Note NA62-12-03 12.04.2012

Studies of muon misidentification in the RK analysis Spasimir Balev, Luigi Di Lella, Evgueni Goudzovski, Italo Mannelli

Abstract This note describes the study of the probability for muon misidentification as an electron in Γ(Ke2) the analysis of RK = . A measurement of this probability was performed by using a lead Γ(Kµ2) wall, which suppresses the electron component before the particles reach the Liquid Krypton calorimeter. A Geant4-based simulation was used in order to estimate the bias introduced by the Pb wall with a precision of 2%.

1 Introduction

The problem of muon misidentification as an electron is of extreme importance in the RK analysis. The background from Kµ2 events in the Ke2 sample is the dominant one, averaging

6% in the range of lepton momentum 13ö65 GeV/c and reaching 14% at momenta 50 ∼ ∼ GeV/c in period 5. As seen in Fig. 1 and 2, the two modes are well separated kinematically in the low momentum range, while they practically overlap at high momenta.

2 Mmiss(e) 0.15

0.1

0.05

0

-0.05

-0.1

-0.15 0 10 20 30 40 50 60 70 80 Leptonall mm2e vs. momentum, p GeV/c

Figure 1: Reconstructed missing mass under the Figure 2: Ke2 andKµ2 kinematic separation electron hypothesis for Ke2 (black) and Kµ2 (red) in standard deviations as a function of lepton events as a function of lepton momentum. momentum.

1 107 Data Electrons 106

5 Muons 10

104

103

102 0 0.2 0.4 0.6 0.8 1 1.2 E/p: Energy/Track momentum

Figure 3: E/p distributions for elec- Figure 4: Sketch of the Pb wall. The muon and elec- trons and muons. tron tracks are represented with red and green lines.

A Kµ2 event can pass the Ke2 selection in case both the following conditions, used essen- tially to identify electrons1, are fulfilled: 1. A cluster in the Liquid Krypton calorimeter (LKr) is present within 12 ns with respect ± to the track time, and the cluster distance from the extrapolated position of the track

2 ö on LKr surface is less than 5 cm (1.5 cm) for momenta 13ö25 GeV/c (25 65 GeV/c) . Such a cluster is referred as associated to the track. If at least one extra cluster, not associated to a track, in time with the event (12 ns window), more than 6 cm away from the impact point of the undeflected track on the LKr surface, and with energy more than 2 GeV is present, the event is rejected. 2. The ratio E/p, calculated by the energy of the associated cluster E in LKr and the

momentum of the corresponding track p, as measured by the magnetic spectrometer, is ö in the range (0.90ö1.1) for momenta below 25 GeV/c and (0.95 1.1) for momenta above 25 GeV/c. The measured E/p distributions for electrons and muons are shown in Fig. 3. These two requirements are highly efficient for electrons3, however they can be fulfilled also by Kµ2 events in case of high energetic muon bremsstrahlung or µ e decay. If the → bremsstrahlung or the decay happens after the magnetic spectrometer, the cluster from the emitted photon or electron can be reconstructed in LKr at a distance small enough to allow for association with track and if the second of the above requirements is fulfilled, this event will pass the Ke2 selection. In order to estimate the probability for muon misidentification as an electron (Pµ→e), several plates of lead (the so called lead wall) were installed between the two hodoscope (HOD) planes (see Fig. 4). The nominal thickness of the lead was 45 mm and together with the two iron holders (each 10 mm thick) the total material inserted between the HOD planes amounted 9X0, which is sufficient to suppress the bremsstrahlung photons or the electrons ∼ from µ e decays. The Pb wall covered 20% of the geometrical acceptance and its nominal → ∼ position (including the iron support) was from -32.15 cm to -13.35 cm in the vertical direction (y) and the full range in the horizontal one. The wall was present from run 20152 to run 20404 4

(periods 1ö4), which is 50% of the data taking time . This electron-free muon sample was ∼ the main experimental tool to measure Pµ→e. In addition, three runs with muons (rather than the standard kaon beam) going through the Pb wall were performed, however their usage in the analysis was limited by the presence of an unknown pion component. The strategy of the Kµ2 background estimation is based both on the direct measurement of Pµ→e and on a detailed simulation. The standard, Geant3-based Monte-Carlo simulation of the RK phase of the NA62 experiment (CMC, version 007) is used to generate large sample of Kµ2 decays in order to estimate the amount of events kinematically compatible with Ke2.

