JHEP09(2005)048 hep092005048.pdf ntineutrino May 31, 2005 August 22, 2005 September 8, 2005 September 19, 2005 . Performing a fit the heavy 3 4 − Received: Revised: m trinos, and then decays –10 trino, which is produced show that extending our iniBooNE running in the 6 responding to a transition tory experiments, and we Accepted: ersion of the decay model, − nts, we show that all data oscillation experiments, we Published: e to introduce CP violation 10 f the electron type. We require ∼ y g http://jhep.sissa.it/archive/papers/jhep092005048 /j Published by Institute of Physics Publishing for SISSA being the neutrino-scalar coupling and g few eV, in the range from 1 keV to 1 MeV and ∼ Neutrino Physics. 4 We propose an explanation of the LSND evidence for electron a 4 m [email protected] [email protected] [email protected] gm Department of Physics and Astronomy, Vanderbilt Universit Nashville, TN 37235, U.S.A. E-mail: Physics Department, Theory Division,CH–1211 CERN Geneva 23, Switzerland E-mail: Scuola Internazionale Superiore diVia Studi Beirut Avanzati 2–4, I–34014E-mail: Trieste, Italy SISSA 2005 c ° to the LSND datacan as be well explained as withinwe all this predict decay relevant a scenario. null-result signal in experime probability In the of the upcoming the MiniBooNE minimal same experiment v model order cor to as two seen nearly inin degenerate LSND. the heavy In decay, which addition, canneutrino it we lead mode. is to possibl a Weshow briefly suppression that of discuss our the signals signal scenario incomment in is future on M implications compatible neutrino in with astrophysics bounds and from cosmology. labora Keywords: mass, e.g. Explaining LSND by a decaying sterile neutrino Sergio Palomares-Ruiz Silvia Pascoli Thomas Schwetz Abstract: appearance based on neutrinoin decay. pion and We introduce decaysinto a because a heavy of scalar neu a particle small andvalues mixing a of with light muon neutrino, neu predominantly o JHEP09(2005)048 1 5 2 13 16 16 17 12 18 3–1998 and observed cs 16 transitions. The KARMEN y speculative physics: four- ing at the same appearance e pheric [3], solar [6], and null- ains a challenge for neutrino w of this, several alternative [20], CPT-violating quantum ¯ ν e than LSND, but no positive scillations [9, 10] (see ref. [11] appearance observed in LSND le neutrino [8] does not lead to llations [18], four neutrinos and uts of sterile neutrinos in extra e → ¯ ν 3 rinos and CPT violation [16, 10], a e µ ν U → µ ν – 1 – [1]. This was interpreted as evidence of ¯ e ν 7.1 Laboratory7.2 bounds Supernova bounds 7.3 Cosmological bounds 5.1 MiniBooNE 5.2 Experiments looking for a non-zero value of with the other evidencephenomenology. It for turns neutrino out oscillations thata introducing [3 satisfactory – a 7] description fourth rem of steri for all a data recent in update) termsresult because of of short-baseline neutrino tight (SBL) o constraints experimentsexplanations from atmos have [2, been 12 – proposed, 14].neutrino some oscillations of plus In neutrino them vie decay involvinglepton [15], ver number three violating neut muon decayCPT [17], five-neutrino violation osci [19],decoherence a [21], low-reheating-temperature mass-varying Universe neutrinos [22], and shortc experiment at the spallationchanel source in ISIS the in years Englandsignal 1997–2001 was was at look found a [2]. slightly different Reconciling baselin the evidence for ¯ 6. CP-violating decays and the7. signal in MiniBooNE Constraints from laboratory, cosmology, and astrophysi 8. Summary and conclusions 14 1. Introduction The LSND experiment at LANSCE in Los Alamos took data from 199 an excess of ¯ Contents 1. Introduction 2. Decay framework and transition3. probabilities LSND and KARMEN 4. Combined analysis of LSND5. and null-result experiments Predictions for MiniBooNE and other future experiments 9 3 1 JHEP09(2005)048 ) 3 as ν (10 , with h L/E n ∼ O sted in the g . The LSND h m by ) neutrinos, ween neutrino oscilla- uently confirmed [30]. ino, produced in pion rio as the possible ex- 02) from the source to olution to neutrino os- s Goldstone boson (the . 0 nt review of the bounds, y via a non-zero vacuum ained by neutrino oscilla- ided by mixing, similar to periment as well as for the arge couplings their energy. e and we assume that at- soon from the MiniBooNE o oscillations and decay is ∼ ly seen in the first data set mass generation mechanism ino decays is by means of a ypical values of masses, the ν alar, similar to the so-called ef. [15]. A fourth neutrino is 1–10 eV, e.g. neutrino masses the mixing and lifetime could ino experiments. fetime much smaller than the β rm arises at low energy as an 6, 27] and the solar neutrino E d KARMEN experiments, and ecay scenario was adopted, we els, we introduce an interaction ∼ latory behaviour in atmospheric s to circumvent the constraints 4 ly ( , LSND data can be explained in mass generation. We show that in 5 − gm 10 , for ∼ 4 appearance in a similar range of g n into a light neutrino, mixed predominantly e ν h – 2 – n → µ ν , light neutrinos and a scalar. However, as we are only intere h n being the distance travelled by the neutrinos and L Light neutrino decay has been considered as an alternative s The decay of an exotic neutral massive particle, called karm An explanation of the LSND result invoking the interplay bet In this work we assume the existence of heavy (mainly sterile complete agreement with the null-results of other SBL neutr cillations, to explainpuzzle the [26, atmospheric 28]. neutrino Although theneutrino anomaly recent [4] observation [2 of and an KamLAND oscil planation [7] of data these excludesnot problems, a excluded a pure yet. decay combinedmospheric, scena scenario We solar of do and neutrin not KamLANDtions. consider neutrino these transitions possibilities are expl her decays was considered asof a possible the explanation KARMEN for experimentThis an [29], hypothetical anoma particle which would however, move was non-relativistical not subseq the detector. If it werebe a placed massive neutrino, from strong anomalous boundssee pion on ref. and [32]). muon Differently decaysassume from [31] here this (for case, a a where Majoron-like rece heavy no type neutrino specific of is d relativistic decay. at Furthermore,we the for require energies t it in the to LSND decayone an before of reaching the the karmino. detector, with a li tions and neutrino decayintroduced has been with considered a previously massMajoron) in of and r a into few light(3+1) neutrinos. eV, four-neutrino which The oscillations, decays signal into whereas infrom a LSND the the massles is CDHS decay prov experiment serve [12]. This approach requires very l around 100 keV and neutrino-scalar couplings phenomenological consequences of such aother term relevant for neutrino the experiments, LSND weeffective ex interaction, assume not that necessarily this relatedthe te to simplest neutrino case of one heavy sterile neutrino, with the electron neutrino. A natural way to introduce neutr term in the lagrangian,Majoron which models couples [25]. neutrinos This to termthrough can a the be light spontaneous related sc to breakingexpectation the of neutrino value of a the lepton scalarterm field. number between symmetr Similarly to these mod signal is explained through the decay of a small mixing with the muon neutrino. We denote their masses LSND, dimensions [23]. A criticalexperiment test [24], of which the is LSND looking signal for will come JHEP09(2005)048 . ,... (2.1) 1 eV, 5 t with , . 