Search for K^+ decays to a muon and invisible particles
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN-EP-2021-01828 January 2021
Search for K + decays to a muon and invisible particles The NA62 Collaboration
Abstract
The NA62 experiment at CERN reports searches for K + → µ + N and K + → µ + νX decays, where N and X are massive invisible particles, using the 2016–2018 data set. The N particle is assumed to be a heavy neutral lepton, and the results are expressed as upperlimits of O (10 − ) of the neutrino mixing parameter | U µ | for N masses in the range 200–384MeV/ c and lifetime exceeding 50 ns. The X particle is considered a scalar or vector hiddensector mediator decaying to an invisible final state, and upper limits of the decay branchingfraction for X masses in the range 10–370 MeV/ c are reported for the first time, rangingfrom O (10 − ) to O (10 − ). An improved upper limit of 1 . × − is established at 90% CLon the K + → µ + νν ¯ ν branching fraction. To be submitted to Physics Letters B a r X i v : . [ h e p - e x ] J a n he NA62 Collaboration ∗ Universit´e Catholique de Louvain, Louvain-La-Neuve, Belgium
E. Cortina Gil, A. Kleimenova, E. Minucci , , S. Padolski , P. Petrov, A. Shaikhiev ,R. Volpe TRIUMF, Vancouver, British Columbia, Canada
T. Numao, Y. Petrov, B. Velghe
University of British Columbia, Vancouver, British Columbia, Canada
D. Bryman , J. Fu Charles University, Prague, Czech Republic
T. Husek , J. Jerhot , K. Kampf, M. Zamkovsky Institut f¨ur Physik and PRISMA Cluster of Excellence, Universit¨at Mainz, Mainz,Germany
R. Aliberti , G. Khoriauli , J. Kunze, D. Lomidze , L. Peruzzo, M. Vormstein, R. Wanke Dipartimento di Fisica e Scienze della Terra dell’Universit`a e INFN, Sezione diFerrara, Ferrara, Italy
P. Dalpiaz, M. Fiorini, I. Neri, A. Norton , F. Petrucci, H. Wahl INFN, Sezione di Ferrara, Ferrara, Italy
A. Cotta Ramusino, A. Gianoli
Dipartimento di Fisica e Astronomia dell’Universit`a e INFN, Sezione di Firenze,Sesto Fiorentino, Italy
E. Iacopini, G. Latino, M. Lenti, A. Parenti
INFN, Sezione di Firenze, Sesto Fiorentino, Italy
A. Bizzeti , F. Bucci Laboratori Nazionali di Frascati, Frascati, Italy
A. Antonelli, G. Georgiev , V. Kozhuharov , G. Lanfranchi, S. Martellotti, M. Moulson,T. Spadaro Dipartimento di Fisica “Ettore Pancini” e INFN, Sezione di Napoli, Napoli, Italy
F. Ambrosino, T. Capussela, M. Corvino , D. Di Filippo, P. Massarotti, M. Mirra,M. Napolitano, G. Saracino Dipartimento di Fisica e Geologia dell’Universit`a e INFN, Sezione di Perugia,Perugia, Italy
G. Anzivino, F. Brizioli, E. Imbergamo, R. Lollini, R. Piandani , C. Santoni INFN, Sezione di Perugia, Perugia, Italy
M. Barbanera, P. Cenci, B. Checcucci, P. Lubrano, M. Lupi , M. Pepe, M. Piccini Dipartimento di Fisica dell’Universit`a e INFN, Sezione di Pisa, Pisa, Italy
F. Costantini, L. Di Lella , N. Doble , M. Giorgi, S. Giudici, G. Lamanna, E. Lari,E. Pedreschi, M. Sozzi INFN, Sezione di Pisa, Pisa, Italy
C. Cerri, R. Fantechi, L. Pontisso, F. Spinella
Scuola Normale Superiore e INFN, Sezione di Pisa, Pisa, Italy
I. Mannelli 2 ipartimento di Fisica, Sapienza Universit`a di Roma e INFN, Sezione di Roma I,Roma, Italy
G. D’Agostini, M. Raggi
INFN, Sezione di Roma I, Roma, Italy
A. Biagioni, E. Leonardi, A. Lonardo, P. Valente, P. Vicini
INFN, Sezione di Roma Tor Vergata, Roma, Italy
R. Ammendola, V. Bonaiuto , A. Fucci, A. Salamon, F. Sargeni Dipartimento di Fisica dell’Universit`a e INFN, Sezione di Torino, Torino, Italy
R. Arcidiacono , B. Bloch-Devaux, M. Boretto , E. Menichetti, E. Migliore, D. Soldi INFN, Sezione di Torino, Torino, Italy
C. Biino, A. Filippi, F. Marchetto
Instituto de F´ısica, Universidad Aut´onoma de San Luis Potos´ı, San Luis Potos´ı,Mexico
J. Engelfried, N. Estrada-Tristan Horia Hulubei National Institute of Physics for R&D in Physics and NuclearEngineering, Bucharest-Magurele, Romania
A. M. Bragadireanu, S. A. Ghinescu, O. E. Hutanu
Joint Institute for Nuclear Research, Dubna, Russia
A. Baeva, D. Baigarashev, D. Emelyanov, T. Enik, V. Falaleev, V. Kekelidze, A. Korotkova,L. Litov , D. Madigozhin, M. Misheva , N. Molokanova, S. Movchan, I. Polenkevich,Yu. Potrebenikov, S. Shkarovskiy, A. Zinchenko † Institute for Nuclear Research of the Russian Academy of Sciences, Moscow,Russia
S. Fedotov, E. Gushchin, A. Khotyantsev, Y. Kudenko , V. Kurochka, M. Medvedeva,A. Mefodev Institute for High Energy Physics - State Research Center of Russian Federation,Protvino, Russia