1 Full description of the standard Ke2 and Kµ2 selections can be found in [1]. 2The tighter cut on the distance between the cluster and the associated tracks for high momenta is necessary to suppress the background from Kµ2 decays with accidental clusters. 3 The efficiency, averaged over the Ke2 sample in period 5 is (99.27 ± 0.05)% [2]. 4The Pb wall between run 20102 and 20151 inclusive (the beginning of period 1) had different thickness for the Sal`eve side (35 mm) and Jura side (45 mm). This period was not used in the Pµ→e analysis.

2 Material Length, mm Al 4 Air 1000 Scintillator BC-480 (first HOD plane) 20 Air 530 Fe 10 Pb 45 Air 25 Fe 10 Air 170 Scintillator BC-480 (second HOD plane) 20 Air 530 Air 760.5 Al 4 Fe 2.5 G10 50 LKr (passive) 15 LKr (active) 1235

Table 1: Materials simulated in Geant4.

Since the muon bremsstrahlung is not simulated at all in Geant3 and µ e decays are → simulated up to the second HOD plane, the probability for a muon to pass the two electron ID requirements in Section 1 should be estimated separately. The Pb wall provides a direct measurement of Pµ→e (see Section 3), however a correction for the following two effects is necessary:

ˆ the ionization losses in the Pb wall, especially relevant at low momenta, induce a decrease of Pµ→e;

ˆ the contribution from muon bremsstrahlung in the last few radiation lengths of Pb and Fe, which increases Pµ→e, is particularly important at high momenta. These two effects are discussed in more details in Subection 4.1. The simulation tool to study the correction to Pµ→e is described in Section 2.

2 Simulation

To estimate the correction due to the Pb wall, a simulation based on Geant4 [3] was developed. The version used was 9.1, patched to fix a bug in muon bremsstrahlung sampling [4]. All relevant electromagnetic processes were included in the simulation:

ˆ for muons: bremsstrahlung [5], ionisation, pair production, decay;

ˆ for electrons and positrons: multiple scattering, ionisation, annihilation, bremsstrahlung; + −

ˆ for photons: photoelectric and Compton effects, conversion to e e pair. The simulation starts from the aluminium window of the helium tank after the last drift chamber. All the materials downstream are simulated as boxes with thickness corresponding to the length of the materials in the actual experimental setup (see Table 1). The active zone of LKr is 1.235 m long and the transverse section is a square of 22 22 cm2, which corresponds × to the size of one cluster in LKr (see Subsection 4.4). No dead material (spacers, electrodes) is simulated inside the active LKr zone (see Subsection 4.5). On average about 8% of the energy of the developed shower is lost outside the active ∼ LKr volume. A correction for this energy loss is applied in a similar manner as the calibration procedure of the actual clusters in LKr. An electron beam with discrete momentum p is transported through the simulated material (with removed Pb and Fe layers) and the ratio p/Ed is calculated for each p, where Ed is the deposited energy in the active LKr zone. The obtained distribution is approximated with the function f(p) = P1 + exp(P2 + pP3) (see

3 1.092 p/Ed 1.09

1.088

1.086

1.084

1.082

1.08

1.078

1.076 10 20 30 40 50 60 70 Lepton momentum, GeV/c

Figure 5: p/Ed for different electron momenta p and fit with the function f(p) (see text).

Fig. 5). The corrected energy is then f(Ed)Ed (see Subsection 4.3 for systematic studies of LKr calibration). The resolution of E/p is simulated by a Gaussian spread according to the nominal mo- mentum (σp) and energy (σE ) resolutions of the magnetic spectrometer and LKr calorimeter, respectively: σ 0.032 0.09 E = 0.0042, E √E ⊕ E ⊕ σ p = 0.0048 0.00009p, p ⊕ where the quantities are in GeV (see Subsection 4.2). The projective geometry of the LKr calorimeter is not simulated and the muon beam is always perpendicular to the material layers. Therefore, the track-shower association is ideal. Due to the time consuming development of the showers inside LKr, all particles in the event are fully tracked only if a muon decays or catastrophic5 bremsstrahlung occurs. A high-speed simulation of the muon bremsstrahlung was developed [6], in order to crosscheck the detailed one and to perform fast systematic studies (see Subsection 4.7).

