The Karmen anomaly can be interpreted as being due to a heavy neutrino of
mass around 137 MeV produced in $\pi_{e 2}$ decays. This interpretation is
consistent with the present limits on the couplings of such an object.Comment: 11pages, 4figures, Te

Levy, J. -M.

Vannucci, F.

English

arXiv

11pages, 4figures, TeXThe Karmen anomaly can be interpreted as being due to a heavy neutrino of mass around 137 MeV produced in $\pi_{e 2}$ decays. This interpretation is consistent with the present limits on the couplings of such an object

Levy, J.-M.

Hal-Diderot

A consistent interpretation of the Karmen anomaly

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The Karmen anomaly can be interpreted as being due to a heavy neutrino of mass around 137 MeV produced in $\pi_{e 2}$ decays. This interpretation is consistent with the present limits on the couplings of such an object

Lévy, J M

Vannucci, François

CERN Document Server

A consistent interpretation of the KARMEN anomalyJ.-M. Levy and F. Vannucci March 22, 2000AbstractThe Karmen anomaly can be interpreted as being due to a heavy neu-trino of mass around 137 MeV and mean life 14 s produced in e2 decays.This interpretation is consistent with the present limits on the couplingsof such an object.∗Laboratoire de Physique Nucleaire et de Hautes Energies, CNRS - IN2P3 - UniversitesParis VI et Paris VII, Paris. Email: jmlevy@in2p3.fr , vannucci@in2p3.fr11 What is the KARMEN anomaly ?The Karmen collaboration has reported a distortion in the time distributionof their events [1]. The experiment studies low energy neutrinos produced bythe dump of 800 MeV protons at the ISIS facility of the Rutherford Labora-tory. The accelarator has a unique time structure which allows to discriminatebetween neutrinos coming from  decaying at rest and from the subsequent decay at rest. It is in this last process that an anomaly was observed in thetime distribution of interactions, which overall reproduces the lifetime of themuon but for an excess of events at a time delay centered on 3:6s w.r.t. thearrival of the protons. The signature is a deposition of energy in the range 11to 35 MeV.This is interpreted by the Karmen collaborators as possibly coming from theproduction of a heavy neutral object X of mass 33.9 MeV, travelling with a = v=c of 1=60 and decaying in the detector, 17:5m away from the dump. TheX particle is produced in  decays :  ! X with a very small branching ratioand decays in turn into the a priori open channels: X ! γ or X ! e+e− orX ! γγThe Karmen experiment nds about 100 events compatible with X produc-tion and decay in a sample of 3000 neutrino interactions. This is a more than4  eect.Experimentaly, there are two unknowns in the problem: the branching fractionBr of ’s decaying into the X particle and the lifetime  of the latter. In orderto reproduce the observed number of events, Br and  must be related by thecurve shown in Fig.1 as given in [1]. For long lifetimes, the probability of decayin the detector is inversely proportionnal to the lifetime. For shorter lifetimes, agood fraction of X’s has decayed before reaching the detector. Observe that, forvery short  , the distribution of excess events in the detector should be unevenbecause of the stronger probability to decay close to the upper end. Taking thisinto account would change the shape of the curve in the low  region. However,Karmen sees no such eect, which can be taken as an indication that of thetwo possible  values corresponding to a given Br, only the higher one must beconsidered.A direct search for X production in 2 decay by looking at the muon spec-trum was performed at PSI [2], [3]. It excludes branching fractions larger than2:6 10−8, as also indicated in Fig. 1.22 Production and decay of massive neutrinosMassive neutrinos, arising, for example, from the introduction of right-handedchiral states, occur naturally in most extensions of the standard model. Theyhave been searched through their decays in various experiments [4, 5]2.1 ProductionIf massive neutrinos exist, the so-called weak eigenstates (associated to chargedleptons via weak currents) which we will call generically , are linear com-binations of mass eigenstates h . Let us call Uh the coecient of h in theexpansion of  ( being e or  for the production processes envisionned here).In any ’’ neutrino beam, there is a h component at the jUhj2 level up tophase space factors and weak currents matrix elements.For example, e2 decays may yield h at the level jUhej2 up to the abovementionned factors, provided that h has a mass below m() − m(e) = 139MeV, while 2 decays would produce h at the level jUhj2 with masses up tom()−m() = 34 MeV.Note that the well known chirality suppression of e2 no longer