S. Kholodenko, V. Kurshetsov, V. Obraztsov, A. Ostankov † , V. Semenov † , V. Sugonyaev,O. Yushchenko Faculty of Mathematics, Physics and Informatics, Comenius University,Bratislava, Slovakia
L. Bician , T. Blazek, V. Cerny, Z. Kucerova CERN, European Organization for Nuclear Research, Geneva, Switzerland
J. Bernhard, A. Ceccucci, H. Danielsson, N. De Simone , F. Duval, B. D¨obrich, L. Federici,E. Gamberini, L. Gatignon, R. Guida, F. Hahn † , E. B. Holzer, B. Jenninger, M. Koval ,P. Laycock , G. Lehmann Miotto, P. Lichard, A. Mapelli, R. Marchevski, K. Massri, M. Noy,V. Palladino , M. Perrin-Terrin , , J. Pinzino , V. Ryjov, S. Schuchmann , S. Venditti University of Birmingham, Birmingham, United Kingdom
T. Bache, M. B. Brunetti , V. Duk , V. Fascianelli , J. R. Fry, F. Gonnella,E. Goudzovski ∗ , J. Henshaw, L. Iacobuzio, C. Lazzeroni, N. Lurkin , F. Newson,C. Parkinson , A. Romano, A. Sergi , A. Sturgess, J. Swallow3 niversity of Bristol, Bristol, United Kingdom H. Heath, R. Page, S. Trilov
University of Glasgow, Glasgow, United Kingdom
B. Angelucci, D. Britton, C. Graham, D. Protopopescu
University of Lancaster, Lancaster, United Kingdom
J. Carmignani, J. B. Dainton, R. W. L. Jones, G. Ruggiero
University of Liverpool, Liverpool, United Kingdom
L. Fulton, D. Hutchcroft, E. Maurice , B. Wrona George Mason University, Fairfax, Virginia, USA
A. Conovaloff, P. Cooper, D. Coward , P. Rubin ∗ Corresponding author: Evgueni Goudzovski, email: [email protected] † Deceased Present address: CERN, European Organization for Nuclear Research, CH-1211 Geneva 23, Switzerland Also at Laboratori Nazionali di Frascati, I-00044 Frascati, Italy Present address: Brookhaven National Laboratory, Upton, NY 11973, USA Also at Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia Present address: Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48, Bratislava,Slovakia Also at TRIUMF, Vancouver, British Columbia, V6T 2A3, Canada Present address: Department of Astronomy and Theoretical Physics, Lund University, Lund, SE 223-62,Sweden Present address: Universit´e Catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium Present address: Institut f¨ur Kernphysik and Helmholtz Institute Mainz, Universit¨at Mainz, Mainz, D-55099,Germany Present address: Universit¨at W¨urzburg, D-97070 W¨urzburg, Germany Present address: European XFEL GmbH, D-22761 Hamburg, Germany Present address: University of Glasgow, Glasgow, G12 8QQ, UK Present address: Institut f¨ur Physik and PRISMA Cluster of excellence, Universit¨at Mainz, D-55099 Mainz,Germany Also at Dipartimento di Fisica, Universit`a di Modena e Reggio Emilia, I-41125 Modena, Italy Also at Faculty of Physics, University of Sofia, BG-1164 Sofia, Bulgaria Present address: Institut f¨ur Experimentelle Teilchenphysik (KIT), D-76131 Karlsruhe, Germany Present address: Institut am Fachbereich Informatik und Mathematik, Goethe Universit¨at, D-60323 Frankfurtam Main, Germany Also at Department of Industrial Engineering, University of Roma Tor Vergata, I-00173 Roma, Italy Also at Department of Electronic Engineering, University of Roma Tor Vergata, I-00173 Roma, Italy Also at Universit`a degli Studi del Piemonte Orientale, I-13100 Vercelli, Italy Also at Universidad de Guanajuato, Guanajuato, Mexico Present address: Institute of Nuclear Research and Nuclear Energy of Bulgarian Academy of Science (INRNE-BAS), BG-1784 Sofia, Bulgaria Also at National Research Nuclear University (MEPhI), 115409 Moscow and Moscow Institute of Physics andTechnology, 141701 Moscow region, Moscow, Russia Present address: DESY, D-15738 Zeuthen, Germany Present address: Charles University, 116 36 Prague 1, Czech Republic Present address: Physics Department, Imperial College London, London, SW7 2BW, UK Present address: Aix Marseille University, CNRS/IN2P3, CPPM, F-13288, Marseille, France Also at Universit´e Catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium Present address: INFN, Sezione di Pisa, I-56100 Pisa, Italy Present address: Department of Physics, University of Warwick, Coventry, CV4 7AL, UK Present address: INFN, Sezione di Perugia, I-06100 Perugia, Italy Present address: Center for theoretical neuroscience, Columbia University, New York, NY 10027, USA Present address: Dipartimento di Fisica dell’Universit`a e INFN, Sezione di Genova, I-16146 Genova, Italy Present address: Laboratoire Leprince Ringuet, F-91120 Palaiseau, France Also at SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA 94025, USA ntroduction All Standard Model (SM) fermions except neutrinos are known to exhibit both chiralities. Theexistence of right-handed neutrinos, or heavy neutral leptons (HNLs), is hypothesised in manySM extensions to generate non-zero masses of the SM neutrinos via the seesaw mechanism [1].For example, the Neutrino Minimal Standard Model [2] accounts for dark matter, baryogenesis,neutrino masses and oscillations by postulating two HNLs in the MeV–GeV mass range and athird HNL at the keV mass scale, which is a dark matter candidate.Mixing between HNLs (denoted N below) and active neutrinos gives rise to HNL productionin meson decays. The expected branching fraction of the K + → µ + N decay is [3] B ( K + → µ + N ) = B ( K + → µ + ν ) · ρ µ ( m N ) · | U µ | , where B ( K + → µ + ν ) is the measured branching fraction of the SM leptonic decay [4], | U µ | isthe mixing parameter, and ρ µ ( m N ) is a kinematic factor which depends on the HNL mass m N : ρ µ ( m N ) = ( x + y ) − ( x − y ) x (1 − x ) · λ / (1 , x, y ) , (1)with x = ( m µ /m K ) , y = ( m N /m K ) and λ (1 , x, y ) = 1 + x + y − x + y + xy ). The factor ρ µ ( m N ) increases from unity at m N = 0 to a maximum of 4.13 at m N = 263 MeV/ c , anddecreases to zero at the kinematic limit m N = m K − m µ . Assuming that the HNL decaysexclusively to SM particles, its lifetime in the mass range m N < m K exceeds 10 − / | U | µ s,where | U | is the largest of the three coupling parameters | U (cid:96) | ( (cid:96) = e, µ, τ ) [5]. Thereforeunder the above assumption, and additionally assuming conservatively that | U (cid:96) | < − , theHNL can be considered stable in production-search experiments.A hypothetical scalar or vector hidden sector mediator X with mass m X < m K − m µ andcoupling preferentially to the muon can be produced in K + → µ + νX decays. The existence ofsuch a light mediator offers a solution to the muon g − X particle is expected to decay promptlywith a sizeable invisible branching fraction. In the case of a vector mediator, gauge invariancerequires the decay X → ν ¯ ν . In the light DM freeze-out model, the decay X → χ ¯ χ is expected,where χ is the DM particle.The K + → µ + νν ¯ ν decay occurs within the SM at second order in the Fermi constant G F ,and the expected branching fraction at leading order in chiral perturbation theory, B SM =1 . × − [7], is experimentally out of reach. The strongest upper limit to date, B ( K + → µ + νν ¯ ν ) < . × − at 90% CL, has been established by the BNL-E949 experiment [8].The K + → µ + N , K + → µ + νX and K + → µ + νν ¯ ν decays with invisible N and X particlesare characterised by a single muon and missing energy in the final state. Searches for thesedecays using the data collected by the NA62 experiment at CERN in 2016–2018 are reportedhere. The N particle is interpreted as a HNL, and the results are presented as upper limits ofthe extended neutrino mixing matrix element | U µ | for m N in the range 200–384 MeV/ c , withthe assumption that the HNL lifetime exceeds 50 ns. For the K + → µ + νX decays (in a numberof m X hypotheses within the range 10–370 MeV/ c ) and the K + → µ + νν ¯ ν decay, upper limitson the branching fractions are reported. The layout of the NA62 beamline and detector [9] is shown schematically in Fig. 1. An un-separated secondary beam of π + (70%), protons (23%) and K + (6%) is created by directing400 GeV/ c protons extracted from the CERN SPS onto a beryllium target in spills of 3 s effectiveduration. The central beam momentum is 75 GeV/ c , with a momentum spread of 1% (rms).5 -1-212
100 150 200 250 Z [m] Y [ m ] GTK
CHANTI LAVKTAGTarget MUV1,2STRAW IRCLKr
Vacuum
MUV3Iron
RICHRICH
DumpCHODSAC S CR C O L M Figure 1: Schematic side view of the NA62 beamline and detector.Beam kaons are tagged with 70 ps time resolution by a differential Cherenkov counter(KTAG) using as radiator nitrogen gas at 1.75 bar pressure contained in a 5 m long vessel.Beam particle positions, momenta and times (to better than 100 ps resolution) are measuredby a silicon pixel spectrometer consisting of three stations (GTK1,2,3) and four dipole magnets.A muon scraper (SCR) is installed between GTK1 and GTK2. A 1.2 m thick steel collimator(COL) with a central aperture of 76 ×
40 mm and outer dimensions of 1 . × . is placedupstream of GTK3 to absorb hadrons from upstream K + decays (a variable aperture collimatorof 0 . × .