3 Pµ→e measurement

In order to measure Pµ→e, a sample of events which satisfy the standard Kµ2 selection [1] is used with some changes. The following requirements are of particular interest:

ˆ The track should fall into the lead wall acceptance. The chosen limits in vertical direc- tion at the second HOD plane ( 31.3

ˆ The conditions 1. and 2. (see Section 1) for electron identification should be fulfilled.

The events selected by the nominal Ke2 trigger are normalised by a sample of muons from Kµ2 decays, selected without electron ID conditions and with the nominal Kµ2 trigger (accounting for its different downscaling in different periods). In order to use the obtained Pµ→e for background estimation, the correlation between E/p 2 and Mmiss should be taken into account [7]. This correlation leads to a significant dependence 2 of Pµ→e as a function of Mmiss (see Fig. 6). The effect, whose real origin is the correlation

5With energy of the bremsstrahlung photon at least 0.7 of muon momentum.

4 2 Figure 6: Pµ→e as a function of Mmiss(µ) for data and for Monte-Carlo events, where linear energy deposition spectrum in the vicinity of E = Emax is assumed.

between E/p and the momentum resolution, is taken into account separately for each of the ten RK analysis momentum bins [8]. Alternatively, Pµ→e can be measured by applying the 2 Mmiss(e) cut under the electron hypothesis, which requires no additional correction due to such correlation, but leads to loss of precision. Pµ→e can be estimated also with Kµ2 events outside the Pb wall in the low momentum range (below 35 GeV/c) where kinematical separation between Kµ2 and Ke2 is possible (see Fig. 1) [10]. This measurement relies on a precise evaluation of all the possible background contributions by using CMC simulated events. Due to the very large backgrounds above 35 GeV/c (mainly from Ke2) and below 20 GeV/c (mainly from Ke3), this study is not used in the RK analysis and only demonstrates the agreement between Pµ→e from data and Geant4 simulation without Pb wall, with limited precision (see Fig. 7 and 8). The Kµ2 background to the Ke2 sample can be estimated directly by applying the standard

Ke2 selection for events passing the Pb wall during periods 1ö4 [9]. An acceptance correction factor f = A(Ke2)/A(Kµ2) is applied, where A is the ratio of Kl2 events falling into the Pb wall geometry and the total number of Kl2 events in the standard geometrical acceptance. This factor is obtained from data collected during period 5 without Pb wall. In the direct measurement extra clusters behind the Pb wall are vetoed in order to suppress the background from K+ π+π0, which is concentrated in the last momentum bin (60-65 GeV/c) and is as → large as the statistical precision of the measurement (of the order of few percents). Fig. 9 presents a comparison between different methods of estimation of the background in period 5, which shows good agreement and results in uncertainty on RK smaller than 0.1%.

5 P(→ e ) P(→ e ) b) Backgrounds: a) Data G4 NO Pb wall Ke2 G4 Pb wall Ke2 (KLOE)

Ke3 e K()2 →

K&K2 D e3D Halo Background-free P(→e ) Track momentum, GeV/c P(→ e )

c)

Track momentum, GeV/ c Track momentum, GeV/c

Figure 7: Estimation of Pµ→e without Pb wall from data for 0.95 < E/p< 1.1. (a) Various back- ground components evaluated in terms of Pµ→e; (b) comparison between data (blue) and Geant4 simulation (red – without Pb wall; green – with Pb wall); (c) difference between Pµ→e obtained from data and the simulated one, fitted with constant.

P(→ e ) P(→ e ) a) Data b) Backgrounds: G4 NO Pb wall

Ke2 G4 Pb wall

Ke2 (KLOE)

Ke3 e K()2 →

K&K2 D e3D Halo Background-free P(→e ) Track momentum, GeV/ c P(→ e )

c)

Track momentum, GeV/ c Track momentum, GeV/c

Figure 8: Estimation of Pµ→e without Pb wall from data for 0.90 < E/p< 1.1. See the caption of Fig. 7.