3 , = 4 2 , h 1 m , in agreement 5 neutrino masses − ) are given, in the thin this scenario, 3 and 1 the minimal decay 10 , 2 , ∼ g plications for cosmology radiction with any other = 1 calculate the event rates. o antineutrinos. Weak in- tirely by the decay, and no l with masses t the same time provide the framework, whereas in sec- diction for MiniBooNE and odel is consistent with exist- 3 r couplings , In the relativistic case, where for a discussion). In contrast, we compare the quality of the inos and complex couplings, it dentify neutrinos and antineu- 2 , is possible [34]. Both processes . , scillation and decay amplitudes, 1 c ν . ght-handed (chiral) antineutrinos φ . Furthermore we assume for the 3 , esults in the relativistic approximation we . It follows from eq. (2.1) that not + 2 , ν +h 1 ν f the involved states are on-shell, a derivative φ m ]. → m/E hR À n n lL ,... ν 5 , – 3 – 4 hl g m l,h X Majorana neutrinos. We take the three light neutrinos , such that the three light neutrinos are stable. Hence will be complex. − N ,... hl = 5 , g 4 L m can occur, but also ¿ φ φ + m ¯ ν with the heavy mass state, and hence it appears to be in conflic . e → 3 ν , 2 n , 1 with the heavy neutrino is required. This allows us to invoke m e ν In the case of Majorana particles, neutrinos are identical t The outline of the paper is as follows. In section 2 we present The case of pseudo-scalar couplings gives exactly the same r 1 mass basis, by the terms in the lagrangian relevant to the decay (with scala scalar mass only the decay while the heavy neutrinos have masses teractions couple to left-handed (chiral)while neutrinos the and propagation ri stateshelicity are and those chirality are of approximatelytrinos definite the with helicity. same, helicity one states can i up to terms of order In general the coupling matrix with existing bounds. responsible for solar and atmospheric oscillations to be 2. Decay framework and transition probabilities Let us consider the general case of framework and deduce theIn probabilities, section 3 which we areand present in needed section our to 4 analysis wenull-result of show experiment LSND that by the and performing decayfit KARMEN a framework to combined data is analysis; the not wi in oneother cont for future oscillations. neutrino In experimentstion section within 6 5 we the we show minimal discuss that,is decay allowing the possible for, to pre at obtain least, awhich two CP-violating would sterile interference suppress between neutr the o neutrinoantineutrino signal signal in in MiniBooNE, LSND. but In a sectioning 7, bounds we from argue that laboratory ourand experiments, m astrophysics. and In we section comment 8 on we im present our final remarks. in the 100 keV range, which in turn permits a small coupling of various bounds on neutrino-scalarin couplings our (see model, section the signal 7 mixing in of the LSND experiment is provided en where here and in the following the ranges for the indexes are will use. It caninteraction also term be can shown that be for rewritten processes in in pseudo-scalar which form all [33 o and a mixing of JHEP09(2005)048 , ) h s n 6= (2.4) (2.6) (2.2) (2.3) (2.5) + r and the < E rs δ l h ν ) n β ] is: ν is converted β ν E < E α ν − dE E α + ν is β E l ν ( ν + δ E 2 , E . rs ¯ ¯ ¯ ¯ ¯ β δ ν ¶ s s ) E β L 6= = ν 2 with energy h , hirality-flipping nature of the r E r Γ cases, helicity-flipping ( 2 α | ent eq. (2.3) can be written also as e we just remark that in the case of . − − . . rs , the differential decay rate of an h ur µ ¶ α h 2 h hl 2 n ν h n neutrino energy are 0 l h . both with energy Γ n ν |M n m , E E h roducts of the helicity-flipping channel are l αh ( s exp E 2 n h E s β is the angle between the of | δ U 2 for n ν πE P ¿ ¶ 2 ) are related to the massive neutrinos in θ hl 0 − ¯ ¯ ¯ ¯ ¯ /E → φ 1 h g α l 32 h L onent of the neutrino (antineutrino) fields, which | r α πE ν ν 1 X ¶ dec 2 h ν dL = 2 m + ,... α E E µ L 16 = + 2 ν m s 2 h l 2 l dP l i s l ν 0 E      ,s ν = ν m 2 – 4 – 1 − ), where . For the former process the suppression is due of helicity i × αl ) s → dL → h µ l 0 and ’ for neutrinos and ‘+’ for antineutrinos, and the r h h U 2 h − n ν L n n 6= r h − 0 µ ≈ m n l E r Z /E exp l ( ( 2 φ X h ν | ) s l ∗ =Γ s with energy in the interval [ ) e,µ,τ,s ν β exp m hl r m = ν ( g hl αh dE → ∗ into a β = | = ) α r h 0, Γ . U r , E r h ν n ( ) h αl α = n α s ), is the same and given by [34] n Γ ≈ ( ( ν U βh s 2 d E l ) | α U E s is then given by Γ ( 3 ( βl = ν 2 for m rs h / h U rs r ) n X θ ¯ ¯ ¯ ¯ ¯ |M W l take the values ‘ X cos + + ¯ ¯ ¯ ¯ ¯ ∓ r, s = (1 ) with energy 2 h α r ν m in the rest frame of 2 E | l ( β hl ν s ν β g ν | → dE = r α ν 2 | In the approximation The flavour neutrinos According to angular momentum conservation the matrix elem Throughout this work we will assume Majorana neutrinos. Her of helicity rs dP 3 2 h and helicity-conserving ( direction of and hence, the partial decay rate for n into an (anti)neutrino of flavour to angular momentum conservation, whileinteraction, for eq. the (2.1), latter is the c responsible for the suppression The total decay rate of Dirac neutrinos the decayunobservable, is since they analogous. are the However,do right-(left-)handed the not comp decay participate in p weak interactions. |M are suppressed by terms of order where the indices For relativistic neutrinos, the limiting values of the final eq. (2.1) by The differential probability that an (anti)neutrino of flavo matrix element is given by JHEP09(2005)048 h is n (2.9) (2.8) (2.7) = +. (2.11) (2.10) /dL r s ) is the β ν β eq. (2.8), ν s , s , → for r α dec ν = 6= , E . ∗ α 2 r r ν ¯ ¯ ¯ ¯ ¯ dP X , and is present E ¶ ( ¢ ≡ decays at the dis- L β rs 2 h ) r ν α r Γ ν W ( E α eglected in the decay − 2 ν X − µ E α ith the heavy mass state. are not coherent with ν β α 2 ν ν l and of light neutrinos, whereas E lt based on sterile neutrinos, exp . Since for SBL experiments , similar to the “appearance ν are assumed to be coherent E E ¡ , ent in the helicity-conserving l l neutrino ¶ s weighted by the probability − ν . h L        tates before they decay. α 4 L n | ν Γ hl = . Adopting the effective operator 2 h × hl s − E Γ β annels. Here r into g ) m e 2 ν | √ β i 2 4 . and h ν ) − A n l for l r ) in eq. (2.6). The term ≡ E ( 4 ν 2 µ β | g h ν − ) X rs s β ( α given in eq. (2.4). The relativistic approxi- βl g , E exp ν | ≡ l U α 2 ) E ν | ν ) r 4 r ( hl l E ( – 5 – α , A ( X → A U X h | rs ∗ h ) ≡ = 0. This implies that the first two lines in eq. (2.6) A r n = 2Θ( W ( = 4 αh hl rs e β = 4, eq. (2.8) becomes ) g U s β g U α ν ν N appearance probability relevant to the LSND and KAR- = h → is independent of the index E X s r α e ( hl dec β dL h ) ν ν s ν l s ν ( A A βl dP → → U dE r h r µ n l ν Γ X ¯ ¯ ¯ ¯ ¯ d 1 we can neglect oscillations of the decay products to derive = hl 1 Γ ¿ s β ν ≡ → ] and the decay product interacts as a ) r α dec dL ν ). The third term describes the appearance of decay products β L/E dL 0 allows us to factor out ν 0 s 2 ll dP + ≈ = , E is the partial decay rate for m is an effective amplitude for the decay of l α r ν hl m hl E L,L ( A In the simplest case in which rs W normalised energy distribution of the decay products: among themselves. Thethe first second term one describes describesthat the oscillations they do oscillations of not the decay.channel heavy ( These terms are only pres for the helicity-conserving as well as helicity-flipping ch method of ref. [35] it can be calculated as tance [ because of the large mass difference, while both the differential probability that the heavy component of the MEN experiments. Unlike other explanations ofour the model LSND resu does notTherefore, require for simplicity a we mixing assume of the electron neutrino w operator” of ref. [35], and it is given by In eq. (2.6), we have used the fact that the light neutrinos but we include the possibility of oscillations of the heavy s mation 3. LSND and KARMEN Let us now calculate the we have ∆ where we have defined the couplings in the flavour basis by Note that inkinematics, the the limit real quantity where the light neutrino masses can be n where we have introduced the notation Here where Γ JHEP09(2005)048 of and (3.2) (3.3) (3.1) µ ν on the + signal as nario, in α , + g e µ # ν ) . We fit these µ → beam with an ¯ ν ν + E µ e ( π ν , ¯ ν e utrinos decay into ¯ ν L/E ) y. ber of signal events L → dE 4 µ . ions vent-by-event analysis Γ ¯ ν orm of 11 data points 2 − | e α dP inos is at most two orders . In case of oscillations, g tion of | ) n − t use the data from decay in µ with a continuous spectrum, ting of the information given (compare to eq. (2.11)). The ¯ ν + (1 data is less significant than in l µ n of the detector and integrate E 4 e ν tors. To calculate the observed ( + g e,µ,τ,s µ X R . In the detector, the appearance e = φ µ 2 | α ν µ 4 events with neutrino energy in the 040)% [1]. We have chosen an error ¯ ν and → µ . = + ¯ is an overall constant containing the 0 e U e 2 p αl | dE ν | ν l C ± U 2 1 4 + µ + g ) max ¯ | ν e e e ¯ ν + E ν ν 264 e . l E Z X , E – 6 – → µ + ≡ ν = (0 + ) 2 E ) µ ( ¯ g P µ π ( ν rs E e W ( ¯ 8 MeV. The total number of neutrinos is in both cases ν e . , ¯ ν = 2 dE → | ) flux from DAR, one does not expect a relevant contribution 2 µ µ α ν ¯ g = 52 µ ν g , and for simplicity we neglect the dependence of | ν 2 4 E dP ( e A 0 µ ν s ≡ e ] is given by max ¯ ν 2 ν from the muon decay will not contribute to the signal because φ e α g ¯ ν E " → dE e = 0. The pion decay leads to a mono-energetic R r µ ν ) ). The expected number of ¯ 8 MeV, whereas the muon decay gives ¯ ν dE e . µ 4 ¯ = 2¯ ν ¯ ν e + dP E from the primary pion decay will give a contribution to the ¯ E U 4 ( e ( ¯ ν µ = 29 µ ν ) φ from the muon decay contribute to the signal. In the decay sce ) is the detection cross section and Cσ , E µ π µ e ( ν e ¯ ν ¯ µ ν ¯ ν = E ν appearance signal from DIF due to the helicity-flipping deca E 2 in eq. (3.1) accounts for the fact that half of the initial ne E dE e ( / e ¯ ν ), rising up to σ ν R is searched for by using the reaction ¯ µ dN ¯ ν dE In LSND, neutrinos are produced by the decay at rest (DAR) of p For the statistical analysis of LSND data we use the total num e = E ν ( 0 µ interval [ φ φ energy of well. Note that the our assumption only the ¯ addition, the of ¯ by the subsequent decay of the to the ¯ factor 1 data with a free normalisationalready in by order the to total avoid number a offlight double events. (DIF) coun In neutrinos, our since analysis thethe we do DAR appearance no sample. signal Moreover, in since these of the magnitude total less number than of the DIF ¯ neutr neutrinos and half of them into antineutrinos. helicity indices, i.e. we neglect complex phases of number of target particles,number efficiencies of and events, geometrical we fold fac eq.over the (3.3) with relevant energy the energy interval. resolutio implied by the transition probability We have used Γ where disappear and using eq. (2.10) we find where we have defined the branching ratios by such that we can reproduce [36, figure 6], which is based on an e of the DAR data.given in [1, Furthermore figure we 24], include where the spectral beam data excess in is shown the as f a func JHEP09(2005)048 ore line from µ ν is the spectral he data given in [1, ecay scenario (see into account, different 2 an be obtained, which will ll energy (see eq. (2.7)), ith other SBL data. 9 dof for oscillations and fact that in the helicity- / line from the primary pion ution of the rgies and too few events e subsequent muon decay. cay with the data. In the 6 rom the pulse structure of = 3.4 eV . µ 4 ν ficant discrimination between LSND data can be explained Although the fit in the decay = 0.92 eV roducts given in eq. (2.7). In 2 = 5 g m he 4 m on the helicity indices due to complex ll goodness of fit (GOF) is still ∆ α 2 min g ). Much as in LSND, also in KAR- χ line contribution µ decay with decay with osc with ν [m/MeV] ν E – 7 – / L 0.8 1 1.2 1.4 background 0.6 line contribution. µ ν value cited above implies a GOF of 29%. Note, however, that a m 0.4 according to eq. (2.11). If this additional freedom is taken 5 0

