2

The K

+

→ π

+

π

0

e

+

e

−

decay

Contents

2.1 Introduction . . . 23

2.2 Theoretical basics and Physics motivations . . . 24

2.3 First signal selection and preliminary conclusions 27

2.4 Improved selections . . . 37

2.5 Conclusions . . . 49

2.1 Introduction

Besides its primary goal, NA62 can exploit the intense kaon flux and detector capabilities to perform other interesting studies on kaon decays. Among them we consider the rare decay K+ _{→ π}+_π0_e+_e−_{, that was first}

detected in the analysis of NA48/2 data. Referring to [11], the branching ratio (BR), based on ∼ 5000 candidates, is

(4.22_{± 0.06}stat± 0.04syst± 0.13ext)× 10−6= (4.22± 0.15) × 10−6 (2.1)

with < 5% background contamination.

In this chapter the perspectives on this decay are discussed in the NA62 experiment. The chapter is organized as follows:

• in the first section the theory for the decay is briefly discussed, to explain its relevance.

• In the second part a first proposal for signal selection is presented, using the NA62 analysis framework, and the problems linked to it. • The third part is devoted to the description of the improvements that

can be introduced.

• The fourth part contains the conclusions. 23

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24 THE K+ → π+_π0_e+_e− _DECAY

2.2 Theoretical basics and Physics motivations

Radiative kaon decays, even if dominated by long distance effects, rep-resent a good environment to study short distance physics and low en-ergy QCD. This is the case for the two decays K+ _{→ π}+_π0_γ _{and K}+ _→

π+π0e+e−, which differs only in the emission of an on-shell and off-shell (later converting as an e+_e− _{pair) photons respectively. The theory}

regard-ing these decays was deeply developed in [12], [13], [14] (and with an updated version in [15]) and [16] from which the essential conclusions have been taken to justify which measures can be performed in the NA62 experiment. Both the decays receive contributions from two different diagrams:

• a long distance contribution, called inner Bremsstrahlung (IB) (lower part of Figure 2.1);

• a direct emission part (DE) (upper part of Figure 2.1), in its turn divided in electric and magnetic parts (DE(E), DE(M)).

Thus the kaon decay width in these channels is a sum of three terms: a pure IB process, a pure DE process and the interactions between them (INT), containing all the possible combinations, i.e. IB-DE(E), IB-DE(M), DE(E)-DE(M). A first measurement of the whole DE and IB-DE(E) terms was per-formed in [17] while the last two contributions, absent in the K+ _{→ π}+_π0_γ

decay because are P-violating and cancels out upon angular integration ([11],[12]), can be measured in the K+ _{→ π}+_π0_e+_e− _{decay , giving a first}

motivation to select this channel. According to [12] and adopting the

for-Figure 2.1: Production mechanisms of the K+_{→ π}+_π0_e+_e− _{decay: the DE}

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25 malism of [16] for the decay

K+(P )_{→ π}+_π0_γ∗

→ π+_(p

1)π0(p2)e+(k+)e−(k−), (2.2)

the amplitude of the process is: A= e

q2j

µ_(k

+, k−)Jµ(p1, p2, q) (2.3)

where jµ_{is the leptonic current}

¯

u(k−)γµv(k+) (2.4)

and Jµ is the hadronic one written in terms of two electric forms factors

F1, F2 and a pure magnetic term (F3)

Jµ= F1p1µ+ F2p2µ+ F3µναβp1νp2αqβ. (2.5)

Giving the standard form for the decay width (Γ) dΓ = 1

2MK|A|

2_dΦ, _(2.6)

being dΦ the invariant phase space for the four body decay dΦ = (2π)4δ4(P − p1− p2− k+− k−)× d3p1 2(2π)4_E 1 d3p2 2(2π)4_E 2 d3k+ 2(2π)4_ε 1 d3k− 2(2π)4_ε₋, (2.7) and the final form of the leptonic tensor once the sum over all the spins states has been performed

tµν = 2(qµqν− kµkν− q2gµν), (2.8)

the convolution between tµν _{and the square of J}

µ gives the final results

|A|2 = e 2 q4(|AE| 2₊ |AM|2+ AEM). (2.9) where

• |AE|2 is the square of pure electric amplitude and is function of |F1|2,

|F2|2 and F1F2∗+ F1∗F2 only;

• |AM|2 is the square of pure magnetic amplitude and is function of |F3|2

only;

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(the complete forms are in equation (8) in [16]). The electric form factors can be written in terms of a sum of a Bremsstrahlung and direct emission pieces,