6 0.16 Kµ2 background 0.14

0.12

0.1

0.08

0.06

0.04

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0 10 20 30 40 50 60 Track momentum, GeV/c

Figure 9: Comparison of Kµ2 background to Ke2 events obtained with different methods: dark blue – direct background estimation as described in the text; red – estimation with CMC events and 2 Pµ→e obtained from data with nominal Mmiss cut under electron hypothesis; green – estimation 2 with CMC events and Pµ→e obtained from data with nominal Mmiss cut under muon hypothesis, 2 with Pµ→e to Mmiss correlation taken into account. The reason for the discrepancy in the last momentum bin is the presence of K+ → π+π0 background, not subtracted from the blue histogram. At low momenta the background contribution measured directly comes mainly from the beam halo. The comparison with the estimation of halo background from K-less and K− runs (light blue) is reasonable, however it is only of illustrative value, since the effect of the pion component in the halo traversing the Pb wall is not taken into account.

4 Systematic studies of Pµ→e and the Pb wall correc- tion 4.1 Introductory remarks

While the Monte-Carlo estimation of Pµ→e can be significantly biased by several effects, related to the relative simplicity of the Geant4 simulation (e.g. no simulation of the electric pulse formation due to the drift of the ionization electrons), the effect of the Pb wall can be simulated with much better precision. In order to estimate the background from Kµ2 to Ke2 the measured 6

probability Pµ→e from Kµ2 events passing the Pb wall during periods 1ö4 is used , multiplied by a correction factor fP b, which is the ratio of simulated Pµ→e without Pb wall to the Pµ→e with Pb wall. This strategy is largely based on substantial cancellation of various effects, related to the LKr response, which are difficult to control and simulate. In particular, in the presence of Pb wall, the emission of a bremsstrahlung photon occurs in LKr for 70% of the muons ∼ misidentified as electrons at high energies, so the only difference with respect to the case without the Pb wall is the additional small ionization loss in Pb and Fe. Possible bias to fP b

6 → 2 The correlation between Pµ e and Mmiss is taken into account.

7 -5 x 10 Pµ→e

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 10 20 30 40 50 60 70 80 Track momentum, GeV/c

Figure 10: Fraction of muons misidentified as electrons, as a function of muon momentum, in the presence of the Pb wall. The red histogram corresponds to cases with bremsstrahlung occurring in LKr, the black one - in the last few radiation lengths of Pb.

−6 −6 Resolution RMS of Pµ→e in 10 Pµ→e in 10 fP b E/P peak (no Pb wall) (45 mm Pb wall)

nominal σE , nominal σp 0.013 3.811 4.538 0.839 no σE , no σp 0.003 3.633 4.362 0.833 no σE , nominal σp 0.012 3.779 4.497 0.840 2 × σE, nominal σp 0.017 3.897 4.642 0.839 3 × σE, nominal σp 0.022 4.000 4.833 0.828

Table 2: Stability of Pµ→e and fP b with respect to energy (σE ) and momentum (σp) resolution.

can come mainly from the simplified simulation of the LKr geometry and from the calibration for the 30% of the misidentified muons with bremsstrahlung in the last Pb and Fe layers ∼ (see Fig. 10). Those systematic effects are discussed in details in the following subsections.

4.2 Resolution effects The nominal energy resolution of the LKr calorimeter used in the simulation is valid for particles starting their shower development near the LKr surface. Since the catastrophic bremsstrahlung can occur deeper inside LKr and still give sufficient energy deposit to satisfy the E/p condition in electron ID, the resolution for such particles could be somewhat different. This bias is difficult to be estimated precisely due to various simplifications in the simulation, but the main contributing effects (the LKr calibration and geometry) are studied in details in subsections 4.3 and 4.4. In order to check the sensitivity of Pµ→e and fpb, the simulated resolution is varied in an extreme range (see Table 2, [11]). While Pµ→e changes by 2% when the RMS of the E/p ∼ peak is varied between its experimental values (from 0.012 to 0.016, depending on the selection requirements and background suppression cuts [12]), the effect on fP b is negligible.

