A Lepton Universality Test at CERN NA62 Experiment
aa r X i v : . [ h e p - e x ] M a y A Lepton Universality Test at CERN NA62 Experiment
Evgueni Goudzovski
School of Physics and Astronomy, University of Birmingham,Edgbaston, Birmingham, B15 2TT, United Kingdom
The NA62 experiment at CERN collected a large sample of K + → e + ν decays during adedicated run in 2007, aiming at a precise test of lepton universality by measurement of thehelicity suppressed ratio R K = Γ( K + → e + ν ) / Γ( K + → µ + ν ). The preliminary result of theanalysis of a partial data sample of 51089 K + → e + ν candidates is R K = (2 . ± . × − ,which is consistent with the Standard Model expectation. Introduction
Due to the V − A structure of the weak interactions, the Standard Model (SM) rates of theleptonic meson decays P + → ℓ + ν are helicity suppressed. Within the two-Higgs doublet models(2HDM), which is a wide class of models including the minimum supersymmetric (SUSY) one,the charged Higgs boson ( H ± ) exchange induces a tree-level contribution to (semi)leptonicdecays proportional to the Yukawa couplings of quarks and leptons 1. In P + → ℓ + ν decays, the H ± exchange can compete with the W ± exchange, thanks to the above suppression.At tree level, the H ± exchange contribution to P + → ℓ + ν decay widths (with P = π, K, B )is lepton flavour independent, and is approximately described by 2∆Γ( P + → ℓ + ν )Γ SM ( P + → ℓ + ν ) ≈ − (cid:18) M P M H (cid:19) tan β ε tan β . (1)Here M H is the charged Higgs boson mass, tan β is the ratio of vacuum expectation valuesof the two Higgs doublets, a fundamental parameter controlling the charged Higgs couplings,and ε ∼ − is an effective coupling. For a reasonable choice of the parameters (tan β = 40, M H = 500 GeV /c ), one expects ∼
30% relative suppression of B + → ℓ + ν decays, and ∼ . K + → ℓ + ν decays. However the searches for new physics in these decay rates arehindered by the uncertainties of their SM predictions.On the other hand, the ratio of kaon leptonic decay rates R K = Γ( K e ) / Γ( K µ ), wherethe notation K ℓ is adopted for the K + → ℓ + ν decays, has been calculated with an excellentaccuracy within the SM 3: R SM K = ( m e /m µ ) m K − m e m K − m µ ! (1 + δR QED ) = (2 . ± . × − . (2)Here δR QED = ( − . ± . K ℓ γ process.The ratio R K is sensitive to lepton flavour universality violation (LFV) effe cts originating atone-loop level from H ± exchange in 2HDM 4 ,
5, and the mixing effects in the right-handedlepton sector, providing a unique probe into this aspect of supersymmetric flavour physics 6. R K receives the following leading-order contribution due to LFV coupling of the Higgs boson:∆ R K R SM K = (cid:18) M K M H (cid:19) (cid:18) M τ M e (cid:19) | ∆ R | tan β, (3)where | ∆ R | is the mixing parameter between the superpartners of the right-handed leptons,which can reach ∼ − . This can enhance R K by O (1%) relative, with no contradiction topresently known experimental constraints (including upper bounds on the LFV τ → eX decayswith X = η, γ, µµ ).The current world average (including only final results, and thus ignoring the preliminaryNA48/2 ones) is R WA K = (2 . ± . × − , dominated by a recent measurement by theKLOE collaboration 8. The NA62 experiment at CERN collected a dedicated data sample in2007–08, aiming at a measurement of R K with a 0 .
4% precision. The preliminary result obtainedwith a partial data sample is presented here.
The beam line and setup of the NA48/2 experiment 9 were used for the NA62 2007–08 datataking. Experimental conditions and trigger logic were optimized for the K e /K µ measurement.The beam line is capable of delivering simultaneous unseparated K + and K − beams derivedfrom 400 GeV/ c primary protons extracted from the CERN SPS. Most of the data, includingthe sample used for the present analysis, were collected with the K + beam only, as the muonsweeping system provides better suppression of the positive beam halo component. A narrowmomentum band of (74 . ± .
