Searches for lepton number violation and resonances in K± → πμμ decays at the NA48/2 experiment

The NA48/2 experiment at CERN collected in 2003-2004 a large sample of charged kaon decays with multiple charged particles in the final state. A new upper limit on the rate of the lepton number violating decay K± → π∓μ±μ± obtained from this sample is reported. Searches for two-body resonances in the K± → πμμ decays (including heavy neutral leptons and inflatons) in the accessible range of masses and lifetimes are presented.


Introduction
The massive nature of neutrinos has unambiguously been demonstrated by the observation of neutrino oscillations, although, within the Standard Model (SM), neutrinos are massless and right-handed neutrino states are not included. The possibility to include right-handed neutrinos is provided, for example, by the Neutrino Minimal Standard Model (νMSM) [1,2], a SM extension in which sterile neutrinos mix with ordinary neutrinos. In the νMSM three massive right-handed neutrinos are introduced to explain neutrino oscillations, dark matter and the baryon asymmetry of the Universe. The lightest among the three massive neutrinos, with mass of O(1 keV/c 2 ), is a dark matter candidate; the other two, with masses in the range of 100 MeV/c 2 to a few GeV/c 2 , give masses to the SM neutrinos via the see-saw mechanism and introduce extra CP violating phases to explain the baryon asymmetry. In a further extension of the νMSM a real scalar field is added to the theory in order to incorporate inflation and provide a common source for electroweak symmetry breaking and for right-handed neutrino masses [3]. The νMSM and its extension predict the existence of new particles which could be produced in kaon decays. In particular, a Majorana neutrino N 4 is produced on shell in K ± → N 4 µ ± and then decays to N 4 → πµ in both the Lepton Number Violating decay (LNV) K ± → π ∓ µ ± µ ± , which is forbidden in the SM, and in the Lepton Number Conserving decay (LNC) K ± → π ± µ ± µ ∓ [4]. An inflaton χ could be produced in the Lepton Number Conserving (LNC) K ± → π ± χ decay with the subsequent decay χ → µ + µ − [5,6]. The large statistics of kaon decays with multiple charged particles in the final state collected in 2003-2004 by the NA48/2 experiment allows to search for the forbidden LNV K ± → π ∓ µ ± µ ± decay, as well as for two-body resonances in K ± → πµµ decays. The search for the K ± → π ∓ µ ± µ ± together with the limits on the products of branching fractions BR(K ± → µ ± N 4 )BR(N 4 → πµ) and BR(K ± → π ± χ)BR(χ → µ + µ − ) [7] are presented here.
2. The NA48/2 apparatus and data taking conditions The NA48/2 experiment was located in the north area (NA) of the CERN SPS accelerator facility and was a successor of the NA48 experiment with almost the same detector set up. The primary goal of NA48/2 was the search of direct CP violation in K ± → π ± π + π − and K ± → π ± π 0 π 0 decays [4] with about 100 days of effective data taking in 2003-2004. The experiment used 400 GeV/c protons provided by the SPS which, hitting on a Beryllium target, produced a secondary hadronic beam. Thanks to a system of magnets and collimators only charged particles with momenta of (60 ± 3) GeV/c were selected and aligned with the longitudinal axis of the detector within 1 mm and with a transverse size of about 1 cm. The experiment was recording the decays of K + and K − mesons inside the fiducial decay region located in a 114 m long cylindrical vacuum tank. After the vacuum tank a thin Kevlar window separated the vacuum from a helium vessel at atmospheric pressure in which a magnetic spectrometer was located. The spectrometer consisted of four drift chambers (DCH) and a dipole magnet, placed between the second and the third chamber, which provided a horizontal momentum kick of p t = 120 MeV/c for charged particles. Each chamber had four different views and a spatial resolution of σ x,y = 90 µm. The nominal momentum resolution of the spectrometer was σ p /p = (1.02 ⊕ 0.044 p)% where p is given in GeV/c. A scintillating hodoscope (HOD) followed the spectrometer. It was divided in four quadrants by a horizontal and a vertical plane of strip-shaped counters. The HOD was used in the trigger chain to provide a fast time measurement for charged particles with a 150 ps time resolution. A quasi homogeneous electromagnetic calorimeter filled with liquid krypton (LKr) and a depth of 27X 0 was used both for photon detection and particle identification. It had an energy resolution of σ E /E = 0.032/ √ E⊕0.09/E⊕0.0042 (E in GeV) corresponding to σ E /E = 0.94% at 20 GeV. The particle identification was completed by a hadronic calorimeter and a muon veto system (MUV). The hadronic calorimeter consisted of alternated iron and scintillator planes, while the MUV of three plastic scintillator strips planes each of them preceded by a 80 cm iron wall. A more detailed description of the experiment can be found in Ref. [5].