15 m outer dimensions was used up to early 2018). Inelastic interactions of beamparticles in GTK3 are detected by an array of scintillator hodoscopes (CHANTI). The beam isdelivered into a vacuum tank evacuated to a pressure of 10 − mbar, which contains a 75 m longfiducial decay volume (FV) starting 2.6 m downstream of GTK3. The beam divergence at theFV entrance is 0.11 mrad (rms) in both horizontal and vertical planes. Downstream of the FV,undecayed beam particles continue their path in vacuum.Momenta of charged particles produced by K + decays in the FV are measured by a magneticspectrometer (STRAW) located in the vacuum tank downstream of the FV. The spectrometerconsists of four tracking chambers made of straw tubes, and a dipole magnet (M) located betweenthe second and third chambers that provides a horizontal momentum kick of 270 MeV/ c . Themomentum resolution achieved is σ p /p = (0 . ⊕ . p )%, where the momentum p is expressedin GeV/ c .A ring-imaging Cherenkov detector (RICH), consisting of a 17.5 m long vessel filled withneon at atmospheric pressure (with a Cherenkov threshold for muons of 9.5 GeV/ c ), is used forthe identification of charged particles and for time measurement with 70 ps precision for particleswell above the threshold. Two scintillator hodoscopes (CHOD), which include a matrix of tilesand two planes of slabs arranged in four quadrants downstream of the RICH, provide triggersignals and time measurements with 200 ps precision.A 27 X thick quasi-homogeneous liquid krypton (LKr) electromagnetic calorimeter is usedfor particle identification and photon detection. The calorimeter has an active volume of 7 m , issegmented in the transverse direction into 13248 projective cells of approximately 2 × , andprovides an energy resolution σ E /E = (4 . / √ E ⊕ /E ⊕ . E is expressed in GeV. Toachieve hermetic acceptance for photons emitted in the FV by K + decays at angles up to 50 mradto the beam axis, the LKr calorimeter is supplemented by annular lead glass detectors (LAV)installed in 12 positions inside and downstream of the vacuum tank, and two lead/scintillatorsampling calorimeters (IRC, SAC) located close to the beam axis. An iron/scintillator samplinghadronic calorimeter formed of two modules (MUV1,2) and a muon detector (MUV3) consistingof 148 scintillator tiles located behind an 80 cm thick iron wall are used for particle identification.6he data sample used for this analysis is obtained from 0 . × SPS spills recorded during410 days of operation in 2016–2018, with the typical beam intensity increasing over time from1 . × to 2 . × protons per spill. The latter value corresponds to a mean instantaneousbeam particle rate at the FV entrance of 500 MHz, and a mean K + decay rate in the FV of3.7 MHz. Data recorded with a minimum-bias trigger based on CHOD signals [10], downscaledby a factor of 400, is used for the analysis. This trigger is 99% efficient for single chargedparticles in the CHOD acceptance. The rates of the signal processes are measured with respect to the K + → µ + ν decay rate.This approach benefits from first-order cancellations of residual detector inefficiencies not fullyaccounted for in simulations, as well as trigger inefficiencies and random veto losses common tosignal and normalization modes.Candidate signal decays, as well as the K + → µ + ν decay, are characterised by a single muonand no other detectable particles in the final state. Backgrounds are due to beam particle decaysupstream of the vacuum tank, decays to multiple detectable particles, and inelastic interactionsof beam particles in GTK3. Event selection is optimized to suppress these backgrounds. Theprincipal selection criteria are listed below. • A positively charged muon track is required to be reconstructed in the STRAW spec-trometer with momentum in the range 5–70 GeV/ c . The track’s trajectory through theSTRAW chambers and its extrapolation to the LKr calorimeter, CHOD and MUV3 shouldbe within the geometrical acceptance of these detectors. The muon time is evaluated usingthe RICH and CHOD signals spatially associated with the track. • Particle identification criteria are applied to the STRAW track to suppress the backgroundsdue to misidentification. The ratio of the energy deposited in the LKr calorimeter, E , tothe momentum, p , measured by the STRAW spectrometer is required to be E/p < . c , a particle identification algorithm is appliedbased on the RICH signal pattern within 3 ns of the CHOD time. In particular, trackswith momenta below the muon Cherenkov threshold must not be identified as positrons.At least one signal in the MUV3 detector must be within 3 ns of the muon time andspatially consistent with the projected track impact point in the MUV3 front plane. • Backgrounds from K + → µ + ν decays upstream of the KTAG and π + → µ + ν decaysupstream of GTK3, in coincidence with a beam pion or proton track in the GTK, aresuppressed by requiring a kaon signal in the KTAG detector within 1 ns of the muon time. • The decay vertex is defined as the point of closest approach of the K + track in the GTKand the muon track in the STRAW, taking into account the stray magnetic field in thevacuum tank. Identification of the K + track in the GTK relies on the time difference,∆ t GK , between a GTK track and the KTAG signal, and spatial compatibility of the GTKand STRAW tracks quantified by the distance, d , of closest approach. A discriminant D (∆ t GK , d ) is defined using the ∆ t GK and d distributions measured with K + → π + π + π − decays [11]. Among GTK tracks with | ∆ t GK | < . D value most consistent with a K + → µ + decay. It isrequired that d < • Background from K + → µ + ν decays between KTAG and GTK3 with pileup in the GTKis suppressed by geometrical conditions. The reconstructed K + decay vertex is requiredto be located in the FV at a minimum distance from the start of the FV, varying from7 .1 - - /c [GeV m ) / c E v en t s / ( . G e V Data ) g ( n + mfi + K(non-Gaussian tail)) g ( n + mfi + K - p + p + pfi + K n + m pfi + KUncertainty on theestimated background /c [GeV m =200 MeV/c X m =300 MeV/c X m nnn + mfi + K /c [GeV m0.40.60.811.21.4 Figure 2: Left: reconstructed m distributions for data and the estimated background. Thefull uncertainties ( ± σ ) in each mass bin of the background spectrum for m > | m | < .