8 1.01 -5 y, cm x 10 Pµ→e 100 1.008 0.5 1.006

0.4 50 1.004

1.002 0.3 0 1

0.998 0.2 -50 0.996

0.1 0.994

-100 0.992 0 10 20 30 40 50 60 70 0.99 -100 -50 0 50 100 Track momentum, GeV/c eop cor x, cm

Figure 11: Pµ→e estimated with calibration correction Figure 12: Calibration correction as a (red) and without calibration correction (blue). The function of x- and y-coordinate at LKr. difference for high momenta is due to the presence of a ”hot” spot, visible on Fig. 12.

-5 x 10 Pµ→e fP b 0.7 1.05

0.65 (a) (b) 1 0.6

0.55 0.95 0.5

0.45 0.9

0.4 0.85 0.35

0.3 0.8 0.25

0.2 0.75 20 25 30 35 40 45 50 55 60 65 70 20 25 30 35 40 45 50 55 60 65 70 Track momentum, GeV/c Track momentum, GeV/c

Figure 13: Simulated Pµ→e (a) and fP b (b) for variations of the calibration correction by ±0.5% (red), ±0.3% (blue), ±0.1% (green) in comparison with the nominal one (black).

9 4.3 Calibration Various corrections to the energy deposited in LKr are applied at different stages – from reconstruction to the analysis itself. The largest among them is the 7% correction, applied ∼ to the energy of the reconstructed cluster, which accounts for the losses outside the 11 11 × cells (or 22 22 cm2) area, used for energy sum [13]. At analysis level, a fine (x,y)-dependent × tuning of the E/p ratio is performed by using electrons from Ke3 decays [14]. The effect of this calibration on the measured Pµ→e is significant (Fig. 11) due to the ”hot spot” below the beam pipe, which is covered by the Pb wall (Fig. 12). While this spot is not accessible for

calibration during periods 1ö4, its presence was noticed also during the 2008 data taking [15], therefore the Pµ→e evaluation relies on the assumption its stability during 2007 data taking. As mentioned in Section 2, the calibration in the simulation has the same purpose as the one for data: to fix the E/p peak at 1 for electrons. Due to the electron energy loss of 50 ∼ MeV upstream LKr, the nominal calibration will tend to overcorrect the E/p ratio for photons by 0.1% at high momenta. Pµ→e and fP b for simulated events were estimated for various ∼ shifts in the calibration correction. It can be seen from Fig. 13(a) that a 0.5% relative change of the calibration factor can lead to more than 15% variation of Pµ→e. At the same time ∼ however, fP b is very stable, varying from 2% at low momenta, where the Kµ2 background ∼ is negligible, to less than 1% at high momenta (see Fig. 13(b)). ∼ Another aspect of the calibration correction, which shows the difficulties of its control in the simulation, is that, while it is obtained from electrons hitting the LKr calorimeter, later on it is applied for photons which may be produced by bremsstrahlung deeper inside the LKr. Since the correction both in data and MC is not z-dependent, it will tend to overcorrect showers which start at depth larger than the averaged one for the particles used for calibration. More details about this effect can be found in [16].

4.4 LKr geometry The geometry of the LKr active volume in the Geant4 simulation is very simple – the energy deposited is calculated inside a box with transverse dimensions 22 22 cm2, which corresponds × to the 11 11 cells around the maximum of the shower’s energy, used in the standard cluster × reconstruction. The projectivity geometry of LKr is not taken into account. By simulating active LKr volumes with different sizes (from the extreme case of 2 2 cm to the other × extreme – infinite transverse dimensions) it can be demonstrated that 1 cm difference in the half-width of the transversal size leads to 2% change of Pµ→e and less than 1% change of ∼ fP b [16]. The difference between Pµ→e with the nominal size of the LKr volume and for infinite transverse dimensions (with 20 times smaller calibration correction in the later case) is 10%. − Accordingly fP b is changing by 6%, which would result in a 0.3% change of RK . This is the ∼ largest variation of fP b observed and is given here only for illustration of its stability. Figures 14, 15, 16 and 17 show various details about the study of the LKr active zone geometry.