2 15 10 for the helicity-conserving and helicity-flipping decays c l excess events excess 4 χ g e spectrum for LSND for decay and oscillations compared with t R ν 9 dof for decay. The reason for the slightly worse fit for decay and / 8 L/E αl . U = 10 First we discuss the compatibility of LSND and KARMEN in the d Our analysis of LSND data gives a best fit value of Note that here we neglected the dependence of the couplings 4 2 min refined analysis of the LSND spectraloscillations data and might decay. allow a In signi by the our following decay we model will and assume we that shall proceed withref. the [36] combination for w a detailedMEN analysis neutrinos in are the produced case by ofHowever, the oscillations in decay of KARMEN pions detailed at rest time and information th is available f scenario is slightly worseacceptable. than The for oscillations, the overa the primary pion decayflipping is decay mode, rather most small.which of implies the This that decay follows they products fall from have below a the the very detection sma threshold. phases in branching ratios modify the relative size of the χ distortion implied by thefigure energy 1 distribution we of compare thedecay the decay scenario best p we fit spectra predictin for the slightly oscillations high too and energy many de part events of at the low spectrum. ene Note that the contrib decay in the decay scenario. figure 24]. The hatched histogram shows the contribution of t Figure 1: JHEP09(2005)048 . ν )]. 02 0 . b (3.4) 10 ution L/E = 5 = 35 m, 2 PG χ LSND -1 L 10 function L, and LSND and e combination of e 2 R χ 2 | 4 is the minimum of the µ decay me cut. LSND experiment and U | ta sets is the parameter aselines ( oscillation analysis by an min -2 anel corresponds to neutrino 2 i, e gy given in [2, figure 11( 10 ata we are using the 9 data χ ¯ ν ity of LSND and KARMEN y-flipping decay of neutrinos ctor. Taking into account the . The reason is that both the line gives a small contribution sed on the → ay scenario. The comparison of , µ µ ν ν min nted in this work. 2 i, -3 χ 1 0 10 -1 numbers have to be evaluated for 2 dof,

