aa r X i v : . [ h e p - e x ] J u l March 26, 2018
New physics limits from kaon decays
G. Ruggiero
CERN, Geneva, Switzerland
Abstract
Searches for lepton flavour violation and lepton number violation inkaon decays by the NA62 and NA48/2 experiments at CERN are pre-sented. A new measurement of the ratio of charged kaon leptonic decayrates R K = Γ( K e ) / Γ( K µ ) to sub-percent relative precision is discussed.An improved upper limit on the lepton number violating K ± → π ∓ µ ± µ ± decay rate is also reported. The future 10% precision measurement of thebranching ratio of the ultra-rare kaon decay K + → π + νν with the NA62experiment is finally reviewed.PRESENTED AT The Ninth International Conference onFlavor Physics and CP Violation(FPCP 2011)Maale Hachamisha, Israel, May 23–27, 2011
Introduction
In the Standard Model (SM) the decays of charged pseudo scalar mesons ( P ) intolepton neutrino are helicity suppressed.Supersymmetric new physics models, like certain 2-Higgs doublet models (e.g.2HDM type II) [1], predict sizable deviations from the SM via new physics contribu-tions already at tree level. In these frameworks the supersymmetric parameters tan β (the ratio of the two Higgs vacuum expectation values) and M H + (the mass of thecharged Higgs) usually describe the new physics contributions. The dependence ofthese decay rates on tan β and ( M P /M H + ) naturally enhances the sensitivity of the B mesons to new physics, like the B + → τ + ν τ decay. Although similar new physicscontributions for K + → l + ν l could result in 100 times smaller effects, leptonic kaondecays still offer the opportunity to search for new physics thanks to a very highexperimental precision [2]. However, precision measurements in this sectors clashwith the poor knowledge of the hadronic matrix elements which severely limits thetheoretical prediction of Γ( P + → l + ν l ). This uncertainty largely cancels in the ratioof the rates of these decays into different lepton families (e.g. with l = e, µ ), like theparameter R K = Γ( K e ) / Γ( K µ ). Processes with eν or µν in the final state, on theother side, are experimentally accessible only in the π and K sector.The SM prediction for R K inclusive of internal bremsstrahlung (IB) radiation is[3]: R SMK = M e M µ ! M K − M e M K − M µ ! (1 + δR QED ) = (2 . ± . × − , (1)where δR QED is an electromagnetic correction due to the IB and structure-dependenteffects. Deviations of R K from the SM require new physics models with sourcesof lepton flavour violation (LFV) [4, 5]. Within the MSSM, for example, the LFVsources appear at the one loop level via the exchange of the charged Higgs bosoncoupled with a right-handed slepton loop. The dominant contribution is R LF VK ≃ R SMK " (cid:18) M K M H (cid:19) (cid:18) M τ M e (cid:19) | ∆ R | tan β , (2)where | ∆ R | is the mixing parameter between the superpartners of the right-handedleptons, which can reach values up to 10 − . After an appropriate tuning of the newphysics parameters, the effect on R K could be up to % level without contradictingany experimental constraints. Already in the 1970s several experiments measured R K [6, 7, 8], while the present PDG value [9], R K = (2 . ± . × − , is largelydominated by a recent result from KLOE [10]. A new measurement of R K based on apart of a data sample collected by the NA62 experiment (phase I) at CERN in 2007[11] is reported here (section 3). 