Fi= FiIB+ FiDE, i= 1, 2 (2.10)

while F3= F3DE. The authors of [14] rewrote the Ai terms using these new

definitions for the form factors and, using the set of variables E∗

γ, Tc∗ and q2

(respectively the energy of the photon and the kinetic energy of the π+ _in

the kaon rest frame and the square of photon four-momentum), obtain d3_Γ dE_γ∗dTcdq2 = d 3_Γ IB dE_γ∗dTcdq2 + d 3_Γ DE(E) dE_γ∗dTcdq2 + d 3_Γ DE(M ) dE_γ∗dTcdq2 + d 3_Γ IN T dE_γ∗dTcdq2 . (2.11) The possibility of rearrange the decay width in this way can be made only in the K+ _{→ π}+_π0_e+_e− _{decay since the value of q}2 _{isn’t restricted to be}

0. The power of (2.11) relies on the fact that the Dalitz plot of the various Γi can be studied, in the (Tc∗, Eγ∗) coordinate, at different values of q2. In

[14] it’s demonstrated that a general trend is that, at increasing values of q2_,

the relative contributions of IB respect to the other terms in (2.11) becomes smaller (see Table 2.1) and also that the different contributions tend to fill different areas of the Dalitz plot. This is fundamental to disentangle the dominant IB contribution from the others, considering that the pure magnetic piece is ∼ 1/70 times smaller, and the pure electric is almost ∼ 120_{− 130 times smaller than the DE(M) term. This give to the interested} decay an important role as a mean to test short distance physics which, in the case of other radiative kaon decay channels would be remained hidden.

From an experimentally point of view the conclusions of the first work on

q (M eV ) BIB[10−8] BIB/BDE(M ) BIB/BDE(E) BIB/BIB−DE(E) BIB/BIB−DE(M )

2ml 418.27 71 4405 128 208 2 307.96 61 3416 111 165 4 194.74 48 2320 90 129 8 109.60 36 1414 71 100 15 56.12 26 789 56 78 35 15.5 16 263 41 54 55 5.62 12 118 38 44 85 1.37 9 46 49 37 100 0.67 8 30 71 36 120 0.24 8 18 458 35 140 0.04 9 10 -45 37 180 0.03 12 5 -19 44

Table 2.1: In the same raw the values of the branching ratio (B) for the Bremsstrahlung process (second column) and relative weight of the other contributions as had been computed by [14] are reported for a fixed value of q2_{. Further details are in Figures 1-4 of [14] in which it’s shown the different}

areas of the Dalitz plot filled by the various contributions of (2.11).

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27 ratio of the decay is in good agreement with theoretical predictions but, for a full determination of the DE and INT contributions a higher statistics than the one of the NA48/2 experiment is required.

2.3 First signal selection and preliminary

conclu-sions

As quoted in section (2.2), the NA48/2 statistics has no sensitivity to the direct emission piece of (2.11). Studying the perspectives on this decay in NA62 means investigating if the estimated number of expected signal events NS could exceed the 5000 of NA48/2, leading to a possible investigation of

the interesting areas of the Dalitz plot as stated in section 2.2. Given the BR, NS will depends on the total number of kaon decays collected in a certain

data taking period (NK+), the acceptance of the applied selection (A_S), the

trigger efficiency of the adopted trigger mask (εtrigger) and its downscaling

factor (Dtrigger):

NS= NK+BR(K±→ π+π0e+e−)A_S

εtrigger

Dtrigger (2.12)

The BR used value is 2.1. AS term is computed by running the analyzer

on the whole MC sample of signal events (Nsimulated), to extract the number

of reconstructed decays (Nreco):

AS= Nreco Nsimulated (2.13) whose error is σAS = s AS(1− AS) Nsimulated (2.14)

εtriggeris the efficiency of the selected trigger mask and is evaluated using a

sample of real data, almost background free. It’s the product of εL0∗ εL1,

the efficiencies of the two trigger levels composing the mask. Both can be further subdivided into the product of the efficiencies of all the sub-detectors used in the logic and condition.

The signal decay is composed by three charged tracks, π+_e+_e−_{, and a neutral}

pion, which can be detected from the two photons it produces. With a rough computation, if the initial energy of the K+ _{is divided in equally parts, the}

π0 _{is expected to release a amount of at least 20 GeV in LKr, satisfying the}

LKr(>20) condition. Moreover, considering the presence of three tracks, a QX condition in the NewCHOD can be easy satisfied. Then, looking at Table 1.5, Mask 4 best matches these features. For these reasons, the efficiency is:

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• εL1 = εKTAG∗ εSTRAW

In this study, εtriggerhas been evaluated, as for the acceptance, using the MC

simulation for the different sub-detectors involved. Mask 4 had Dtrigger= 2

in 2016 and Dtrigger= 8 in 2017/2018.