occurs as soonas m  a few MeV .For the X particle,  =  and the mixing discussed in Fig 1 is Uh . Since mXis supposed to be at the limit of the available phase-space in 2 (in order toensure  = 1=60), one would expect it to be produced more abundantly in K2.The ratio of the branching ratios Br(K!X)Br(!X)  18 instead of :63 for massless’s. However, this is very sensitive to the precise value of mX .2.2 DecaysSeveral decay modes can be investigated. Heavy neutrinos with masses below1 MeV can only decay radiatively by emitting one or two photons. As soon asthe mass is above 1 MeV, the most favoured decay mode is e+e−e. The matrixelement is analogous to that of muon decay and the width is given byΓ(h ! e−e+) = G2F1923m5hf(mh)jUhej2where f tends rapidly to 1 for masses above 10 MeV ([5]) and jUhej is the samemixing which appears at production if h is produced together with an electron.For higher masses, other decay channels open: e; e−+; −+; −+:::each one involving a mixing matrix element which depends on the nal stateleptons.33 X or X particle?The X particle could be such a massive neutrino undergoing weak decays. How-ever for a 33:9 MeV object e+e−e is the only open non-radiative channel andits width, far above those of the radiative modes, dominates the lifetime. Anupper limit of jUhej2  5  10−6 has been obtained [4] for such a mass. Thistranslates into a limit   120 s which is reported in Fig. 1 and excludes mostof the allowed parameter region. For the highest mass eigenstate, publishedlimits on Γ( ! e)=Γ( ! ) ([8]) allow to infer jUhej2  1:23  10−6 and  500 sMoreover, taking the experimental Karmen curve (see Fig. 1) into account, thisimpliesBr(+ ! +X)  4:5 10−9 which is barely compatible with the upper limitsfrom the two PSI groups who tried a direct X search [2], [3]) 1An alternative interpretation has been proposed [6] in terms of exotic muondecays. It involves unknown scalars. We study here yet another possibility,which implies an ’ordinary’ massive neutrino, call it X.As already remarked, many channels open as soon as phase-space permits.If we assume a e2 production mode, masses up to 139 MeV are possible, ande decays are allowed for suciently high mX∗ , as schematically shownin Fig. 2 . For such modes, the time delay between beam on target and theevents in excess in the Karmen detector would be the sum of the nal statemuon lifetime with the time necessary for X to fly from the proton target tothe detector. Indeed, the kinetic energy of  is small and that of e may fallshort of the Karmen detection energy threshold, depending on mX∗ , renderingit necessary to wait for the muon to decay. 2This would yield an average (electron) energy around 36 MeV after an averagedelay of 2:2s following the undetected X decay.The Karmen anomalous events appear to be rather tightly clustered in time ifthey are interpreted in the lines of [1] and their apparent dispersion cannot beunderstood as due to a muon decay. However, the authors of [6] show that arather narrow bump can be interpreted as the superposition of two exponen-tials, both with the same (muon) decay time constant, but with the secondshifted by a more or less xed amount representing a time of flight.1As quoted in the Review of Particle Physics [7] the PSI results would seem to contradictthe lower bound we have just given and rule out altogether the Karmen solution. Howeverthe PDG are wrong in that they call limits on jUXj2 gures which are really limits on thebranching ratio. Since, on the other hand, the way the PSI groups compute their upperbounds does not yield the tightest possible result, their is ample room for argument, and verylittle room, if any, for X2for X∗ at rest, one nds Ee  14 MeV and T  2 MeV.43.1 Model for the time distributionTherefore, we have tried to perform a two component t to the Karmen timedistribution. The rst component is an exponential reflecting ordinary muondecay in the target followed by practically instantaneous interaction of the nor-mal light neutrinos thus produced in the detector (the ToF is about 60 ns)The second component is the convolution of a uniform and an exponential dis-tribution representing the sum of the transit time of a heavy neutrino from thetarget to the detector (which is also the heavy neutrino lifetime in the lab andis practically uniform in the window of interest) plus the lifetime of the muonproduced in the heavy neutrino decay.However, this turned out to be inconsistent. The tted ToF of the heavyneutrinos implies a mass close to 137 MeV which in turn means a positronenergy distribution (in X ! −e+) rather evenly distributed around an ex-pectation value of 14 MeV, thereby invalidating the hypothesis that the delaywould always comprise the  lifetime. It was