1aon decays may also contribute to the search for lepton number violation viadecays like K ± → π ∓ µ ± µ ± . They violate the lepton number by 2 units and canproceed only if the ν is a Majorana particle: consequently the limit on their branchingratio provide constraints on the effective Majorana neutrino mass [12]. Such processeswere already studied experimentally by the BNL E865 experiment in 1997 [13]. TheNA48/2 experiment at CERN collected a πµµ sample about 8 times larger thanthe one from E865. It allows improving the limits on the K ± → π ∓ µ ± µ ± processsignificantly [14] (section 4).Among the many rare flavour changing neutral current K and B decays, the ultrarare decays K → πνν play a key role in search for new physics through underlyingmechanisms of flavour mixing. The SM branching ratio can be computed to anexceptionally high degree of precision and the prediction for the K + → π + νν channelis (7 . ± . ± . × − [15]. The first error comes from the uncertainty onthe CKM matrix elements, the second one is the pure theoretical uncertainty. Theextreme theoretical cleanness of these decays remain also in new physics scenarios likeMinimal Flavour Violation (MFV) [16] or non-MFV models [17] and even not largedeviations from the SM value (for example around 20%) can be considered signals ofnew physics. The decay K + → π + νν has been observed by the experiments E787and E949 at the Brookhaven National Laboratory and the measured branching ratiois 1 . +1 . − . × − [18]. However only a measurement of the branching ratio with atleast 10% accuracy can be a significant test of new physics. This is the main goal ofthe NA62 experiment at CERN-SPS [19] (section 5). The NA48/2 and NA62 (phase I) experiments at CERN collected data in 2003-04and 2007-08 using the same beam line and experimental set-up, respectively. NA48/2aimed to the study of the CP violation in the decay of the charged kaons into threepions [20], NA62 to the measurement of the above defined R K ratio. They were fixedtarget experiments which used a 400 GeV/c primary proton beam, extracted fromthe SPS accelerator at CERN, which produced a secondary charged kaon beam afterimpinging on a beryllium target. A 100 m long beam line selected the momentum ofthe secondary beam to (60 ±
3) GeV/c in 2003-04 and (75 ±
2) GeV/c in 2007-08.Finally the beams entered a decay volume, housed in a 100 m long vacuum tank. Witha primary beam intensity of about 7 × protons per SPS spill of 4.8 s duration,the positive (negative) beam flux at the entrance of the decay volume was 3 . × (2 . × ) particles per pulse. The fraction of kaons decaying in the decay volumewas about 20%, depending on the beam energy.The detector was designed to see the charged and neutral products of the kaons de-caying in the vacuum region. A magnetic spectrometer tracked the charged particles.2t was housed in a tank containing He and separated from the vacuum region by aKevlar window. An aluminum beam pipe of 16 cm diameter with vacuum inside, tra-versed the spectrometer and allowed the not decayed beam particles passing throughwithout touching the sensitive detector volume. The spectrometer consisted of fourdrift chambers (DCH) separated by a dipole magnet, which gave to the charged par-ticles an horizontal transverse momentum kick of 120 MeV/c (265 MeV/c) 2003-04(2007-08). The momentum resolution was σ p /p = (1 . ⊕ . × p )% in 2003-04 and σ p /p = (0 . ⊕ . × p )% ( p in GeV/c) in 2007-08.An hodoscope (HOD), made of two orthogonal planes of 64 plastic scintillatorslabs each, followed the magnetic spectrometer. It provided the time reference for theother detectors and the main trigger for the events with charged particles.An electromagnetic calorimeter (LKr), placed after the hodoscope, was used forphoton detection and particle identification. It was a quasi-homogeneous calorimeterwith liquid kripton as active material. A system of Cu-Be ribbons electrodes al-lowed the collection of the ionization signal. In total 13248 projective cells segmentedthe active volume transversely to the beam axis. The total length of the detec-tor corresponded to about 27 X . The measured energy resolution was σ ( E ) /E =0 . / q ( E ) ⊕ . /E ⊕ . E in GeV).An hadronic calorimeter (HAC) and a muon detector (MUV) followed the elec-tromagnetic calorimeter.A detailed description of the NA48/2 layout can be found elsewhere [21]. R K with NA48/2 The measurement of R K has been performed using 40% of the data collected in 2007by NA62. The analyzed data