6) GeV/ c was used to minimize the corresponding contribution toresolution in kinematical variables.The fiducial decay region is contained in a 114 m long cylindrical vacuum tank. With1 . × primary protons incident on the target per SPS pulse of 4 . . × particles per pulse. The fractions of K + , π + , p , e + and µ + in the beam are 0.05, 0.63, 0.21, 0.10 and 0.01, respectively. The fraction ofbeam kaons decaying in the vacuum tank at nominal momentum is 18%. The transverse sizeof the beam within the decay volume is δx = δy = 7 mm (rms), and its angular divergence isnegligible.Among the subdetectors located downstream the decay volume, a magnetic spectrometer,a plastic scintillator hodoscope (HOD) and a liquid krypton electromagnetic calorimeter (LKr)are principal for the measurement. The spectrometer, used to detect charged products of kaondecays, is composed of four drift chambers (DCHs) and a dipole magnet. The HOD producingfast trigger signals consists of two planes of strip-shaped counters. The LKr, used for particleidentification and as a veto, is an almost homogeneous ionization chamber, 27 X deep, segmentedtransversally into 13,248 cells (2 × each), and with no longitudinal segmentation. A beampipe traversing the centres of the detectors allows undecayed beam particles and muons fromdecays of beam pions to continue their path in vacuum.A minimum bias trigger configuration is employed, resulting in high efficiency with relativelylow purity. The K e trigger condition consists of coincidence of hits in the HOD planes (the socalled Q signal) with 10 GeV LKr energy deposition. The K µ trigger condition consists of the Q signal alone downscaled by a factor of 150. Loose lower and upper limits on DCH activityare also applied.The main data taking took place during four months starting in June 2007. Two additionalweeks of data taking allocated in September 2008 were used to collect special data samples forstudies of systematic effects. The present analysis is based on ∼
40% of the data sample.
Analysis strategy and event selection
The analysis strategy is based on counting the numbers of reconstructed K e and K µ candidatescollected concurrently. Consequently the result does not rely on kaon flux measurement, andseveral systematic effects (e.g. due to reconstruction and trigger efficiencies, time-dependenteffects) cancel to first order.To take into account the significant dependence of signal acceptance and background levelon lepton momentum, the measurement is performed independently in bins of this observable:10 bins covering a lepton momentum range of [15; 65] GeV/ c are used. The ratio R K in eachbin is computed as R K = 1 D · N ( K e ) − N B ( K e ) N ( K µ ) − N B ( K µ ) · A ( K µ ) A ( K e ) · f µ × ǫ ( K µ ) f e × ǫ ( K e ) · f LKr , (4)where N ( K ℓ ) are the numbers of selected K ℓ candidates ( ℓ = e, µ ), N B ( K ℓ ) are numbers ofbackground events, A ( K µ ) /A ( K e ) is the geometric acceptance correction, f ℓ are efficiencies of e / µ identification, ǫ ( K ℓ ) are trigger efficiencies, f LKr is the global efficiency of the LKr readout,and D = 150 is the downscaling factor of the K µ trigger.A detailed Monte Carlo (MC) simulation including beam line optics, full detector geometryand material description, stray magnetic fields, local inefficiencies of DCH wires, and time vari-ations of the above throughout the running period, is used to evaluate the acceptance correction A ( K µ ) /A ( K e ) and the geometric parts of the acceptances for background processes enteringthe computation of N B ( K ℓ ). The K ℓ γ ) processes are simulated in one-photon approximation3;the resummation of leading logarithms 10 is neglected at this stage. Simulations are used to alimited extent only: particle identification, trigger and readout efficiencies are measured directly.Due to topological similarity of K e and K µ decays, a large part of the selection conditionsis common for both decays: (1) exactly one reconstructed particle of positive electric charge;(2) its momentum 15 GeV /c < p <
65 GeV /c (the lower limit is due to the 10 GeV LKr energydeposit trigger requirement in K e trigger); (3) extrapolated track impact points in DCH, LKrand HOD are within their geometrical acceptances; (4) no LKr energy deposition clusters withenergy E > < K e and K µ decays. K ℓ kinematic identification is based on the reconstructed squared missing mass assuming the trackto be a positron or a muon: M ( ℓ ) = ( P K − P ℓ ) , where P K and P ℓ ( ℓ = e, µ ) are the four-momenta of the kaon (average beam momentum assumed) and the lepton (positron or muonmass assumed). A selection condition | M ( e ) | < M is applied to select K e candidates, and | M ( µ ) | < M for K µ ones, where M varies from 0.009 to 0.013 (GeV /c ) among leptonmomentum bins depending on M resolution. Particle identification is based on the ratio E/p of track energy deposit in the LKr calorimeter to its momentum measured by the spectrometer.Particles with 0 . < E/p < . E/p < .