i 10

2

10

10

4 X

χ [eV] g m g signal in KARMEN, and the first term in − e ν 0 min – 8 – , 10 in eq. (3.1), have the same dependence on 2 tot L χ 4 = -1 2 PG χ 10 97 for decay. These θ . 2 2 = 4 sin minimum of all data sets combined and -2 s compared with the pion lifetime of 26 ns, a possible contrib 2 10 2 PG µ oscillations χ χ 2 . is the -3 line does not contribute to the ¯ 10 µ min Allowed regions for LSND (solid) and KARMEN (dashed) at 99% C = 18 m). In addition, as discussed above, the , . Applying this method to the case of LSND and KARMEN we find ν i 1 0 2 tot -1

χ

10 10

10

[eV m ]

∆ A powerful tool to evaluate the compatibility of different da In figure 2 we show the allowed regions for LSND, KARMEN, and th

2 2 KARMEN for oscillations and data set where to the LSND signal, which is absent in KARMENgoodness because of of fit the (PG) ti criterion discussed in ref. [37]. It is ba L This allows usthe to KARMEN accommodate null both result, by the taking positive into signal account the in different the b both experiments for the casethe of left oscillations and and for right the panelsin dec of the figure decay 2 scenario showsoscillation is that phase, at the and the compatibil the same exponent level Γ as for oscillations eq. (3.3) is absent.points For as the well statistical as analysis the of expected KARMEN background d for the prompt ener appropriate time cut. Hence,from in the contrast to LSND the helicit of neutrinos from the pion decay was suppressed in the ¯ Figure 2: muon lifetime of 2 the beam and the excellent time resolution of the dete KARMEN combined (shaded regions) atoscillations 90% and and the 99% right CL. panel The to left the p decay scenario prese JHEP09(2005)048 2 m (4.1) (4.4) (4.3) (4.5) (4.2) he case and ∆ θ 2 disappearance 2 with the heavy µ µ ation within the ν ν 0 for the branching is rather poor in the ≈ 4 sets (sin µ tions of the light mass L -dependent effects enter U µ,τ ffect in . The recent update of a 2 41 L . l E disappearance comes from R is the mass-squared differ- ound in ref. [38]. 4 e a non-trivial bound on the m P L dependent term in eq. (4.1). disappearance is expected in , 4 se µ l ∆ Γ e e following the appearance of L ν , P ν rino data performed in ref. [11] − 2 e ) e analysis of SBL disappearance e . 2 ATM survival probability 4 ≈ 1 and n the decay scenario the survival L | , m . 4 µ L 4 )sin is given to a good approximation by µ | ≈ ν 4 2 4 | events in a near and far detector are Γ U e µ 4 µ | − ν µ µ R U e | ν + . Following ref. [39], in the case of (3+1) U 4 | 2 2 | enters also in 4 + ) 4 µ − | l 2 2 µ | | U P 4 | 4 U (1 | µ µ 2 ≈ – 9 – | + U U 4 | l µ 065 (99% C = 0 in eq. (2.6), no ¯ 05eV, where ∆ P . osc . − | µ , U 4 0 ν for decay). This yields a PG of 8.1% for oscillations 0 | the sensitivity of CDHS to e ≈ 4 4 → 4 U ≤ | µ ∼ ATM − ν 4 2 = (1 dec | = 1. However, since we need mixing of µ µ , gm P 4 ν e U µ µ | ¯ ν → dec = 1 ν , 2 ATM U µ | → ATM ν and ¯ → e m µ ¯ ν µ P osc e ν SBL , ν ∆ P R → P 2 µ q | SBL ν , which leads to significantly stronger constraints than in t 4 range the most stringent bound on 2 P µ | À ν 4 U | µ 4 U | m L/E with heavy mass states, i.e. on µ ν is an effective survival probability involving only oscilla , which is obtained by numerically solving the evolution equ l l m P As shown in ref. [39], also atmospheric neutrino data provid in the decay products, i.e. we adopt the choice µ decay scenario. Eq. (4.1) has to be compared to compared. Therefore this experiment is only sensitive to th Since this term enters only via the CDHS experiment [12], where the number of In the relevant ratios of the decay. Then eq. (2.6) yields for the SBL experiments. To simplify theν analysis, we will neglect in th states in order to explain the LSND signal, one expects some e four-neutrino analysis of atmospheric [3],gives and the K2K bound [5] neut which holds for Earth matter. Note that the parameter SBL reactor experiments: states where for oscillations and experiments. Under the assumption and 8.3% for decay. 4. Combined analysis of LSND andLet null-result us experiments now discuss the survival probabilities relevant to th oscillations, the survival probability of atmospheric of decay. Technical details of our CDHS data analysismixing can of be f ence responsible for atmosphericprobability neutrino of oscillations. atmospheric neutrinos I is modified to corresponding to the two parameters in common to the two data for oscillations in a (3+1) four-neutrino scheme. In this ca already at order JHEP09(2005)048 2 µ | ν 4 µ U 0 | 2 10 | 0 for the 4 e otentially ≈ U | produced in r e µ,τ ν = 4 nce+atmospheric -1 , R 41], as well as 1 eff 10 θ . (4.3) and (4.5) we ding effects in atmo- 2 2 ≈ | ) from [11, figure 19], 4 2 e µ 2 | ount also oscillations of tigate the compatibility t (see e.g. refs. [38, 39]) EN compared with the R U 4 decay | µ will be doubly-suppressed U -2 | ent work. d we include data from the ong-baseline experiment [5], contribution (suppressed by io. In figure 3 we show the ( s relevant to LSND, we have 10 2 by the quadratic appearance 2 ATM itude sin χ igation of atmospheric neutrino n of these data (shaded regions) at m The dash-dotted curve in the right ations in the (3+1) mass scheme and -3 1 0 10 -1