contained only positive kaons.The measurement relied on counting the numbers of reconstructed K e and K µ candidates collected simultaneously. Consequently R K did not depend on the absolutekaon flux and the ratio allowed for a first order cancellation of several systematiceffects, like reconstruction and trigger efficiencies and time dependent biases. Thebasic formula is: R K = 1 D · N ( K e ) − N B ( K e ) N ( K µ ) − N B ( K µ ) · A ( K µ ) f µ ǫ ( K µ ) A ( K e ) f e ǫ ( K e ) · f LKr . (3)Here N ( K l ) and N B ( K l ) are the number of the selected K l events and the expectednumber of background events, respectively; D is the downscaling factor applied tothe K µ trigger; A ( K l ) the geometrical acceptance of the selected K l ; f e and f µ the identification efficiencies of electrons and muons, respectively; ǫ ( K l ) the triggerefficiencies for the selected K l ; f LKr the global LKr efficiency.3 detailed Monte Carlo simulation (MC) was developed, including beam lineoptics and time-dependent detector inefficiencies. The computation of the acceptancecorrection A ( K µ ) /A ( K e ) and the geometrical part of the acceptance entering in thebackground computation relied on MC. The particle identification efficiencies, thereadout and the trigger efficiencies, instead, were measured directly on data. Becauseboth the signal acceptance and the background depended strongly on the leptonmomentum, the measurement was performed in bins of this observable by dividingthe range between 13 and 65 GeV/c in 10 intervals.A large part of the selection was in common between K e and K µ , because ofthe similar single-track topology. Exactly one positive track in the final state, recon-structed in the spectrometer and whose extrapolation passed through the downstreamdetector acceptance, was required; it had to have a momentum within 13 and 65 GeVand the reconstructed longitudinal position of the kaon decay vertex had to be locatedwithin the fiducial decay region. Events with deposits of energy greater than 2 GeVnot associated with the charged tracks in the LKr calorimeter were rejected in orderto further suppress backgrounds with photons in the final state.The event kinematics and the lepton identification were effective to separate K e and K µ . The M miss = ( P K − P l ) characterized completely the kinematics of thesingle track decays. Here P K and P l are the kaon and lepton 4-momenta respectively;the average P K was measured on spill basis using the K + → π + π + π − decays; P l wascomputed in the electron or muon mass hypothesis. A cut around the M miss peak,according to the M miss resolution and dependent on the lepton momentum, selectedthe K l candidates. The ratio E/p of the track energy deposit in the LKr calorimeterto its momentum measured by the spectrometer, identified positrons (0 . < E/p < .
1) and muons (
E/p < . K e and K µ candidates were 59813 and 1 . × ,respectively. The total background was 8 . ± . M miss ( K e ) and thebackground contamination as a function of lepton momentum are shown in figure 1.The background was strongly momentum dependent. In particular for momentahigher than 35-40 GeV/c, the K e kinematics resembled more and more the K µ oneand K µ with a muon mis-identified as a positron became the largest backgroundsource. The accuracy of its evaluation was critical to keep the total systematic un-certainty smaller than the statistical one. The ’catastrophic’ bremsstrahlung in orin front of the LKr was the dominant source of the muon-positron mis-identification.The corresponding probability P µe was measured on data as a function of lepton mo-mentum. During a first period of the 2007 run, data were taken with a 9.2 X leadwall in front of the LKr, covering about 20% of the total geometrical acceptance. Thisset-up allowed the collection of a muon sample free from the about 10 − contamina-tion due to µ → e decays. The sample used for the measurement of R K , however, wastaken without the lead wall. Let P P bµe be the probability of muon mis-identificationin presence of the lead wall and P µe the one without: because of ionization energy4 ) (e), (GeV/c M-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.0401000200030004000500060007000