85) are identified as positrons (muons). K µ decay with a mis-identified muon is the main background source in the K e sample.Sufficient kinematic separation of K e and K µ decays is not achievable at high lepton momentum( p >
30 GeV/ c ), as shown in Fig. 1a. The probability of muon identification as positron in thatmomentum range ( E/p > .
95 due to ‘catastrophic’ bremsstrahlung in or in front of the LKr)is P ( µ → e ) ∼ × − , which is non-negligible compared to R SM K = 2 . × − . A direct rack momentum (GeV/c) ) ( G e V / c m i ss M -0.0200.020.040.06 Ke2 2 µ K Data
Electron mass hypothesis !
Track momentum, GeV/c0 10 20 30 40 50 60 70 80 90 100 e ) → µ P ( -6 × Data (Pb wall)MC (Pb wall)MC (no Pb wall)
Figure 1: (a) Missing mass squared in positron hypothesis M ( e ) vs lepton momentum for reconstructed K e and K µ decays: kinematic separation of K e and K µ decays is possible at low lepton momentum only. (b)Measured and simulated probability of muon identification as electron/positron P ( µ → e ) vs its momentum: datawith the Pb wall, MC simulations with and without the Pb wall (the signal region is marked with arrows). measurement of P ( µ → e ) to ∼ − relative precision is necessary to validate the theoreticalcalculation of the bremsstrahlung cross-section 11 in the high γ energy range used to evaluatethe K µ background.The available muon samples are typically affected by ∼ − electron/positron contaminationdue to µ → e decays in flight, which obstructs the P ( µ → e ) measurements. In order to obtainsufficiently pure muon samples, a 9 . X thick lead (Pb) wall covering ∼
20% of the geometricacceptance was installed in front of the LKr calorimeter (between the two HOD planes) duringa period of the data taking. In the samples of tracks traversing the Pb and having
E/p > . ∼ − by energy losses in Pb.The momentum dependence of P ( µ → e ) for muons traversing the Pb has been measuredwith a data sample collected during a special muon ( µ ± ) run of 20h duration, and compared tothe results of a dedicated Geant4-based MC simulation of the region downstream the spectrom-eter involving standard energy loss processes and bremsstrahlung 11. The data/MC comparison(Fig. 1b) shows good agreement in a wide momentum range within statistical errors, which val-idates the cross-section calculation at the corresponding precision level. The simulation showsthat the Pb wall modifies P ( µ → e ) via two principal mechanisms: 1) muon energy loss in thePb by ionization decreasing P ( µ → e ) and dominating at low momentum; 2) bremsstrahlung inPb increasing P ( µ → e ) and dominating at high momentum.To estimate the K µ background contamination, the kinematic suppression factor is com-puted with the standard setup simulation, while the validated simulation of muon interactionin the LKr is employed to account for P ( µ → e ) suppression. Uncertainty of the backgroundestimate is due to the limited size of the data sample used to validate the simulation. K µ decay followed by µ → e decay contributes significantly to the background. How-ever energetic forward daughter positrons compatible to K e topology are suppressed due tomuon polarization 12. K e γ (SD) decay , a background by R K definition, has a rate similar to that of K e : theworld average 7 is BR = (1 . ± . × − . Theoretical rate calculations depend on the formfactor model, and have a similar precision. Energetic positrons ( E ∗ e >
230 MeV in K + frame)with γ escaping detector acceptance contribute to the background. MC background estimationhas a 15% uncertainty due to limited knowledge of the process. A recent measurement byKLOE 8, published after announcement of the NA62 preliminary result, is not used. Beam halo background in the K e sample induced by halo muons (undergoing µ → e ) (e), (GeV/c M-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08110 Data ν + µ→ + K ) + e → + µ ( ν + µ→ + K ) + (SD γν + e → + KBeam halo ν + e π→ + K π + π→ + K ν + e → + K Track momentum, GeV/c15 20 25 30 35 40 45 50 55 60 65010002000300040005000600070008000 candidates ν + e → + K ν + µ→ + K 25 × ) + e → + µ ( ν + µ→ + K 5 × ) + (SD γν + e → + K 5 × Beam halo