Finally NK+ is estimated from the data, as specified in [18] (section "K+→

π+νν Signal Event Sensitivity"), performing a K¯ + _{→ π}+_π0 _selection.

The final value for the 2016 run is

NK+ = (1.21± 0.02_syst)× 1011 (2.15)

the systematic uncertainties are due especially to data/MC agreement, and variation of measured K+ _{flux as a function of positive pion momentum.}

Always referring to [18], the estimated kaon decays in the fiducial volume in the 2017 run is

∼ 3 × 1012 _(2.16)

Projections on the number of collected decays in 2018 are available but, since at the time of this work only a part of the data were available for physical analysis, only 2016-2017 data samples are considered.

In [11] a event selection technique to maximize Nreco is described.

Con-sidering the NA48/2 experimental setup (Figure 2.2), the first criterion ap-plied is the identification of a 3 tracks vertex with total charge qvtx = ±1

(NA48 had two beams of K±_{) in the fiducial decay volume. The tracks}

are built using a spectrometer composed by 4 Drift Chambers (DC) with a magnet giving a pT = 120 MeV/c. Track timing, useful to discriminate

from background, is performed using the hits associated to each track at the Hodoscope (Hodo). The LKr is used only for the π0 _{reconstruction,}

through the identification of 2 isolated clusters (meaning not associated to the charged tracks as extrapolated from (DC4)) within 5 ns from the average of track times. If such clusters exist, their energy is used to build the four-momenta of the 2 photons, considering them as originating from the vertex. The following passages are used for the PID:

• the e−_(e+₎ _{is the negative (positive) track if q}

vtx = 1(−1) ;

• the two same-sign tracks are tagged by trying each of the two mass assignment (π±_{mass to first track and e}±_{mass to the second and vice}

versa) and by computing for both the final kaon and π0 _{masses, M}

K+

and Mπ0, and looking at which combination lie in the region

|Mπ0− 0.42 ∗ M_K+ 73.2| < 6 MeV/c2 (2.17)

This procedure works well because of the strong correlation existing between Mπ0 and M_K+, visible in Figure 2.3 (taken from [11]), and has an efficiency

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29

Figure 2.2: Sketch of NA48/2 with the names of the sub-detectors used in [11] in the signal selection process. The K± _{direction is indicated by the}

black arrow while the green and blue lines represent charged tracks.

of 96.5% measured on simulated signal events, permitting to reach an overall signal acceptance AS = 0.67%. The acceptance was computed in [11] using

the relation:

AS =

AIB+ ADE∗ wDE+ AIN T ∗ wIN T

1 + wDE+ wIN T (2.18)

where the wi are the weights of the different production mechanisms exposed

in section (2.2), i.e. if wIB = 1 the wDE ∼ 1/70 and wIN T ∼ 1/(120 ÷ 130).

Considering that some of the exploited NA48/2 sub-detectors for the event reconstruction can be reused in a NA62 study, the first proposed selection has been similar to the one used in the previous experiment. The introduced changes concern the order of the cuts, applying first the PID of the charged tracks permitting to identify the interaction vertex, and later the π0_{, and}

on the choice to involve the LKr in the analysis in the discrimination of the charged particles. This is a way to achieve a proof that the analyzed event could be signal exploiting the strong discrimination power of the E/p ratio, shown in Figure 2.4 for MC events involving π, e, µ. Assigning the positron mass to the positive charged track with E/p > 0.9, only 0.8% of the pions are misidentified. This probability is almost 0 for the µ+ _{because, in the}

majority of the events, the muons release the equivalent of a MIP in LKr. Even if the selection is performed on MC events, before starting, a filter must be selected. This is mandatory if one wants to maintain the same analyzer both for MC and data, considering that, in the latter, the filter has been already applied. Since the signal decay involves three tracks, the Restricted3TrackVtx filter best matches its characteristics with the minimum loss of signal events. It accepts the events in which at least a vertex is present, reconstructed with the Least Square Fit (LSF) algorithm (see [19]). Moreover it is required to have the following characteristics:

• only three tracks are used to built it; • the χ2 _{of the Least Square Fit is below 40;}

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Figure 2.3: Mπ0−M_K+ correlation in simulated signal events. The kinematic

cut 2.17 is shown in black, while the red vertical line is the lower limit on M_K+ used in [11].