01 GeV /c used for normal-isation are indicated with arrows. Top-right: the region m > .
03 GeV /c , with simulatedhypothetical K + → µ + νX (scalar mediator model, two m X values) and K + → µ + νν ¯ ν signalswith branching fractions of 10 − . Bottom-right: ratio of data and simulated spectra in the region m > .
03 GeV /c with the full uncertainties. Systematic components of the uncertaintiesare correlated among the bins.8 m to 35 m depending on the angle between the K + momentum in the laboratory frameand the muon momentum in the K + rest frame. • Backgrounds from K + decays to multiple detectable particles are suppressed by veto condi-tions. The muon track must not form a vertex with any additional STRAW track segment.Energy deposits are not allowed in the LKr calorimeter that are spatially incompatible withthe muon track within 12 ns of the muon time. No activity is allowed in the large-angle(LAV) or small-angle (SAC, IRC) photon veto detectors within 3 ns of the muon time,or in the CHANTI detector within 4 ns of the muon time. No more than two signalsin the CHOD tiles within 6 ns of the muon time, and no more than three signals in theRICH PMTs within 3 ns of the muon time, spatially incompatible with the muon track,are allowed. Data loss due to the veto conditions from accidental activity (random veto)averaged over the data sample is measured to be about 30%.The squared missing mass is computed as m = ( P K − P µ ) , where P K and P µ are thekaon and muon 4-momenta, obtained from the 3-momenta measured by the GTK and STRAWspectrometers under the K + and µ + mass hypotheses.Monte Carlo simulations of particle interactions with the detector and its response are per-formed with a software package based on the Geant4 toolkit [12]. The m spectra of theselected events from data and simulated samples, and their ratio, are displayed in Fig. 2. Thesignal from the SM leptonic decay K + → µ + ν is observed as a peak at m = 0 with a reso-lution of 1 . × − GeV /c , and the SM signal region is defined in terms of the reconstructedsquared missing mass as | m | < .
01 GeV /c . In contrast, the K + → µ + N , K + → µ + νX and K + → µ + νν ¯ ν decays are characterised by larger m values.8 Normalisation to the K + → µ + ν decay The effective number of K + decays in the FV, denoted N K , is evaluated using the number of K + → µ + ν candidates reconstructed in the data sample. The quantity N K is not correctedfor trigger inefficiency and random veto effects, which cancel between signal and normalisationthus making the N K value specific to this analysis. The background in the SM signal region isnegligible (Fig. 2). It is found that N K = N SM A SM · B ( K + → µ + ν ) = (1 . ± . × , where N SM = 2 . × is the number of selected data events in the SM signal region, A SM =0 . ± .
005 is the acceptance of the selection for the K + → µ + ν decay evaluated usingsimulations, and B ( K + → µ + ν ) = 0 . ± . A SM , which dominates that of N K , is mainly systematic due to the accuracyof the simulation, and is evaluated by variation of the selection criteria including the algorithmused for identification of the K + track in the GTK. The main backgrounds to the potential signals at large m values are due to the K + → µ + νγ , K + → π µ + ν ( π → γγ ) and K + → π + π + π − decays inside and upstream of the vacuumtank. Their contributions are estimated with simulations. The K + → µ + νγ decay is simulatedincluding inner bremsstrahlung (IB) and structure-dependent processes, and the interferencebetween these processes [13].The K + → µ + νγ and K + → π µ + ν backgrounds arise from the photon detection inefficiencyin the hermetic NA62 photon veto system, and photon conversions in the STRAW and RICHdetectors. Photon detection inefficiency is modelled for the simulated events using the LAV,LKr, IRC and SAC inefficiencies measured as functions of photon energy using a K + → π + π decay sample [14]. To evaluate the systematic uncertainties in the background estimates, analternative photon veto response model is used for the simulated events involving photon detectorinefficiencies increased by one sigma of the measurements, and a conservative assumption thatphotons converting upstream of the STRAW spectrometer dipole magnet are not detected inthe LAV, IRC and SAC systems. The latter assumption accounts for the different photon vetoconditions used in this analysis with respect to those used for the inefficiency measurements [14].The resulting systematic uncertainty of the estimated background comes mainly from the limitedaccuracy of the LAV inefficiency measurements. In particular, the LAV inefficiency is measuredto be (0 . ± . K + → µ + νγ decays intercepting the LAV geometrical acceptance.The accuracy of the description of the non-Gaussian m tails of the K + → µ + ν ( γ ) decayis affected by the limited precision in the simulation of beam particle pileup and inefficiency inthe GTK. This leads to a deficit of simulated events in the negative tail of the m distributionpopulated by the K + → µ + ν ( γ ) decays only (Fig. 2). For example, a 40% deficit is observed inthe region m < − .
05 GeV /c . To account for the missing component in the positive tail, itis assumed that the non-Gaussian tails of the m spectrum are left-right symmetrical. A “tail”component (shown separately in Fig. 2) is added to the estimated background in each m binin the region m > m = 0. A 100% uncertainty is conservatively assignedto this component to account for the above assumption.9able 1: Estimated backgrounds in the kinematic region m > . /c with their uncer-tainties. The uncertainties labelled “PV” are systematic due to the accuracy of the photon vetoefficiency modelling (positively correlated among the background sources), and the one labelled“tail” is systematic and accounts for the accuracy of the non-Gaussian m tail simulation.Background source Estimated background K + → µ + νγ ± stat ± PV ± tail K + → π µ + ν ± stat ± PV K + → π + π + π − ± stat Total background 7549 ± stat ± syst The composition of the estimated background in the kinematic region m > . /c is reported in Table 1. The largest component is the radiative K + → µ + νγ (IB) tail, andits uncertainty is dominated by a contribution due to the accuracy of the description of thenon-Gaussian tail. Further systematic uncertainties due to beam tuning, calibrations, triggerand reconstruction efficiency are negligible compared with the overall systematic uncertaintyfrom the sources considered. The background represents an O (10 − ) fraction of the numberof reconstructed SM K + → µ + ν candidates. Within the region m > .