4.5 Passive material in LKr In the Geant4 simulation the passive material inside the active LKr volume (electrodes, spacers, Neutral Hodoscope) is not simulated. If 1 cm of active LKr at depth 9.5X0 is replaced by ∼ passive LKr (which corresponds approximately to the material of the Neutral Hodoscope inside LKr, placed at the averaged maximum of shower development), the calibration correction reaches 10%. The Pµ→e value for 50 GeV increases by 8% with respect to the nominal ∼ ∼ one, while the Pb wall correction fP b changes by less than 1% [17].

4.6 µ → e decays 7 Kµ2 followed by µ e decays after the second HOD plane can contribute to Pµ→e if the → electron is carrying more than 95% of the muon energy and is almost collinear with it. The fact that muons from Kµ2 are fully polarized strongly suppresses this effect to a negligible level [18].

7 The background from Kµ2 followed by µ → e decays before HOD is simulated separately using CMC.

10 Calibration correction 2.305 1.035

1.034 2.3 1.086

1.033 2.295 2 × 2cm 22 × 22cm 40 × 40 cm 1.084 1.032 2.29 1.031 2.285 1.082 1.03 2.28 1.029 1.08 2.275 1.028

2.27 1.078 1.027

2.265 1.026 25 50 75 25 50 75 25 50 75 Track momentum, GeV/c Figure 14: Momentum dependence of the calibration correction for different transverse sizes of the active LKr volume.

-5 -5 x 10 x 10 Pµ→e 0.5 0.5 0.45 0.45 0.4 0.4 0.35 0.35 0.3 0.3 0.25 0.25 0.2 0.2 -5 5 10 15 20 -5 5 10 15 20 x 10 (a) x 10 (b) 0.6 0.6 0.55 0.55 0.5 0.5 0.45 0.45 0.4 0.4 0.35 0.35 0.3 0.3 5 10 15 20 5 10 15 20 a1/2, cm (c) (d)

Figure 15: Pµ→e as a function of the active LKr zone half-width (a1/2) for 4 momentum intervals (in GeV/c): 15-20 (a), 30-35 (b), 40-45 (c) and 60-65 (d). A fit with linear function is shown around the nominal half-width of 11 cm.

11 -7 x 10 ∆Pµ→e -0.1

-0.2

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-0.9 10 20 30 40 50 60 70 80 90 100 Track momentum, GeV/c

Figure 16: ∆Pµ→e for difference of 1 cm in the half-width of the active LKr zone as a function of muon momentum.

fP b 1 1 1

0.95 0.95 0.95

0.9 0.9 0.9

0.85 0.85 0.85

0.8 0.8 0.8

0.75 0.75 0.75

0.7 0.7 0.7 10 20 10 20 10 20 35-40 40-45 45-50 1 1 1

0.95 0.95 0.95

0.9 0.9 0.9

0.85 0.85 0.85

0.8 0.8 0.8

0.75 0.75 0.75

0.7 0.7 0.7 10 20 10 20 10 20 50-55 55-60 60-65 a1/2, cm

Figure 17: fP b as a function of the active LKr zone half-width for the last 6 momentum intervals. A fit with a linear function is shown around the nominal half-width of 11 cm.

12 -5 x 10

0.55 Pµ→e (a) 0.5 0.45 0.4 0.35 0.3 0.25 10 20 30 40 50 60 70 80 Track momentum, GeV/c 1.3 fP b (b) 1.2 1.1 1 0.9 0.8 0.7 10 20 30 40 50 60 70 Track momentum, GeV/c

Figure 18: (a) Comparison between Pµ→e obtained with the fast simulation (markers) and full Geant4 simulation (points with error bars), for the case with Pb wall (green and blue) and without Pb wall (red and black). The agreement at high momenta is satisfactory. (b) Comparison between fP b obtained with the fast simulation (red markers) and with the full Geant4 simulation (points with error bars). The agreement is excellent over the entire momentum range.

4.7 Fast simulation

The fast simulation mentioned in Section 2 is based on 36 layers of material, each with 1 X0 (9 layers corresponding to the Pb wall and the iron holders, 1 for the dead material before LKr and 26 for the active LKr). For the development of the shower in the LKr, shower libraries produced by Geant4 are used. Muon ionisation loses are simulated, as well as the energy and momentum resolution. The size of LKr in transverse dimensions is infinite. Millions of events with high energy deposit can be simulated in few minutes. The comparison with the full Geant4 simulation shows excellent agreement (see Fig. 18).