10

10

10 4

[eV] m g the constraint obtained for oscillations applies – 10 – 4 | 4 µ -1 U 10 | . However, under the assumption r µ for atmospheric neutrinos, and some of the ν 0 eff 2 ll θ -2 2 m 2 10 sin transition probability for atmospheric neutrinos, which p s e ν (3+1) oscillations → -3 r µ ν 10 P . In the following decay analysis we will neglect such sublea Allowed regions for LSND+KARMEN (solid) and SBL disappeara 2 | 1 0 -1 3

e reactor experiments Bugey [13], [40], and Palo Verde [

10 10 -like events. In addition, in general one has to take into acc

10

1 for atmospheric baseline and energy ranges. Comparing eqs

] [eV m U e e

∆ 4 ¯ 2 2 ) to the ν µ 2 À In the left panel of figure 3 we reproduce the well-known resul Now we turn to the global analysis of all SBL data, and we inves | U 4 | → L µ 4 e U ¯ is tightly constrained from the disappearance experiments data from CDHS [12], atmospheric neutrinosas [3], described and above. the K2K l that, for (3+1) mass schemes, the effective oscillation ampl of LSND and null-resultallowed experiments regions within from the the decaybound appearance scenar implied experiments from LSND+KARM disappearance experiments. In this boun which has been obtained fordata oscillations. within the A decay detailed scenario invest is beyond the scope of the pres ν spheric neutrinos, and we will use as an approximation the by branching ratios, oscillations of the decay products with ∆ the decay will oscillate back to affects also in the case of| decay. Note that the decay will give a small the decay products with ∆ find that neglecting the small term Figure 3: neutrino experiments (dashed) at90% 99% and CL, 99% and CL. the Thethe left combinatio right panel corresponds panel to to neutrinopanel the oscill shows decay the scenario 99% CL presented constraint in from this CDHS. work. where in the last stepΓ we have used the fact that for decay rate JHEP09(2005)048 are (4.9) (4.6) (4.8) (4.7) 5 . − , parameters 1%, slightly = 98 . illations there = 2 e rest. Then the s, thanks to the KARMEN, which (ATM) e transparent if we he rather small PG iments, whereas the +1 (3+2) h the rest of the data. ality of the fit further 6 indicates that decay eriments, i.e. similar to . o oscillations in a (3+2) tants of order 10 ined from combining all . the absolute values of the m atmospheric neutrinos rom reactor experiments, 3 ta. . ed PG = 8 . within the decay framework. lear from the right panel of 2 ne can see in figure 3 that the or the decay scenario th data sets. The only relevant (Palo Verde) χ = 88 4 eV % . +1 3 dec , − = 3 10 2 min 4 × 6 % (LSND vs rest) 8 (CHOOZ) ¯ gm . . +1 , χ 9 . , – 11 – . In contrast, in case of decay, appearance and 2 | PG=4 PG=1 4 016 µ (Bugey) = 96 . U | osc , = 0 +60 2 , | and 2 min , 4 8 . χ µ 2 2 . | U 4 | (CDHS) e U = 6 = 21 | +15 2 PG 2 PG χ χ values have been evaluated for 2 dof corresponding to the two 2 dec: osc: χ minimum. We find 2 (KARMEN) χ +9 worse than the one for decay. test the compatibility offigure appearance 3, and we divide disappearance the exp global data into LSND+KARMEN and all th in common to theis two a data severe sets. disagreementPG between The LSND is PG and acceptable numbers all within showeven the the that for other decay for decay exper framework. osc comesis from The present the reason in slight for any conflict t ofmass between scheme, the LSND a scenarios. similar and analysis Note performed that in ref. for [18] five-neutrin yield where the global provides a significantly better description of the global da Applying eq. (3.4) to this case we find Although the GOF impliedlarge by number these of numbers is data good points in (see both eq. case (4.6)), the ∆ (LSND) 3. The better agreement of the data for decay becomes even mor 1. First we compare the fit for oscillations and decay by using 2. Next we use the PG [37] to test the compatibility of LSND wit 11 sufficient to make theusing decay three different fast statistical enough. tests. Let us quantify the qu disappearance experiments are infigure 3; perfect there is agreement, a asconstraint large overlap is from of the c disappearance allowed regionsshown data for in bo comes eq. from (4.4).and, the in bound agreement As with fro mentioned theconstraint above discussion from no CDHS related is to constraint too eq.The arises weak (4.1), shaded f to o contribute regions significantly indata, where the the figure total show number data the points allowed is regions obta The global analysis gives the following best fit parameters f of the small parameters Hence, for neutrino masses in the range 100 keV coupling cons JHEP09(2005)048 (5.1) neutrinos , µ ¸ ν ) e ed, since they ν E ( ailable to describe ¯ σ antineutrinos), and ers confirm our con- Although the heavy ) µ riments are in perfect decreases with energy. ν , the antineutrinos give E e e ( ¯ ν ν e r to the case of oscillations. maller impact on the final ¯ ν ect a significant change of E experiment [24], which is have performed the analysis hat, according to eq. (2.7), he spectrum rises monotoni- → dE te that the spectral distortion general grounds this can only utrinos and antineutrinos, the µ ill have low energies, for which MiniBooNE the appearance of and ¯ ν 540 m. In the minimal decay e on cross section for antineutrinos dP ν ' L % )+ will also contribute to the signal. We 2 appearance in a beam of e − ν e φ ν e E 10 ¯ ( ν σ × ) → 5 µ . 4 ν n – 12 – E e ( ν e ν → dE PG = 55 % (app. vs disapp.) (4.10) PG=2 µ ν = 0. This reduces the number of parameters, and hence µ dP · , R , which we extract from [24, figure 3]. ) , µ µ , ν ν 6 700 MeV at a baseline of . = 1 2 E . ( e ) will be less pronounced in MiniBooNE than in LSND because of ∼ φ β R ν = 1 = 16 µ ν , E 2 PG 2 PG α dE ν χ χ e ν E ∞ ( E = 0 and Z rs 4 dec: osc: e ) is the total charged-current cross section for neutrinos ( W ∝ U σ e (¯ the fit of the decay scenario, since more parameters become av ν σ dN ) is the initial flux of PG analysis gives In this analysis theare added conflict up between to LSND oneclusion and single from data KARMEN figure set. 3 isagreement that Therefore, remov in the appearance the above and decay numb disappearance scenario. expe dE µ The spectral shape predicted by eq. (5.1) is shown in figure 4. Before concluding this section, let us mention again that we ν produced in the helicity-flipping decay events with a probability of the same order as in LSND, simila E ( e e ¯ calculate the differential number of events as ν Since the MiniBooNE detector cannot distinguish between ne with a mean energyframework discussed of in the previousν sections we predict for the very different initial spectra. In the LSND experiment, t cally up to aTherefore, maximum energy, degrading whereas the the energyspectrum MiniBooNE of in spectrum the the decay case products of MiniBooNE. has a s only a small contributionmost to of the the decay products total fromthe signal. the detection helicity-flipping cross decay The w section reason isis is small. roughly t a Moreover, the factor two detecti smallerimplied than by the one for neutrinos. No neutrino mass state decays with equal probability into simplifies the analysis considerably.our results Although by relaxing we theseimprove do assumptions, not we stress exp thatthe on data. 5. Predictions for MiniBooNE and other5.1 future MiniBooNE experiments A critical test of thecurrently LSND taking signal will data. come This from experiment the looks MiniBooN for where by setting φ JHEP09(2005)048 spectral cteristic . However, e ν → µ iniBooNE [42]. In ν e of oscillations for 2.5 odels in the case of a ons is provided by the gy spectrum, since the 2 01, and thus at the edge well as (3+2) oscillations . m tangle it from oscillations ents such as T2K [43] or 0 ∆ cts. Moreover, in detectors ations depends strongly on ussed above in relation with scenario. The disappearance ∼ 2 e uncertainties [42]. Therefore, 2 stics, as well as on experimental | 3 e 4 e appearance of “wrong-helicity” ears to be rather challenging first µ U U in the case of oscillations (solid curves). | from the helicity changing decay. 2 e large or small 2 m ν 1.5 by exploring the chanel appearance signal in MiniBooNE for decay with 3 decay e = 0.9 eV e [GeV] , which are not taken into account in figure 4. 2 ν ν U ν m E – 13 – 2 E ∆ 1 = 2 eV 2 m ∆ 0.5