03 GeV /c , theestimated background agrees with the data within uncertainties as shown in Fig. 2. K + → µ + N decays The K + → µ + N process is investigated in 269 mass hypotheses, m N , within the HNL searchregion 200–384 MeV/ c . Distances between adjacent m N values considered are 1 (0.5) MeV/ c below (above) the mass of 300 MeV/ c . The decay is characterised by a narrow peak in thereconstructed missing mass ( m miss ) spectrum. Therefore the K + → µ + N event selection requiresthat | m miss − m N | < . σ m for each mass hypothesis m N , where σ m is the mass resolutionevaluated with simulations, as shown in Fig. 3 (left). The resolution improves by a factor ofthree with respect to the NA62 2015 data sample collected without the GTK spectrometer [15].Considering the peaking nature of the K + → µ + N signal, the background in each m N hypothesis is evaluated using sidebands in the reconstructed m miss spectrum of the data events.This method is more precise than one based on simulation. Sidebands are defined in each masshypothesis as 1 . σ m < | m miss − m N | < . σ m , additionally requiring that m miss is within therange 188–386 MeV/ c . The number of expected background events, N exp , within the ± . σ m signal window is evaluated with a second-order polynomial fit to the sideband data of the m miss spectrum, where the bin size is 0 . σ m . The uncertainty, δN exp , in the number of expectedbackground events includes statistical and systematic components. The former comes from theuncertainties in the fit parameters, while the latter is evaluated as the difference between valuesof N exp obtained from fits using second and third order polynomials. The dominant contributionto δN exp is statistical, although systematic uncertainties become comparable as m N approachesthe boundaries of the HNL search region. Systematic errors due to possible HNL signals inthe sidebands are found to be negligible; this check is made assuming | U µ | to be equal to theexpected sensitivity of the analysis. The uncertainty in the background estimate, δN exp /N exp ,increases from 1–2% for m N below 300 MeV/ c to 10% at the upper limit of the HNL searchregion.The signal selection acceptance, A N , as a function of m N obtained with simulations assuminginfinite HNL lifetime is displayed in Fig. 3 (right). The acceptance for a mean lifetime of 50 ns(considering decays to detectable particles) is lower by O (1%) in relative terms, making theresults of the search valid for lifetimes in excess of 50 ns. For shorter lifetimes, the HNL meandecay length in the laboratory frame becomes comparable to or smaller than the length of the10
00 150 200 250 300 350 ] HNL mass [MeV/c012345678 ] M a ss r e s o l u t i on [ M e V / c
100 150 200 250 300 350 ] HNL mass [MeV/c00.050.10.150.20.25 A cc ep t an c e Figure 3: HNL mass resolution σ m (left) and acceptance A N of the selection (right) evaluatedfrom simulations as functions of the HNL mass. Boundaries of the HNL search region areindicated by vertical arrows.apparatus. Acceptances for lifetimes of 5 (1) ns decrease by factors up to 2 (10), dependingon m N . Simulations reproduce the m resolution at the K + → µ + ν peak to a 1% relativeprecision. Modelling of the resolution outside the peak is validated using data and simulated K + → π + π + π − decay samples; the corresponding systematic effects on A N do not exceed 2%in relative terms [16].The number of observed events, N obs , within the signal window and the quantities N exp and δN exp are used to compute the local signal significance for each mass hypothesis. It is foundthat the significance never exceeds 3, therefore no HNL production signal is observed. Upperlimits at 90% CL of the number of K + → µ + N decays, N S , in each HNL mass hypothesis areevaluated from the quantities N obs , N exp and δN exp using the CL S method [17]. The values of N obs , the observed upper limits of N S , and the expected ± σ and ± σ bands of variation of N S in the null (i.e. background-only) hypothesis are shown in Fig. 4 (left).The single-event sensitivity (SES) branching fraction B SES ( K + → µ + N ) and mixing param-eter values | U µ | , corresponding to the observation of one signal event, are defined in eachHNL hypothesis as B SES ( K + → µ + N ) = 1 N K · A N and | U µ | = B SES ( K + → µ + N ) B ( K + → µ + ν ) · ρ µ ( m N ) , with the kinematic factor ρ µ ( m N ) given in Eq. (1). They are shown as functions of the HNLmass in Fig. 4 (right). The expected number of K + → µ + N signal events, N S , is written as N S = B ( K + → µ + N ) / B SES ( K + → µ + N ) = | U µ | / | U µ | , which is used to obtain upper limits at 90% CL of the branching fraction B ( K + → µ + N ) andthe mixing parameter | U µ | from those of N S .The upper limits obtained for | U µ | are compared with the results from earlier searches forthe K + → µ + N decay [15, 18, 19, 20], and the Big Bang nucleosynthesis (BBN) constraint [21],in Fig. 5. The results of the current study represent the first HNL production search in themass range 374–384 MeV/ c , and improve on previous NA62 results in the mass range 300–374 MeV/ c [15] by more than an order of magnitude. In the range 200–300 MeV/ c , thesensitivity achieved is similar to that of the BNL-E949 experiment [18].11