• vertex momentum is < 90 GeV/c, defined as the magnitude of the sum of the momentum of the three tracks ;

• the reconstructed coordinate along the beamline (Z) must be > 102 m. The drop in the number of events passing the filter is shown in the his-togram of Figure 2.5. The difference between two neighboring bins represents the events lost after a cut. Starting with all the available (O(106_{)) MC events}

("AllEvents"), the filter ("Restricted3TrackVtx") causes a decrease of a factor of ≈ 102_{. "Cedar" indicates the requirement of an event in which}

the Cedar has > 5 sectors enabled. While the filter selection has implicitly selected events where at least 3 tracks are present, the sample is still com-posed by events with a number of tracks ≥ 3. Cuts from "Best 3 Timing" to "Track Timing" discriminate the best three Spectrometer Candidates in each event. Each track is assigned a time (Ti

track) that is the one of the

associated Candidate in the CHOD1 _{or, in absence of it, in the NewCHOD}

or, in absence of both, the time of the Spectrometer Candidate. This search order reflects the timing resolution of the detectors. Using the trigger time

1

In this case the Candidate is a composition of the informations coming from the two planes of the CHOD detector.

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31 h_El_EoP_Positive Entries 10042 Mean 0.2458 Std Dev 0.233 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 E/p ratio 1 10 2 10 3 10 # Events h_El_EoP_Positive Entries 10042 Mean 0.2458 Std Dev 0.233 ± π

E/p ratio distribution for

h_El_EoP_Positive Entries 10042 Mean 0.2458 Std Dev 0.233 + π -π (a) h_El_EoP_Positive Entries 49328 Mean 0.6324 Std Dev 0.4658 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 E/p ratio 1 10 2 10 3 10 # Events h_El_EoP_Positive Entries 49328 Mean 0.6324 Std Dev 0.4658 ± and e + µ

E/p ratio distribution for

+ , e + µ -e (b)

Figure 2.4: (a) E/p ratio for pions obtained using a simulation of K3π

events. (b) E/p ratio distribution obtained from a simulation of a K+ _→

µ+π0_Dνµ (Kµ3D). In this plots simulated decay are preferred since in this

way each different structure of the plot can be assigned to a specific particle.

(Ttrigger), the 3 tracks with the lowest

∆Ti=_|T_tracki _{− T}trigger|, i = 0, 1, ..., Ntracks (2.19)

are taken. Moreover, condition ∆Ti _< _{10 ns} _{is required ("TrackTiming"}

in Figure 2.5). "Qtot" filters events in which the 3 best tracks have total

charge 1, while with "min|−→p |", "χ2 < 30", "4 Chamb" quality checks are indicated, performed on each track, regarding minimum track momen-tum (> 5 GeV/c), fitted χ2_{as returned by the reconstruction algorithm, and}

number of STRAW chambers used to make the fit. The reason for cut on the minimum momentum is clear by looking at Figures 2.6 (a), (b) and (c), in which the efficiency of the reconstruction algorithm of the spectrometer is plotted, defined as the probability to correctly reconstruct a particle track when it passes all the spectrometer stations. Each plot, one for each charged particle, is the result of a bin per bin ratio of two histograms, filled with signal MC events, which have same range and number of bins, containing a "control" sample and a "good events" sample. Each control sample is com-posed by all the events in which the corresponding charged particle reaches the 4 STRAW chambers. To be eligible for the association to a MC parti-cle, a track must be within the geometric acceptance of all the 4 chambers, ensuring that the points extrapolated at each chamber exist. Then each re-constructed point must be within 25 mm from the "truth" position in all the chambers and the difference in the momentum magnitude between the reconstructed track and the MC particle must be less then 1 GeV/c. Finally the charge of the fitted track must be the same of the MC particle. If two tracks can be associated to the same particle, the event is not included in the "good events" sample. In Figure 2.7 the reconstruction efficiency of all

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All EventsRestricted3TracksCedar >=3 RecoTracksBest 3 TimingQtot | p

min |χ2_<304 ChambTrack TimingNeg InLKrAcc≥_{1 Pos InLKrAcc}≥ 4 LKr Clustersno 3_πe- Diff Asso Clusterse±_π₊CDA<20 cmCDA B/VZ Vertπ0 Final Selection

2 10 3 10 4 10 5 10 6 10 # Events

Figure 2.5: Histogram showing the number of events after each selection cut. On the horizontal axis short names of each cut appear. The name of each cut is explained in the text.

three particles is plotted. This is a subset of the described sample, since it also requires that the associated tracks are different from each other. In this case the "control" sample is given by all the events in which all the charged particles reach all the spectrometer chambers.