. One observes that in principle the decay predicts a specific

2 0 Signal in MiniBooNE (arb. units) (arb. MiniBooNE in Signal m . Much as in MiniBooNE, the signal from decay will have a chara 3 e U disappearance is predicted, which should be observable in M Energy spectrum predicted for the µ ν 4 eV (shaded region) and for various values of ∆ . . Whether it will be possible to distinguish between the two m A [44] looking for a non-zero value of =3 Another method to discriminate between decay and oscillati In figure 4 we show also the predicted spectral shape in the cas 2 ν 4 m ¯ spectral shape, as impliedcapable by of the distinguishing spectrum neutrinos of from the antineutrinos decay th produ of the sensitivity for thoseto experiments. observe Therefore, an it app effectinduced of by our decay scenario, and second to disen the appearance probability would be proportional to In general theNO decay will contribute to the signal in experim contrast, the signal is expectedsearch to in be MiniBooNE very smallnormalisation is in of limited the the total decay to number ofthe a events signal suffers shape for from larg decay analysiseq. is of (4.1) suppressed the and for the the ener CDHS same experiment. reason as5.2 disc Experiments looking for a non-zero value of disappearance channel in MiniBooNE.sizeable In the case of (3+1), as several values of ∆ positive signal in MiniBooNE depends onfactors the such available stati as the energy resolution for shape of the signal,∆ whereas the actual spectrum from oscill The blue/dark-shaded region shows the contribution of ¯ gm Figure 4: JHEP09(2005)048 e e ν ν ap- = 5 (6.1) (6.3) (6.2) 1 km e → ν N µ ∼ ν → , i µ , because of ) 3 ν , e L . 5 U osc α 2 54 ν 2 +Γ m E 4 +Γ 2 /T2K near detectors ∆ Γ ation of γ ffects is quite challeng- [46]. This would imply ≡ ≡ + ode) can be significantly , one finds E a new experiment at a δ Γ L osc le to obtain an interference that a positive signal for ¯ e an optimal experiment to Γ o heavy neutrinos, i.e. os. cay scenario, since our model the decay scenario. Neverthe- cos( ese beams might suffer from a n-zero value of ad to CP violation in the decay. A, but no corresponding signal L , Γ ν ination for electrons is a difficult beam of T2K in the KamLAND lity to explore the decay scenario 5 , − e A µ 4 ν osc Γ − A Γ ) | . 3 β γ Γ e 5 ≡ + g + U ¢ γ || δ L β h 4 from the Γ g tan | a experiment [45], which will be placed − e cos( – 14 – 2 ν e h ν γ disappearance is suppressed, whereas the ≡ − , e β 1 ) ν ¡ cos R β β | ∗ 5 ν hβ 5 g 0 α β → R 4 α U 2 , which is needed in order to accommodate the LSND result. dec g , ν | dL || 2 | 5 4 2 h 4 αh α α dP µ A 0 = 5 and performing the integral over U U U 2 | h | U 4 | | , such that ¯ ∗ Γ α dL 1 2 β N 3 hβ e U L R g 0 U | h ) background. Z + X 2 e ν arg( (¯ ≡ ≡ = ≡ e β ν hβ ν δ R → α dec ν P disappearance in reactor experiments such as Double-Chooz e Using eq. (2.8) for In summary, we stress that a direct measurement of the decay e Another manifestation of the decay model could be the observ ν stopped pion neutrino sourceconfirm as or proposed exclude our in decay ref. model. [47] could b 6. CP-violating decays and the signalIn in this section MiniBooNE we extend ourmassive model neutrinos. and consider the We case willbetween of oscillation show tw and that decay amplitudes in [35], thisIn which this may case le way it the issuppressed signal possib with in respect MiniBooNE to (running the in LSND the signal neutrino from m antineutrin Therefore, if the LSND signal should be confirmed by MiniBooN the rather small mixing, ing for present and near-future experiments looking for a no disappearance in reactor experimentsis cannot perfectly exclude compatible the with de a sizeable value of appearance signal is dominated by the decay. Note, however, very small values of pearance in accelerator experiments such as T2K or NO for ¯ detector. Let us note that also the Miner away from the targetcould within be the suitable places NuMI tolarge neutrino look intrinsic beam, at or these effects, the although K2K th with the following definitions for the branching ratios neutrinos with low energies wouldless, be this a is generic prediction alsoexperimental of very task. challenging, because In charge thismight discrim respect, be an to interesting possibi look for the appearance of ¯ and phases JHEP09(2005)048 . δ 2 1, ∼ (6.4) 1 eV γ Γ with ∼ = le the neu- 5 2 54 m . The phase and tan . = Γ 5 i n 4 ) ,π L have to be replaced transition probabil- e osc 6= 0 and ν hβ δ g 4 = 1, Γ → n µ +Γ eed to accommodate the e dec e keV range and a mass ν γ R P violating decay scenario. he standard three neutrino and a by a combined analysis of tes he two heavy mass states in iBooNE data taking with an eriment in the neutrino mode = on are sin( αh o obtain CP violation, the two e interference of the amplitudes LSND signal e and U L 5 e Γ according to eq. (6.1). The shaded neutrino signal for ∆ ¯ ν R s, − e → e ν = µ dec ¯ ν e → e − e few eV, the last condition shows that ν µ P 4 ] dec ν γ 2 − ν R − P ∼ µ µ ν ν sin [eV h h 2 54 m and 003, δ m observed in LSND. The chosen parameter values . h ∆ e g e ¯ ν ¯ – 15 – ν sin → = 0 → µ γ µ dec ¯ ν , and we obtain the CP asymmetry: 2 ¯ ν | δ P 5 β P µ ν cos U | → . Using ¯ | 5 α →− dec 2 54 α ν = δ P U m 2 || | 4 − ∆ 4 keV) have to be highly degenerate. range for α µ β ¯ ν ∼ U U σ | > | 2. → π β h α 0.1 1 10 0 dec 8 ¯ π/ ν R