00 220 240 260 280 300 320 340 360 380] HNL mass hypothesis [MeV/c10 N u m be r s o f e v en t s Observed number of eventsObserved UL (90% CL) bands) s – Expected UL ( /c Squared HNL mass [GeV
100 150 200 250 300 350 ] HNL mass [MeV/c - - S i ng l e e v en t s en s i t i v i t y N) + mfi + BR(K | m |U Figure 4: Left: observed number of events N obs , observed upper limit at 90% CL of the numberof signal events N S , and expected ± σ and ± σ bands of the upper limit in the null hypothesisfor each HNL mass value considered. Right: single event sensitivity values of B SES ( K + → µ + N )(dashed line) and | U µ | (solid line) as functions of the assumed HNL mass. Boundaries ofthe HNL search region are indicated by vertical arrows.A comparison of the above upper limits of | U µ | with the upper limits of | U e | obtainedfrom HNL production searches in K + → e + N [15, 16, 20] and π + → e + N [22, 23] decays isshown in Fig. 6. Upper limits of O (10 − ) obtained on | U µ | in the mass range 16–34 MeV/ c from searches of the π + → µ + N process [24] are not shown. In comparison to the limits of | U µ | obtained from direct HNL decay searches [25, 26], the limits from production searchesare weaker but more robust because they are based on fewer theoretical assumptions. K + → µ + νX and K + → µ + νν ¯ ν decays The K + → µ + νX process is investigated in the framework of the scalar and vector mediatormodels, defined for non-zero mediator mass m X [6]. In total, 37 mass hypotheses equally spacedin the range 10–370 MeV/ c are examined. The K + → µ + νν ¯ ν decay is investigated assumingthe SM differential decay rate distribution [7].The true missing mass spectrum lies in the m X ≤ m miss ≤ m K − m µ range for the K + → µ + νX decay, and in the 0 ≤ m miss ≤ m K − m µ range for the K + → µ + νν ¯ ν decay (neglectingthe neutrino mass). In both cases, a signal would manifest itself as an excess of data events overthe estimated background at large reconstructed m values as shown in Fig. 2 (top-right).Therefore the event selection requires that m > m . The m value is optimized to obtain thestrongest expected upper limit of the decay rate in the null hypothesis, considering that signalacceptances and backgrounds both decrease as functions of m . The optimization is performedindependently for each of the possible signals listed above.The numbers of background events, N exp , and their uncertainties, δN exp , estimated withsimulations (Section 4) are shown as functions of m in Fig. 7 (left). Also shown are the expectedupper limits at 90% CL of the number of signal events, N S , and their ± σ and ± σ bands ofvariation in the null hypothesis, obtained from N exp and δN exp using the CL S method [17] foreach m value considered. 12
00 150 200 250 300 350 ] HNL mass [MeV/c - - - - a t % C L | m UU ppe r li m i t s o f | BBNBNL E949KEK NA62 (2015 data)OKAThis result
Figure 5: Upper limits at 90% CL of | U µ | obtained for each assumed HNL mass, comparedto the upper limits established by earlier HNL production searches in K + → µ + N decays atNA62 [15], BNL-E949 [18], OKA [19] and KEK [20]. The lower boundary of | U µ | imposed bythe BBN constraint [21] is shown by a dashed line.
50 100 150 200 250 300 350 400 450] HNL mass [MeV/c - - - - a t % C L | l UU ppe r li m i t s o f | ) eN p TRIUMF ( ) eN p PIENU ( 2015 data ) eN KNA62 (2016-2018 data) eN KNA62 ( ) N m KE949 ( ) N m KOKA (2015 data ) N m KNA62 ( 2016-2018 data) N m KNA62 () N m K, eN KKEK (
Figure 6: Summary of upper limits at 90% CL of | U e | (red solid lines) and | U µ | (blue solidlined) obtained from HNL production searches in K + decays: this analysis, NA62 [15, 16],BNL-E949 [18], OKA [19], KEK [20]; and in π + decays: TRIUMF [22], PIENU [23]. The lowerboundaries of | U e | and | U µ | imposed by the BBN constraint [21] are shown by the lower andupper dashed lines, respectively. 13 .05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14] /c cut [GeV Lower m N u m be r s o f e v en t s Observed number of events exp N d– exp Expected background: NObserved UL (90% CL) bands) s – Expected UL (
50 100 150 200 250 300 350 ] Assumed X mass [MeV/c - - - X ) a t % C L n + mfi + U ppe r li m i t o f B R ( K Scalar X modelVector X model
Figure 7: Left: expected background, its uncertainty, and expected ± σ and ± σ bands ofthe upper limit on the number at 90% CL of signal events N S in the null hypothesis, for eachlower squared missing mass cut ( m ) considered to optimize the definition of the K + → µ + νX and K + → µ + νν ¯ ν signal regions. Observed numbers of events and upper limits of N S areshown for m values found to be optimal for certain m X hypotheses. Right: upper limits of B ( K + → µ + νX ) obtained at 90% CL for each m X hypothesis for the scalar and vector mediatormodels.For the K + → µ + νX decay in m X hypotheses of 320–370 MeV/ c , the signal region isdefined m = m X (rounded up to the nearest multiple of 0 .