4.8 Application of HOD veto The Pb wall correction can be minimised by rejecting muons which interact more intensively with the Pb wall and therefore produce signals in the counters of the second HOD plane larger than what is expected from a single MIP [19]. Before using the pulse height as a veto for such muons, it should be corrected for the light attenuation in the scintillating slab, depending on the x-coordinate of the hit. This is done separately for each of the six horizontal counters, covered by the Pb wall, on a run-to-run basis (see Fig. 19). The correction essentially puts the maximum of the pulse height distribution to 200 ADC counts, which roughly corresponds ∼ to the expectations for one MIP. Since the HOD uses 10 bit ADC, the maximum available pulse height is 1023 ADC counts. A muon which produces catastrophic bremsstrahlung most likely will give an overflow in the HOD ADC. In order to use the HOD veto in the simulation, the deposit in the second scintillator plane should be calculated. The comparison between the corrected pulse height distribution (from data) and the energy deposited in the HOD plane (from the simulation) is shown in Fig. 20. Several upper limits for the corrected pulse height are selected in order to study the veto effect: 250, 300, 350, 400, 450, 500, 550 ADC counts. The corresponding energy deposits from the

13 Average pulse height

300

275

250

225

200

175

150

125

100 0 20 40 60 80 100 120 |x|, cm Figure 19: An example of pulse height correction for light attenuation in one counter. The average pulse height as a function of x position of the track on HOD (black histogram) is fitted with cubic function (red curve). The blue histogram is the corrected pulse height.

x 10 2

6000 5000 (a) 4000 3000 2000 1000 Average pulse height 0 0 200 400 600 800 1000 1200

20000 17500 (b) 15000 12500 10000 7500 5000 2500 EHOD , GeV 0 0 2.5 5 7.5 10 12.5 15 17.5 20 22.5

Figure 20: (a) Corrected pulse height in ADC counts from data and (b) energy deposit in the second HOD plane from the simulation. The ”knee” right from the peak, which corresponds to approximately two times the MIP energy deposition, is due to e+e− pair production.

14 4.4 3.7 5 5 4.3 Pµ→e×10 (a) Pµ→e×fP b × 10 (c)

4.2

4.1 3.65

4

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3.6 250 300 350 400 450 500 550 no 3.55 1

0.98 fP b (b)

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0.88 3.45 0.86

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0.8 3.4 250 300 350 400 450 500 550 no 250 300 350 400 450 500 550 no HOD veto cut

Figure 21: (a) Measured Pµ→e for different cuts on the corrected HOD pulse height. The last bin represents the nominal values, obtained without HOD veto. (b) Simulated fP b for corresponding cuts on the energy deposited in the second scintillator. (c) Corrected probability for muon misiden- tification (Pµ→e×fP b) for different HOD veto cuts. The error in the last bin corresponds to the statistical precision of the measurement of Pµ→e; the errors on the other points are uncorrelated with respect to the last one.

Monte-Carlo (in MeV) are: 4.69, 5.63, 6.56, 7.50, 8.44, 9.37, 10.31. The effect on Pµ→e from data and on the simulated correction fP b is significant – applying the most relaxed cut leads to a 12% drop of Pµ→e, averaged over the momentum interval from 35 to 65 GeV/c (Fig. 21 (a)), while the corresponding cut in the simulation leads to an almost three times smaller correction (Fig. 21 (b)). The corrected Pµ→e is presented in Fig. 21 (c), which shows stability within the total statistical uncertainty and only 1% difference for the most relaxed cut, far from the peak of the distributions, where imperfections in the simulation and in the correction procedure are expected to play a role.

4.9 Stability with respect to E/p cut

The background contribution from Kµ2 decays strongly depends on the lower limit of the E/p cut used for electron identification. Pµ→e and fP b were obtained for different lower limits of E/p cut: from 0.90 to 0.97 in 0.01 steps. The background for the extreme E/p > 0.90 cut increases by a factor of three with respect to the nominal one (see Fig. 22), while RK in period 5 changes only by 0.4% (see Fig. 23), fully consistent with the total systematic error on RK coming from muon misidentification (0.22%) [20].