Figure 2: (a) Reconstructed squared missing mass distribution M ( e ) for the K e candidates: data (dots)presented as sum of MC signal and background contributions (filled areas). (b) Numbers of K e candidates andbackground events in lepton momentum bins. Source N B /N tot Source N B /N tot Source N B /N tot K µ (6 . ± . K e γ (SD) (1 . ± . K e . K µ ( µ → e ) (0 . ± . . ± . K π . . ± . Table 1: Summary of the background sources in the K e sample. decay in flight or mis-identified) is measured directly by reconstructing K + e candidates from acontrol K − data sample collected with the K + beam dumped. Background rate and kinematicaldistribution are qualitatively reproduced by a halo simulation. The uncertainty is due to thelimited size of the K − sample. Beam halo is the only significant background source in the K µ sample, measured to be 0 .
25% (with a negligible uncertainty) with the same technique as for K e decays.The number of K ℓ candidates is N ( K e ) = 51 ,
089 (about four times the statistics col-lected by KLOE 8) and N ( K µ ) = 15 . × . The M ( e ) distributions of data eventsand backgrounds are presented in Fig. 2a. Backgrounds integrated over lepton momentum aresummarized in Table 1; their distributions over lepton momentum are presented in Fig. 2b. is measured directly as a function of momentum and LKrimpact point using pure samples of electrons and positrons obtained by kinematic selection of K + → π e + ν decays collected concurrently with the K e sample, and K L → π ± e ∓ ν decaysfrom a special K L run of 15 hours duration. The K + and K L measurements are in good agree-ment. The measured f e averaged over the K e sample is (99 . ± . The geometric acceptance correction A ( K µ ) /A ( K e ) is strongly affected by the radia-tive K e γ (IB) decays. A conservative systematic uncertainty is attributed to approximationsused in the K e γ IB simulation. The resummation of leading logarithms 10 is not taken into ac-count, however no systematic error is ascribed due to that. An additional systematic uncertaintyreflects the precision of beam line and apparatus description in the MC simulation.
Trigger efficiency correction ǫ ( K e ) /ǫ ( K µ ) = 99 .
9% accounts for the fact that K e and K µ decay modes are collected with different trigger conditions: the E >
10 GeV LKr energy rack momentum, GeV/c15 20 25 30 35 40 45 50 55 60 65 × K M eas u r e m e n t s o f R Uncertainties indicated:+halo µ statistical+Ktotal 5 × K R Clark (1972)Heard (1975)Heintze (1976)KLOE (2009)NA62 (2009) final resultpreliminary
PDG’08 June’09 averageSM
Figure 3: (a) Measurements of R K in lepton momentum bins. (b) The world average of R K . Source δR K × Source δR K × Source δR K × Statistical 0.012 Beam halo 0.001 Geom. acceptance 0.002 K µ K e γ (SD) 0.004 IB simulation 0.007 Table 2: Summary of uncertainties of R K : statistical and systematic contributions. deposition signal enters the K e trigger only. A conservative systematic uncertainty of 0.3% isascribed due to effects of trigger dead time which affect the two modes differently. LKr globalreadout efficiency f LKr is measured directly to be (99 . ± . The independent measurements of R K in lepton momentum bins, and the result combinedover the momentum bins are presented in Fig. 3a. The uncertainties of the combined R K aresummarised in Table 2. The preliminary result is R K = (2 . ± . stat . ± . syst . ) × − =(2 . ± . × − , which is consistent with the SM expectation. Analysis of the whole2007–08 data sample is expected to decrease the uncertainty of R K down to 0.4%. A summaryof R K measurements is presented in Fig. 3b: the current world average is (2 . ± . × − . References
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