Data ν + µ→ + K ) + e → + µ ( ν + µ→ + K ) + (SD γν + e → + KBeam halo ν + e π→ + K π + π→ + K ν + e → + K NA62
Lepton momentum, GeV/c20 30 40 50 600100020003000400050006000700080009000 candidates ν + e → + K 5 × ν + µ→ + K 50 × ) + e → + µ ( ν + µ→ + K 5 × ) + (SD γν + e → + K 5 × Beam halo
NA62
Figure 1: Left: reconstructed M miss ( K e ) for K e and backgrounds. Right: leptonmomentum distributions of the K e candidates and the dominant backgrounds.loss and bremsstrahlung in lead P µe and P P bµe differed significantly. Consequently, thevalue measured with the wall was corrected for using a dedicated simulation based onGeant4 [22]. The measured P P bµe varied in the range of (3-5) × − according to themuon momentum and was in agreement with the simulation within the uncertain-ties (about 10% from simulation). The correction f P b varied from +10% to − P P bµe depending on lepton momentum. Its uncertainty was around 2%. The K µ background in the K e sample integrated over lepton momentum was (6 . ± . P P bµe measured on data and f P b from simulation. Thiscombination allowed the minimization of the total uncertainty.The other background components coming from kaon decays were evaluated usingthe MC simulation. The beam halo background induced by halo muons undergoingdecay in flight or mis-identified, was measured by reconstructing positive K e amongdata collected from K − beam with the K + beam blocked while its halo was not. Thesize of the control sample limited the evaluation of the background uncertainty.The acceptance correction was evaluated using MC. The contribution to the K e acceptance due to the radiative K + → e + νγ inner bremsstrahlung process was takeninto account following [23, 24, 25]. The bremsstrahlung suffered by the positrons inthe material upstream of the spectrometer magnet, induced about 6% loss of K e acceptance, as a consequence of the M miss cut. The effect was computed by studyingspectra and rates of bremsstrahlung photons produced by 25 GeV/c (40 GeV/c)electron (positron) beam steered into the DCH acceptance, collected by NA48/2 in2006 (2004). The knowledge of the helium purity in the spectrometer tank was thesecond largest source of systematic uncertainty.The R K value was extracted from a χ fit to the measurements in the lepton5omentum bins, taking into account the bin-to-bin correlations between the system-atic uncertainties. Table 1 summarizes the uncertainties. All the assigned systematicerrors were checked a posteriori by varying the selection criteria and the analysisprocedure. Lepton momentum, GeV/c20 30 40 50 60 × K M eas u r e m e n t s o f R NA62 × K R Clark et al. (1972)Heard et al. (1975)Heintze et al. (1976)
KLOE (2009) = PDG 2010
NA62 (2011) partial data set
PDG’08 Jan’11 average SM Figure 2: Left: measurements of R K in lepton momentum bins. The band indicatesthe average R K and its total uncertainty. Right: the new world average including thepresent result. Source δR K × Statistical 0.011 K µ K decays 0.001Beam halo background 0.001Helium purity 0.003Acceptance correction 0.002Spectrometer alignment 0.001Positron identification efficiency 0.0011-track trigger efficiency 0.002LKr readout inefficiency 0.001Total systematic 0.007Total 0.013Table 1: Summary of the uncertainties on R K .The result is ( χ / ndf = 3.6/9): R K = (2 . ± . stat ± . syst ) × − = (2 . ± . × − . (4)6he individual results in lepton momentum bins and the new world average arepresented in figure 2. The search for K ± → π ∓ µ ± µ ± decay was performed on the NA48/2 2003-04 data,using the K ± → π ± π + π − ( K π ) decay as a normalization channel. A three-trackevent topology was required, with tracks compatible with pion ( E/p < .