5 Conclusions and effect on RK

The measured Pµ→e is shown in Fig. 24 in comparison with the simulated one. Various studies described in details in Section 4 suggest that the control over Pµ→e with the developed Geant4 simulation is difficult. In order to simulate Pµ→e with a precision better than 10% ∼ a complete description of the LKr geometry, digitization and reconstruction is needed – a task which is currently in progress for the K+ π+νν¯ program of the NA62 experiment. →

15 0.18 2.505

B/S RK 0.16 2.5 0.14

0.12 2.495 0.1 2.49 0.08

0.06 2.485 0.04 2.48 0.02

0 2.475 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 (E/p) cut (E/p) cut

Figure 22: Kµ2 background in the Ke2 sam- Figure 23: RK stability with respect to the ple for different lower limits of the E/p cut in lower limit of the E/p cut in period 5. period 5. 6 5.5 1.15e Pb µ 10

NA62 /P NA62 × e e µ 1.1 Pb µ MC

5 =P Pb

f 1.05 E/p>0.95 4.5 1

4 0.95 0.9 Data 3.5 0.85

3 0.8

Mis-identification probability P E/p>0.90 0.75 2.5 0.7 10 20 30 40 50 60 70 10 20 30 40 50 60 70 Muon momentum, GeV/c Muon momentum, GeV/c

Figure 24: Pµ→e for muons traversing the lead Figure 25: fP b for two different E/p cuts and wall for 0.95 < E/p < 1.1 as function of mo- ±2% error bands as a function of lepton mo- mentum: measurement (solid circles with er- mentum. ror bars) and simulation (solid line). The sys- tematic uncertainty of 10% is represented by dotted line.

16 However, the quality of this simple simulation is sufficient to extract the correction due to the muon interactions with the Pb wall with 2% precision (see Fig. 25). In terms of the RK ∼ uncertainties from the Kµ2 background estimation (excluding the contribution from µ e → decays) the different components of the total systematic error are as follows [21]:

ˆ 0.16% due to the limited size of the Kµ2 sample used for Pµ→e measurement with Pb wall;

ˆ 0.12% due to the uncertainty of fP b from Geant4 simulation; 2 ˆ 0.08% due to the model dependence of the Mmiss vs E/p correlation.

The total background from Kµ2 decays in period 5 is (6.10 0.22)% averaged over the ± entire lepton momentum range. The total systematic uncertainty from this background is two times smaller than the statistical error of RK .

References

[1] NA62 analysis web page, http://goudzovs.web.cern.ch/goudzovs/ke2/selection.html. [2] Winhart A., Talk at NA62 analysis meeting from 20.05.2010, slide 13. [3] Geant4 Physics Reference Manual. [4] Goudzovski E., Talk at NA62 analysis meeting from 13.12.2007, slide 3. [5] S.R.Kelner, R.P.Kokoulin, A.A.Petrukhin. Phys. Atomic Nuclei, 60 (1997) 576. [6] Mannelli I., Talk at NA62 analysis meeting from 25.10.2007. [7] Di Lella L., private communication. [8] Goudzovski E., Talk at NA62 analysis meeting from 25.03.2010, slides 3-7. [9] Mannelli I., Balev S., Talk at NA62 weekly meeting from 04.03.2010., slides 11-12. [10] Balev S., Talks at NA62 analysis meetings from 29.10.2009, slides 30-31 and from 09.12.2009, slides 9-10. [11] Balev S., Talk at NA62 analysis meeting from 25.03.2010, slide 6. [12] Winhart A., private communication. [13] Unal G., NA48 note, 95-10; Norton A., Talk at NA48 analysis meeting, February 2004. [14] Winhart A., Various talks at NA62 analysis meetings, 2007-2010. [15] Winhart A., private communication. [16] Balev S., Talks at NA62 analysis meetings from 11.12.2008 and from 23.03.2010, slides 10-12. [17] Balev S., Talk at NA62 analysis meeting from 25.03.2010, slide 13. [18] Balev S., Talk at NA62 analysis meeting from 28.01.2009. [19] Di Lella L., Talk at NA62 analysis meeting from 12.07.2007. [20] Goudzovski E., Talk at NA62 analysis meeting from 16.12.2010. [21] C.Lazzeroni, et al, PLB 698 (2011) 105-114.

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