The second part of the selection is devoted to tag each of the Spectrometer Candidates. Since the calorimeter is exploited, the geometric acceptance of each track on the LKr surface is checked, propagating it with a straight line from its position at STRAW chamber 4. Moreover clusters close to each track impact point, within 50 mm are looked for. If two or more clusters are found in this search, the closest is considered. These requirements are applied to the negative-charge track ("Neg InLKrAcc") and to at least one positive track ("≥ 1 InLKrAcc"). This allows to increase the accep-tance, recovering 30% of events in which the π+ _{is in the LKr acceptance}

but doesn’t produce a cluster.

The condition "≥ 4 LKr Clusters" guarantees the presence of the sufficient number of reconstructed Candidates in the LKr in the association process (1 assigned to the electron, 1 to the positron, two for π0 _{identification) while}

"Diff Asso Clusters" checks that the associated clusters are different from each other. If a negative and a positive track with E/p > 0.9 are found, they

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33 0 10 20 30 40 50 60 70 | [GeV/c] p | 0 0.2 0.4 0.6 0.8 1 ∈ (a) 0 5 10 15 20 25 30 35 40 45 | [GeV/c] p | 0 0.2 0.4 0.6 0.8 1 ∈ (b) 0 5 10 15 20 25 30 35 40 45 | [GeV/c] p | 0 0.2 0.4 0.6 0.8 1 ∈ (c)

Figure 2.6: Reconstruction efficiency of the STRAW chambers plotted re-spect to the three momentum magnitude for the three decay particles: (a) π+, (b) e+, (c) e−.

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34 THE K+ → π+_π0_e+_e− _DECAY 0 10 20 30 40 50 60 70 | [GeV/c] + π p | 0 10 20 30 40 50 60 70 | [GeV/c]-_e p + +_e p| 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 2.7: The plot shows the reconstruction efficiency of all three particles as a function of the π+ _{and e}± _{momentum. The latter is the magnitude of}

~

pe++ ~p_e−.

are considered as the electron and the positron and their energy is computed using the mass-shell relation with the masses of [1], otherwise the event is discarded. The remaining track is assumed to be the π+ _{whose energy is}

evaluated using mπ+ of [1].

The "no 3π" condition is used to suppress K3π events, demanding that

3 X i=1 ~ pi <70 GeV/c (2.20)

where i is the index of the charged tracks. The cut is determined by looking at the distribution of this quantity both in signal and K3π simulated events,

shown in Figure 2.8. In K3π decay, ≈ 98% of events arriving at this cut are

in the interval [70, 78]GeV/c while ≈ 29% in the signal.

The interaction vertex is built using the Closest Distance of Approach (CDA) algorithm, which takes as input the parametric form of the 3 tracks

~

ri = ~r₀i + tiuˆi, i= 1, 2, 3 (2.21) where ~r0, ˆu represent the position and slope at STRAW chamber 1, and i

is the track index. ~r indicates the final computed position. The output is the set of parameters (t1_{, t}2_{, t}3₎ _{at which each track minimize its distance}

respect to the other two. "CDA < 20 cm" set the upper limit on it. The cut value is selected by looking at the distribution of the CDA in simulated signal events, shown in Figure 2.9 (a), and permits to have an acceptance of ≈ 97%.

The distance of the interaction vertex from the nominal beam position is required to be 10 cm ("CDA B/V" ), even in this case getting a 100%

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35 h_Tot_P Entries 2918353 Mean 74.91 Std Dev 0.9497 70 71 72 73 74 75 76 77 78 79 80 | [GeV/c] i p 3 i=1 ∑ | 3 10 4 10 5 10 6 10 #Events/(50 MeV/c) h_Tot_P Entries 2918353 Mean 74.91 Std Dev 0.9497 h_Tot_PSignal Entries 569589 Mean 72.61 Std Dev 1.593 h_Tot_PSignal Entries 569589 Mean 72.61 Std Dev 1.593 π 3 K Signal

Figure 2.8: Superposition of the

P3

i=1~pi

distribution in signal and K3π MC events, normalized to the same number of simulated kaon decays.