Events selection
Two different samples are selected on the data: candidates for the Lepton Number Violating decay K ± → π ∓ µ ± µ ± (K LN V πµµ ) and Lepton Number Conserving K ± → π ± µ + µ − (K LN C πµµ ) events for the search of resonances. Due to the decay vertex resolution, the signature given by a particle X produced in K → µX (πX) and promptly decaying to X → πµ (X → µ + µ − ) is indistinguishable from a real three-track decay. Therefore the trigger logic of three-track events (the main trigger of the experiment) can be used for the searches presented here. The K ± → π ± π + π − (K 3π ) decay is used as a normalization channel: the same three-track topology and the small difference in mass between π and µ allow a first order cancellation of systematic effects due to possible imperfect kaon beam description and detector and trigger inefficiencies. The three-track event selection requires a total charge of the three tracks equal to one and a vertex inside the 98 m long fiducial decay region. For each track a momentum between 5 and 55 GeV/c is required and a total momentum for the three tracks inside the range 55-65 GeV/c, compatible with the beam momentum. A cut is applied to the total transverse momentum of the three tracks with respect to the beam direction, that is measured using the K 3π sample (p t < 10 MeV/c). The three tracks forming the vertex must be consistent in time with the trigger and within 10 ns from the average time of the three tracks. Each track is required to be inside the geometric acceptance of the DCH, HOD, LKr and MUV detectors. If more than one vertex satisfies the requirements above only the one with the lowest fit χ 2 is taken into account. The K πµµ signal candidates are selected applying particle identification and kinematic constraints. The three tracks have to consist of a π ± candidate and two muons with the same/opposite sign for K LN V πµµ and K LN C πµµ , respectively. The pion candidate is selected by requiring the ratio between the energy deposited in the LKr and the momentum measured in the spectrometer to be E/p < 0.95 and that no in-time associated hits are in the MUV. For muon identification E/p < 0.2 and associated hits in the first two planes of the MUV are required. The signal region satisfies |M πµµ − M K | < 5(8) MeV/c 2 where M πµµ is the invariant mass of the three tracks in the π ∓ µ ± µ ± (π ± µ + µ − ) hypothesis and M K is the nominal K ± mass [10]. The selected region corresponds to ±2 and ±3.2 times the resolution of M πµµ respectively for K LN V πµµ and K LN C πµµ , where σ M (πµµ) = 2.5 MeV/c 2 . The different cuts on the mass resolution is due to the different background composition in the two samples. The data/Monte Carlo agreement is studied in the control region 456 MeV/c 2 < M πµµ < 480 MeV/c 2 . For the K 3π normalization channel the pion identification criteria used for the signal is applied only for the track with opposite electric charge with respect to the kaon and the invariant mass of the three pions must satisfy |M 3π − M K | < 5 MeV/c 2 that corresponds to ±3σ 3π (± 5.1 MeV/c 2 ) where the three-pion mass resolution is 1.7 MeV/c 2 . The number of K ± decays in the fiducial region is measured to N K = 1.637 × 10 11 using the normalization channel K 3π with N 3π = 1.367 × 10 7 and the acceptance A 3π = 14.96%. The events passing the signal selection are shown in Figure 1 for both data and Monte Carlo simulation. Only one event is observed in the signal region for the K LN V πµµ sample while 3489 candidates are selected in the K LN C πµµ sample.  4. Upper limit on BR(K ± → π ∓ µ ± µ ± ) Only one event remains after applying the signal selection. The background expectation is N bkg = 1.16 ± 0.87 stat. ± 0.12 syst. . The background is evaluated with Monte Carlo simulation and is mostly composed of K 3π events in which two pions decay into muons. Since no signal is observed an upper limit is set on BR(K ± → π ∓ µ ± µ ± ) applying the Rolke-Lopez method [11] to find the 90% confidence intervals for the case of a Poisson process in presence of multiple Poisson backgrounds with unknown mean: where D = 100 is the trigger downscaling, N LN V πµµ < 2.92 the upper limit on the signal events at 90% CL and A(K LN V πµµ ) = (20.62 ± 0.01)% the signal acceptance evaluated with Monte Carlo simulation.

Search for two-body resonances
The search for the two-body resonances is performed on all events that survived K ± → µ ± X(X → πµ) and K ± → π ± X(X → µ + µ − ) in the K LN V πµµ and K LN C πµµ selections respectively. Figure 2 shows the obtained signal acceptances as a functions of the resonance mass and lifetime.
In the scan of the invariant mass M ij (ij = πµ, µ + µ − ) the mass step are given by σ(M ij )/2, where σ(M ij ) is the mass resolution, and the signal window by ±2σ(M ij ) at each mass M ij . This means that the results obtained in neighbouring mass hypotheses are highly correlated, as the signal mass window is 8 times larger than the mass step. In total, 284 and 267(280) mass hypotheses have been tested, covering the full kinematic range of the M πµ (M µµ ) distributions for the K LN V πµµ and K LN C πµµ candidates. In the K LN C πµµ selection a total of 3489 candidates is observed where the background contamination from K 3π is estimated to be (0.36 ± 0.10)% using Monte Carlo simulation. This level of purity allows to consider K LN C πµµ as the only background for resonance searches in that sample. For the search of two-body resonances also the Rolke-Lopez statistical method is used. The number of considered background events for the K LN V πµµ (K LN C πµµ ) candidates is N=4 (N=1). The number of observed events and the obtained upper limits at 90% confidence level are shown in Figure 3.  Figure 3. The numbers of observed data (black) and expected background events (K ± → π ± π + π − in green, K ± → π ± µ + µ − in red) are shown for (  For each mass hypothesis of the three resonance searches the local significance z is evaluated as where N obs and N exp are the number of observed and expected background events with their uncertainties δN obs and δN exp . The results for z are also shown in Figure 3. Since the local significances never exceed 3 standard deviations no signal is observed, and upper limits are set on the product BR(K ± → p 1 X)BR(X → p 2 p 3 ), with the three possibilities p 1 p 2 p 3 = µ ± π ∓ µ ± , µ ± π ± µ ∓ , π ± µ + µ − . The upper limits are calculated as a function of the resonance lifetime τ for each mass hypothesis m i by using the values of the signal acceptances (these also depend on the resonances mass and lifetime) and the upper limits on the number of signal events in each mass hypothesis.
The obtained upper limits on the products BR(K ± → p 1 X)BR(X → p 2 p 3 ) are shown in Figure 4.