Precision measurements with Kaon decays at CERN

. The NA62 experiment at CERN collected the world’s largest dataset of charged kaon decays in 2016–2018, leading to the first measurement of the branching ratio of the ultra-rare K + → π + νν decay, based on 20 candidates. Recent results from analyses of K + → π 0 e + νγ , K + → π + µ + µ − and K + → π + γγ decays, using a data sample recorded in 2017–2018, are reported. Preliminary results of the first observation and analysis of the K ± → π 0 π 0 µ ± ν decay, based on the NA48 / 2 data collected in 2003-2004, are also shown.

1 The NA62 experiment NA62 is a fixed target experiment at CERN, designed to measure the branching ratio (BR) of the K + → π + νν decay.Its high-performance experimental apparatus [1,2] is key to this goal, and allows for the study of a broad physics programme: other than the precision measurements reported in the following, recent results have been obtained in direct searches for new physics, which were shown in a dedicated contribution to this conference [3].
2 Measurement of BR(K + → π + νν) The K + → π + νν decay is driven by a flavour changing neutral current s → d, and, as such, the Standard Model (SM) prediction of its BR is of the order of 8 × 10 −11 , with an overall uncertainty of about 10 % which is largely driven by the knowledge of the CKM matrix parameters [4][5][6].Such a process is a golden channel for searching for physics beyond the SM, as many new physics models predict a significant deviation from the SM estimate [7].
The experimental signature of this decay is extremely weak.The key kinematic variable is m 2 miss = (P K + − P π + ) 2 : choosing an appropriate signal region (kept masked until completion of the analysis) gives a factor O(10 4 ) rejection of the background from other kaon decays such as K + → µ + ν, K + → π + π 0 and K + → 3π.This is complemented by an O(10 7 ) muon rejection and an O(10 7 ) photon rejection, which rely on timing between subdetectors of O(100 ps).The estimation of the background from other kaon decays, and from accidental beam particles, is data-driven.The results of the analysis of 2016-2018 data are summarized in figure 1: 20 events were observed, with 10.01 ± 0.42 syst ± 1.19 ext expected SM events and 7.03 +1.05 −0.82 expected background events.This corresponds to a measurement of BR(K + → π + νν) = 10.6 +4.0 −3.4 stat ± 0.9 syst × 10 −11 [8].
Figure 1.Estimated background events and observed events in the K + → π + νν signal region [8].Data are divided in categories depending on hardware configuration and π + momentum.
3 Study of the K + → π 0 e + νγ decay The experimental study of the K + → π 0 e + νγ decay is an important test of Chiral Perturbation Theory (ChPT) [9].Due to infrared and collinear divergences, the decay is studied in three kinematic regions, defined in terms of energy of the radiative photon (E γ ) and angle between the photon and the positron in the K + rest frame (θ eγ ): ) and S 3 (E γ > 10 MeV, 0.6 < cos θ eγ < 0.9).A normalization sample of 6.6 × 10 7 K + → π 0 e + ν events has been selected with a background contamination of 1.6 × 10 −4 .Results of the measurements of R j = BR(K + →π 0 e + νγ|S j ) BR(K + →π 0 e + ν) are shown in table 1: a sub-percent relative uncertainty has been achieved, which constitutes an improvement of a factor at least 2 compared to previous measurements.
ChPT By studying the distribution of the T -odd observable ξ = ⃗ p γ • ⃗ p e × ⃗ p π / m 3 K c 3 (where ⃗ p are the 3-momenta of the particles in the K + rest frame, and m K is the K + mass), a test of T -asymmetry can be performed.The asymmetry A ξ corresponding to this observable is predicted by both the SM and models of new physics to be in the range [−10 −4 , −10 −5 ], apart from one SM extension which predicts −2.5×10 3 [13].The results, which are consistent with no T -asymmetry, have uncertainties larger than all theoretical predictions and are summarized in table 2.

Study of the
Its form factor is parametrized in ChPT by two real parameters a + and b + [15,16].A sample of 27679 K + → π + µ + µ − events has been selected; this sample is almost background free, with an estimation of 7.8 ± 5.6 background events.It is the largest collected sample of this decay, improving by a factor almost 9 from the previous sample, collected by NA48/2 [17].The number of effective kaon decays is estimated to be N K = 3.48 ± 0.09 syst ± 0.02 ext × 10 12 from a normalization sample of K + → π + π + π − events.The signal sample is subdivided in 50 equipopulated bins of z = m 2 µµ /m 2 K (where m µµ is the dimuon invariant mass), and the differential decay rate dΓ/dz is evaluated in each z bin.A chi-square fit is performed on dΓ/dz to extract a + and b + , and the results are shown in figure 2. From the integration of dΓ/dz, the model-independent measurement BR(K + → π + µ + µ − ) = (9.15± 0.08) × 10 −8 is also extracted.Uncertainties on a + , b + and on the BR are dominated by the statistics [18].A measurement of the forward-backward asymmetry A FB , defined as the asymmetry of cos θ Kµ , where θ Kµ is the angle between K + and µ − in the dimuon rest frame, is also performed: A FB = 0.0 ± 0.7 stat ± 0.2 syst ± 0.2 ext × 10 −2 at 68 %CL.This can be translated into the upper limit |A FB | < 0.9 × 10 −2 at 90 %CL [19].

Study of the K + → π + γγ decay
The K + → π + γγ decay is dominated by long distance contributions, and allows for important ChPT tests.The kinematic variable to describe this decay is z = m 2 γγ /m 2 K (where m γγ is the diphoton invariant mass).The O(p 6 ) differential decay width is parametrized by a single real parameter ĉ6 [20].
A sample of 4039 K + → π + γγ decays, with 393 ± 20 background events estimated, has been selected.In each event, the z variable is measured as P K + − P π + 2 /m 2 K , exploiting the excellent spectrometer resolutions.Background comes from photon cluster merging in K + → π + π 0 γ and K + → π + π 0 π 0 decays, or from photons emitted in interaction of undetected pions in K + → π + π + π − decays, and is estimated with simulated samples.A simulated signal sample is reweighted for different values of ĉ6 ; a scan on ĉ6 is performed to find the value which gives the maximum likelihood of the observed data.During the whole procedure, external ChPT parameters are fixed to the values quoted in [21,22]; K 3π amplitudes fit parameters have been recently updated in [23].The resulting preliminary measurement is ĉ6 = 1.713 ± 0.075 stat ± 0.037 syst , and the corresponding signal distribution is plotted in figure 3. A preliminary measurement of the model-dependent BR is also extracted from this fit: BR(K + → π + γγ) = 9.73 ± 0.17 stat ± 0.08 syst × 10 −7 .6 The NA48/2 experiment and study of the K ± → π 0 π 0 µ ± ν decay The NA48/2 experiment collected data in 2003-2004 with simultaneous K ± beams; a detailed description of its apparatus can be found in [24].

Figure 3 .
Figure 3. Preliminary best fit of the K + → π + γγ event candidates.The signal region is defined by z > 0.25.

Figure 4 .
Figure 4. Missing mass squared distributions of the selected data events and simulated signal and background.Vertical lines show the signal region.

Table 2 .
Results from the A ξ measurements and comparison with OKA.Uncertainties are quoted as in table 1.