Entries 310 Underflow 0 Overflow 9 0 20 40 60 80 100 120 140 160 180 200 220 240 CDA [mm] 0 20 40 60 80 100 #Events/(10 mm) Entries 310 Underflow 0 Overflow 9 (a) Entries 297 Underflow 0 Overflow 0 0 5 10 15 20 25 30 35 40 45 50 Distance [mm] 0 10 20 30 40 50 60 70 80 #Events/(10 [mm]) Entries 297 Underflow 0 Overflow 0 (b)

Figure 2.9: Distributions of (a) three tracks CDA and (b) distance of nominal beam position from interaction vertex in simulated signal events.

signal acceptance (Figure 2.9 (b)). The use of the nominal beam position instead of the one measured by the GTK is to overcome the inefficiency of the latter (but this can be achieved only partially, because the GTK is employed in the initial filter, in the search of a 3 track vertex). The final cut on the vertex concerns its Z coordinate which must be in the region 105 − 175 m ("Z Vert").

Pairs of isolated LKr Candidates within 6 ns from Ttrigger, not associated

to charged tracks, with a total reconstructed energy greater than 2 GeV are used to compute

M_πreco0 =p(k1+ k2)2 (2.22)

k1, k2 being the 4-momenta of the photons and M_πreco0 the reconstructed

neutral pion mass. Considering the very short lifetime of the π0 _(O(10−17_s))_,

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treated as originating in the primary vertex. Then ki = Ei 1, ~ri− ~rvertex |~ri− ~rvertex| (2.23) where Ei is the energy of the ith cluster in LKr and ~ri its position on the

calorimeter surface. ~rvertex is the position of the vertex computed using

the CDA. The "π0_{" label indicates the cut requiring at least two clusters}

to compute Mreco

π0 . At each computation of M_πreco0 corresponds a value of

M_Kreco+ , the reconstructed kaon mass, calculated as the invariant mass of the

sum of all the reconstructed 4-momenta. To discriminate the best pair the quantity:

λ= s _Mreco π0 − Mπ0 σπ 2 + _Mreco K+ − MK+ σ_K+ 2 (2.24) is used, where the Mi are the masses of the indicated particles found in [1].

The σi are the mass resolutions from a Gaussian fit around the peak of the

mass distributions Mπ0, M_K+ for a set of real data, after a π+π_D0 selection.

The cuts applied and the exploited sub-detectors to select K+ _{→ π}+_π0 D

and K+ _{→ π}+_π0_e+_e− _{events are identical, except the request of only one}

isolated cluster in LKr. Otherwise the BR is ≈ 600 times higher and then a reasonable statistics can be reached using few Runs. The fits are shown in Figure 2.10, from which:

σπ = 1.76± 0.02 MeV/c2

σ_K+ = 2.44± 0.03 MeV/c2

(2.25) The photon pair which minimizes λ is selected, and if the corresponding

Entries 22143 Mean 135 Std Dev 3.335 / ndf 2 χ 68.35 / 52 Prob 0.06367 Constant 383.2 ± 4.2 Mean 135.7 ± 0.0 Sigma 1.761 ± 0.024 120 122124 126 128 130 132134 136138 140 142 144146 148 150 ] 2 Mass [MeV/c 0 π 0 50 100 150 200 250 300 350 400 ) 2 #Events/(0.1 MeV/c Entries 22143 Mean 135 Std Dev 3.335 / ndf 2 χ 68.35 / 52 Prob 0.06367 Constant 383.2 ± 4.2 Mean 135.7 ± 0.0 Sigma 1.761 ± 0.024 (a) Entries 22143 Mean 493.6 Std Dev 3.785 / ndf 2 χ 90.18 / 79 Prob 0.1832 Constant 249.1 ± 2.9 Mean 494.1 ± 0.0 Sigma 2.437 ± 0.030 480 482 484486 488 490 492494 496 498 500 502504 506 508 510 ] 2

Kaon Mass [MeV/c 0 50 100 150 200 250 ) 2 #Events/(0.1 MeV/c Entries 22143 Mean 493.6 Std Dev 3.785 / ndf 2 χ 90.18 / 79 Prob 0.1832 Constant 249.1 ± 2.9 Mean 494.1 ± 0.0 Sigma 2.437 ± 0.030 (b)

Figure 2.10: The distributions of (a) Mreco

π0 and (b) M_Kreco+ , for selected K+→

π+_π0

D decays fitted with Gaussian to get the value of the resolution.

M_πreco0 and M_Kreco+ masses lie in a 3σ range around the average of the