02 GeV /c ), avoiding a significantloss of signal acceptance. For the K + → µ + νX decay in m X hypotheses of 10–310 MeV/ c , andfor the K + → µ + νν ¯ ν decay, the signal region is defined as m = 0 . /c . The backgroundcomposition for this m value is reported in Table 1. Optimal sensitivity is obtained in this casewith a reduced signal acceptance. In particular, the acceptance for the K + → µ + νν ¯ ν decaydecreases from A µννν = 0 .
277 to A µννν = 0 . N S for the above set of m values aredisplayed in Fig. 7 (left). Upper limits of B ( K + → µ + νX ) in the scalar and vector X models asfunctions of the assumed m X , obtained from those of N S similarly to the HNL case, are shownin Fig. 7 (right). The limits obtained in the scalar model are stronger than those in the vectormodel due to the larger mean m miss value.In the search for the K + → µ + νν ¯ ν decay, N obs = 6894 events are observed in the signalregion m > . /c , with an expected background of N exp = 7549 ±
928 events. Thisleads to an observed (expected) upper limit at 90% CL of 1184 (1526) events for the numberof signal events N S . An upper limit is established on the decay rate using the relation N S = N K · B ( K + → µ + νν ¯ ν ) · A µννν : B ( K + → µ + νν ¯ ν ) < . × − at 90% CL , improving by a factor of 2.4 on the most stringent previous limit obtained by the BNL-E949experiment [8]. Both this and BNL-E949 K + → µ + νν ¯ ν results are obtained assuming the SMdifferential rate. However the reconstructed missing mass intervals analysed are complementary: m miss >
316 MeV /c in this study, and 230 < m miss <
300 MeV /c at BNL-E949.14 ummary A search for HNL production in K + → µ + N decays has been performed using the data setcollected by the NA62 experiment in 2016–2018. Upper limits of the HNL mixing parameter | U µ | are established at the level of O (10 − ) over the HNL mass range of 200–384 MeV/ c withthe assumption of mean lifetime exceeding 50 ns, improving on the previous HNL productionsearches. The first search for K + → µ + νX decays has been performed, where X is a scalar orvector hidden sector mediator in the mass range 10–370 MeV/ c , which decays to an invisiblefinal state. Upper limits obtained at 90% CL on the decay branching fraction range from O (10 − )for low m X values to O (10 − ) for high m X values. An upper limit of 1 . × − is obtainedat 90% CL on the branching fraction of the K + → µ + νν ¯ ν decay, assuming the SM differentialdecay rate, which improves on the earlier searches for this process. Acknowledgements
It is a pleasure to express our appreciation to the staff of the CERN laboratory and the technicalstaff of the participating laboratories and universities for their efforts in the operation of theexperiment and data processing. We are grateful to Diego Redigolo and Kohsaku Tobioka forfruitful discussions and for the inputs provided on the K + → µ + νX decay phenomenology.The cost of the experiment and its auxiliary systems was supported by the funding agenciesof the Collaboration Institutes. We are particularly indebted to: F.R.S.-FNRS (Fonds de laRecherche Scientifique - FNRS), Belgium; BMES (Ministry of Education, Youth and Science),Bulgaria; NSERC (Natural Sciences and Engineering Research Council), funding SAPPJ-2018-0017 Canada; NRC (National Research Council) contribution to TRIUMF, Canada; MEYS(Ministry of Education, Youth and Sports), Czech Republic; BMBF (Bundesministerium f¨urBildung und Forschung) contracts 05H12UM5, 05H15UMCNA and 05H18UMCNA, Germany;INFN (Istituto Nazionale di Fisica Nucleare), Italy; MIUR (Ministero dell’Istruzione, dell’Univer-sit`a e della Ricerca), Italy; CONACyT (Consejo Nacional de Ciencia y Tecnolog´ıa), Mexico; IFA(Institute of Atomic Physics) Romanian CERN-RO No.1/16.03.2016 and Nucleus ProgrammePN 19 06 01 04, Romania; INR-RAS (Institute for Nuclear Research of the Russian Academyof Sciences), Moscow, Russia; JINR (Joint Institute for Nuclear Research), Dubna, Russia;NRC (National Research Center) “Kurchatov Institute” and MESRF (Ministry of Educationand Science of the Russian Federation), Russia; MESRS (Ministry of Education, Science, Re-search and Sport), Slovakia; CERN (European Organization for Nuclear Research), Switzerland;STFC (Science and Technology Facilities Council), United Kingdom; NSF (National ScienceFoundation) Award Numbers 1506088 and 1806430, U.S.A.; ERC (European Research Council)“UniversaLepto” advanced grant 268062, “KaonLepton” starting grant 336581, Europe.Individuals have received support from: Charles University Research Center (UNCE/SCI/013), Czech Republic; Ministry of Education, Universities and Research (MIUR “Futuro inricerca 2012” grant RBFR12JF2Z, Project GAP), Italy; Russian Foundation for Basic Re-search (RFBR grants 18-32-00072, 18-32-00245), Russia; Russian Science Foundation (RSF19-72-10096), Russia; the Royal Society (grants UF100308, UF0758946), United Kingdom;STFC (Rutherford fellowships ST/J00412X/1, ST/M005798/1), United Kingdom; ERC (grants268062, 336581 and starting grant 802836 “AxScale”); EU Horizon 2020 (Marie Sk(cid:32)lodowska-Curie grants 701386, 842407, 893101). 15 eferences [1] J. Beacham et al. , J. Phys. G47 (2020) 010501.[2] T. Asaka and M. Shaposhnikov, Phys. Lett.
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