therefore necessary to add a thirdcomponent representing those ’direct’ positrons. Thus, there are altogether 5parameters representing the intensities of the three components and the lowerand upper limits of the time window corresponding to the passage of the X’sin the Karmen detector.In principle, this gives us a potential consistency check of the fact that theanomaly is really due to a particle since its speed can be estimated from thelast two parameters using the average distance between the proton target andthe detector on the one hand, and the length of the latter on the other hand.However, the data at our disposal are not accurate enough to decide betweendierent t results which do or do not conform with this expectation. Giventhe large errors on the tted parameters, the results presented on Fig. 3 cannotbe considered as inconsistent with the expectation.Here, T1 and T2 are the lower and upper edges of the time window, and thethree following items are constants multiplying the three normalized distribu-tions superposed in the t. Since the bin width is :5s, the correspondingnumber of − ! e− and X ! e+ are about 66 and 38 respectively.The t yields: ToF = 3:66s, hence  = :0159 and mX∗  137:3 MeV.3.2 InterpretationIt must be remarked now that for an ’ordinary’ heavy Dirac neutrino, there arereally two (non mutually exclusive) possibilities:- either it decays to e− and a virtual W+ which yields +- or it decays to − and the virtual boson goes into e+e.The rst possibility involves the same mixing matrix element, namely Uhe,which appears at production, whilst in the second case, the decay is due to UhClearly enough, in any case Uhe 6= 0 and the e+e−e mode is also widely open.If we assume the rst channel, the unknown mixing cancels in the ratio of the5two modes which is given by the following formula:Γ(e−+)Γ(e−e+e)= (1− 8r + r2)(1 − r2)− 12rLog(r)where r = (m=mX∗)2 and me = me = m = 0 [5]. The width ratio is about0:5% for mX∗ = 137 MeV.This shows two things: rst, for the range of masses of interest, the lifetimeis dominated by the e+e−e mode, which gives us another relation betweenjUhej and  and allows to draw further conclusions. Second, decays throughthis mode must have occured abundantly in the Karmen experiment, but thecorresponding (large) deposition of energy is probably rejected by the Karmenselection.The results of this analysis are summarized on Fig. 4 It reproduces the Karmen’eciency’ curve corrected for the  decay mode considered here (The unknownconstant was taken from the asymptotic direction of the Karmen plot [1]); alsodrawn is the branch of hyperbola corresponding to the Br value xed by theX mass and the hypothesis of an e−e+ dominated X lifetime. The latter isfound to be X∗  14s and the + ! e+X branching ratio is around 410−10This entails a mixing matrix element jUX∗ej2  4:2 10−8 compatible with thepreviously published upper limits [4, 5]Here again,this object should be much more abundantly produced in kaon de-cays. The ’ratio of ratios’ is around 100 in this case.Of course, we do not claim that this is "the" solution, but only wish to point outanother possibility. It could probably be easily disproved through confrontationwith more detailed Karmen data.4 ConclusionIn short, the Karmen collaboration have chosen to explain their anomalousevents by assuming they originate from a rare 2 decay, because a ’neutrino’with a mass at the edge of phase-space (around 34 MeV) has both a low enoughvelocity to explain the 3:6s delay and a low enough mass to explain the 30 MeVenergy deposition. We claim that both features can be explained by a e2 decayyielding a much heavier ’neutrino’ which decays itself through a el channel,the signature of which is a visible energy in the range of interest after the(apparently) observed delay. The more mundane eel channel is supposedlyhidden by the experimental energy cut o and the apparent clustering in timedue to a xed time of flight followed by a short detectability window is notspoiled upon taking the muon lifetime into account.6Fig. 17e-µνν+eeX*+++µµeU U*piµpropagates from target to detector decays in detector+-νX*e X*eX*Fig. 2 The process hypothetized in this paper8Fig. 39Fig. 410References[1] B. Armbruster et al., Phys. Lett. B348 (1995) 19[2] R. Bilger et al, Phys. Lett. B363 (1995) 41[3] Daum et al, Phys. Lett. B361 (1995) 179[4] G. Bernardi et al. Phys.Lett. B166 (1986) 479[5] J.M. Levy, These de doctorat d’Etat, Universite de Paris VI (1986)[6] S.N. Gninenko and N.V. Krasnikov, hep-ph 9804364[7] Review of Particle Physics in Eur. Phys. J. C 3 (1998) p. 326[8] D.I. Britton et al, Phys. Rev D46, R885 (1992)11

A consistent interpretation of the Karmen anomaly

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