95) or muonhypothesis (
E/p < . ), GeV/c - µ + µ ± π M(0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 E ve n t s π K µµπ K ), GeV/c µµπ M(0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 E ve n t s π K Figure 3: Reconstructed M πµµ spectra for candidates with different (left) and samesign (right) muons. Dots are the data.Figure 3 shows the invariant mass spectra of the reconstructed π ± µ ± µ ∓ and π ∓ µ ± µ ± candidates. The K ± → π ± µ ± µ ∓ decay was studied separately [14]. Simu-lations showed that 52 . ± . | M πµµ − M K | < ), mainlydue to K π decays: 52 were found in data. The Feldman-Cousins method [26] wasapplied for the evaluation of the confidence interval, also taking into account thesystematic uncertainty of the background evaluation. This lead to an upper limit of BR ( K ± → π ∓ µ ± µ ± ) < . × − at 90% CL, which improves the best previous limitby almost of a factor 3. 7 The ultra-rare kaon decays: future prospectswith the NA62 experiment
The goal for the future of the NA62 experiment is the measurement of the branchingratio of the K + → π + νν decay with 10% precision. Therefore NA62 aims to collectof the order of 100 K + → π + νν events in about two years of data taking and tokeep the total systematic uncertainty small. To this purpose, at least 10 K + decaysare required, assuming a 10% signal acceptance and a K + → π + νν branching ratioof 10 − . To keep the systematic uncertainty small requires a rejection factor forgeneric kaon decays of the order of 10 , and the possibility to measure efficienciesand background suppression factors directly from data. In order to match the aboverequired kaon intensity, signal acceptance and background suppression, new detectorsmust replace the existing NA62 apparatus.The CERN-SPS extraction line, already used for NA48, can deliver the requiredintensity, asking for 30% more SPS protons on target only. Consequently the NA62experiment will be housed in the CERN North Area High Intensity Facility (NAHIF)where NA48 was located. Considerations about signal acceptance drive the choice ofa 75 GeV/c charged kaon beam with 1% momentum bite. The use of a decay-in-flighttechnique to identify K + decay products is the experimental principle of NA62.The experimental set-up is close to the one used for NA48: a 100 m beam lineto select the appropriate beam, a 80 m evacuated decay volume and detectors down-stream which measure the secondary particles from the kaon decays occurring in thedecay volume.The signature of the signal is one track in the final state matched to one K + track in the beam. The integrated rate upstream is about 800 MHz (only 6% ofthe beam particles are kaons, the other are π + and protons). The rate seen by thedetector downstream is about 10 MHz, mainly due to K + decays. Timing and spatialinformation are needed to match the upstream and downstream track.Backgrounds come from all the kaon decays with one track left in the final stateand from accidental tracks reconstructed downstream matched by chance to a trackupstream. The background suppression profits from the high momentum of the kaonbeam. Different techniques have to be employed in combination in order to reachthe required level of rejection. Schematically they can be divided into: kinematicrejection, precise timing, high efficient photon and muon vetoes, precise particle iden-tification systems to distinguish π + , µ + and positrons.The above requirements drove the design and the construction of the subdetectorssystems. The main subdetectors forming the NA62 layout are: a differential Cerenkovcounter on the beam line to identify the K + in the beam; a Si-pixel beam tracker; aguard-ring counters surrounding the beam tracker to veto catastrophic interactions ofparticles; a downstream spectrometer made by straw chambers in vacuum; a RICH to8istinguish pions and muons; a charged hodoscope; a system of photons veto includinga series of annular lead glass calorimeters surrounding the decay and detector volume,the NA48 LKr calorimeter and a small angle calorimeter to keep the hermetic coveragefor photons emitted at zero angle; a muon veto detector.The design of the experimental apparatus and the R&D of the new subdetectorswas completed in 2010. The experiment is under construction and the first technicalrun is foreseen at the end of 2012. Kaon decays exhibit good sensitivity to new physics thanks to the high experimentalprecision achieved. In most of the cases the sensitivity is complementary to the oneobtained measuring B decays.The NA62 experiment at CERN provided in 2007 the most precise measurementof the lepton flavour parameter R K : R K = (2 . ± . × − . It is consistent withthe SM value and can be used to constrain multi-Higgs new physics scenario. NA48/2improved the upper limit on the branching ratio of the lepton number violating decay K ± → π ∓ µ ± µ ± , which is now 1 . × − .The ultra-rare K → πνν decay is a unique environment where to search fornew physics. The NA62 experiment at CERN-SPS proposes to follow this road bycollecting O (100) events of the K + → π + νν decay. The experiment has been approvedand funded. After three years of successful R&D program, the NA62 experiment isnow under construction. References [1] O. Deschamps, S. Descotes-Genon, S. Monteil, V. Niess, S. T’Jampens andV. Tisserand, Phys. Rev. D (2010) 073012.PHRVA,D82,073012;[2] M. Antonelli et al. , Eur. Phys. J. 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