/ 0.1

m 0.3 0.2 0.4 P Probability (%) Probability 2 h = MeV, δ m = 2 ≡ / 2 h value relevant to LSND and MiniBooNE. Clearly, in this examp g P , which implies ν 75 m ∆ ∗ . hβ or ¯ 0 g The transition probabilities L/E osc ' 4 eV, and . Γ and ν ∼ =3 ∗ αh In figure 5 we show a numerical example for the h Γ L/E U m h ¯ This result confirms the previousheavy observation that neutrinos in have order to t difference be in very the degenerate, eVLSND with signal range. with masses a Whether possible in null-resulthas this th of to the mechanism MiniBooNE be allows exp investigated ind afterthe two the experiments release within of this theantineutrino framework. beam MiniBooNE In would dat that be case, necessary Min in order to test the CP- trino signal is strongly suppressed with respect to the anti ities for an are by region corresponds to the 1 the heavy neutrinos ( is the analogue ofoscillation the framework. Dirac In phase fact, leading in to the case CP of violation antineutrino in t g Figure 5: One observes that necessary conditions to obtain CP violati analogy to eq. (3.1), whereas thefor second term decay results and from th oscillations of the two heavy neutrino mass sta The first term in eq. (6.1) describes the incoherent decay of t i.e. JHEP09(2005)048 , 5 − were 10 3 , 2 × , 1 contribute m few 01, whereas e . 0 À < ixing of heavy 6= h 2 ∼ os. For the very α and a light scalar g m cs 2 e | ν ent, and these data 4 for µ = 0 for the branching U | eα d present an additional g f order re completely unaffected. µ,τ he heavy neutrino in such o scalars, with a spectrum metric) coupling matrix in o strong constraints on the ch as in a supernova and the eta decay [50] experiments. alars. However, in this case y the lagrangian in eq. (2.1) , R ions to the effective neutrino cessary to explain the LSND pernovae. For the discussion . ction 4. f the two-neutrino double-beta r emission was not observed in ¯ g [51] apply only to the coupling atory experiments and, for their = 1 4 os. On the other hand, effects in µ e ve neutrino with U R le neutrino mixing. ' . From dimensional considerations, it eµ νe g and couplings between active neutrinos and → and 5 component can be produced in the Sun, and = 0. The coupling between ¯ νe g h – 16 – 4 n e 1 MeV. Mixing of neutrinos with smaller masses ' U with the heavy mass state, & es g (1). µ h ν O m = 0, no 4 g < e U , are non-zero: αβ = 0. Furthermore, the assumption g 4 τ U in our scenario are stable, there is no decay of solar neutrin = l ν 4 e U The decay of pions and kaons has been used to set bounds on the m First we note that in our model solar neutrino oscillations a See ref. [48] for a recent analysis of various bounds on steri , which can be arbitrary small in our scenario. The couplings 5 ee much too weak to constrain our model. 7.2 Supernova bounds To estimate the effect of ourearly model Universe in let thermal environments us su to compare the the rate one of of processes weak induced processes b of the type are compatible with these bounds. Furthermore, light scala pion and kaon decays [52, 53]. The most stringent bounds are o produced in such decays,monochromatic the line. energy spectrum Nomixing of positive for the signal neutrino muon was with woul found, masses leading t in principle to double-betathe decay limits with are the very emission weak [51]: of two sc neutrinos (see ref. [32] and references therein). If a massi would induce double-beta decayfor with the the two emission electrons of whichdecay. is one distinguishable or Relatively from tw strong the bounds oneg o for single scalar emission same reason the decayare has entirely also explained by noatmospheric oscillations effect neutrino of in experiments the the have light been KamLAND neutrin discussed experim in se 7.1 Laboratory bounds In general, the mixingmasses of a in heavy neutrinoless neutrino double-beta leadsNote, to however, decay contribut that [49] in andexperiments our because tritium scenario of our b there assumption will be no effect of t since the ratios of the decaythe implies flavour that basis, only two elements of the (sym Because of the assumption we set 7. Constraints from laboratory, cosmology, and astrophysi Mixing between active and sterile neutrinos, implications in the evolutionof of these the constraints early we Universe willsignal: and focus of we on su require the minimal only scenario mixing ne of a light scalar, have been extensively studied, both in labor JHEP09(2005)048 , 0 h . 44 He . 3 n 4 1 (7.1) (7.2) ≤ ↔ ≤ ν φ ν l N ν δN ≤ 6 3 . 3: 1 reactions are ≥ ↔ ν N are strongly coupled , we find 57, which appears to f the primordial . h φ n h , = 4 mber of neutrino flavours e of a supernova and could n . s add that there might be e. Therefore, we can treat and 6 the heavy neutrino is large he neutrinosphere, avoiding ν 10 MeV, 2 4 − , substantially modifying the xing [54] as well as Majoron , because of the systematical h ↔ tive ones. − N m present at the time of Big ¶ ∼ n l s are introduced [57]. Analyses , as in vacuum. From eq. (7.1) eutrino flux distortions [53, 56]. h are beyond the scope of the ¶ ence on input priors. ν upernova SN1987A, this energy- h g, heavy mostly-sterile neutrinos l lead to the limits 2 E n 1 denotes processes like he bounds on ν E , E ↔ the sterile neutrinos are thermalized within 1 MeV φφ os see ref. [33]. 1 MeV µ µ 2 ↔ 4 ´ l ´ ν h l 5 However, to draw reliable conclusions from ν − ¯ g , where 2 1 eV 7 ¯ gm 2 10 – 17 – ³ ³ /E 10 2 4 ¯ g is the typical energy of the involved particles. Using 10 10 are produced, they are thermalized together with the ∼ E h ∼ ∼ 3. The discrepancy between these two exemplary results n 2) − 1 reactions. Hence, one additional neutrino and one scalar 1) 2) of our decay model are initially generated by mixing with ν ↔ N h ↔ ↔ ↔ weak weak (2 n , where σ σ ≡ σ (2 (2 2 ν σ σ E 2 F and δN G 4 2 indicates processes like ∼ /E ↔ 2 h m weak 2 σ ¯ g ∼ , and 2 φ 1) → In the early Universe, If heavy neutrinos and light scalars were produced in the cor times faster than weak interactions. This implies that ↔ Note that also in four- or five-neutrino oscillation schemes For a careful analysis of these processes for active neutrin h , are relevant when light particles such as sterile neutrino 7 6 4 ν n (2 l be disfavoured by the limits quoted above. scalar due to the verydegree fast of 2 freedom will be present during BBN, leading to active neutrinos [60]. As soon as illustrates that such bounds have to be considered with care uncertainties in light-element abundances, and the depend (95% CL) [59], where abundance and its uncertainty, has substantially relaxed t (95% CL) [58]. A recent analysis, that uses a new assessment o of cosmological data, including light-element abundances to the active neutrinos,any and energy hence, loss they due areadditional to effects, trapped such particles as within modification escaping t of from leptonThe number the analysis or n core. of such Letpresent effects work. u requires detailed studies, whic 7.3 Cosmological bounds Constraints on the numberBang of Nucleosynthesis relativistic (BBN), degrees usuallyN of parametrized freedo by the nu 10 ν it follows that for typical energies in the supernova cores, the standard BBN scenario [57]. follows that In addition to these reactions inducedare by produced the scalar via couplin oscillations due to their mixing withescape the freely, they ac would carrysupernova away evolution. a large Together with amount the of observations fromloss energy s argument has beencoupling, used see to e.g. constrain sterile refs.compared neutrino [33, with mi 55]. the mattermixing, In potential as our within well scenario as the the the supernova reactions cor mass involving of the scalar and σ JHEP09(2005)048 6 ∼ at − the 2 | φ 10 e 4 µ ν × U | and ta might resence of 0 may be few h 5 [58], and appearance . n 6 . e < ¯ ν g ≤ of order → ν me level as in the µ µ N hat of the standard depends in a rather ν ν ns have a recoupling appearance based on ν beam produced in the pochs of the Universe. e ng sterile neutrinos and N ical potential for µ null-result short-baseline ν with ν l data of LSND, we find 100 keV (see eq. (7.2)). 0 as well as 4 re events at the lower part ive weaker, decays into the scalar and a han the light neutrinos, does one obtains a characteristic ermalization of n N. Couplings & icle and light neutrinos. We ns, although still acceptable would be manifest [64]. ons, i.e. their strength grows ing of acoustic oscillations at he recombination era, effects > 4 l heating temperature [20]. The during the eV era rather than voured by structure formation T n ν nce there are many effects which ement of the ¯ nal state contains a large fraction δN [62], a matter potential induced by 3 − through mixing. This could be achieved h n appearance signal observed in LSND. Taking e – 18 – ν component is contained in the initial ¯ 4 n 9 dof). A more detailed investigation of the LSND spectral da 57 is allowed. Moreover, a detailed simulation of BBN in the p / . 8 . = 4 flavour, it will give rise to the ¯ can occur because the radiation energy density differs from t ν e = 10 l ν N 2 processes would not be efficient in producing and thermalizi We have performed a global fit to all relevant data, including As can be seen from eqs. (7.1) and (7.2) the scalar interactio Finally, we note that our scenario, with the scalar heavier t 2 decay ↔ 01, such that a small -neutrino decay performed in ref. [61] showed that the effect . χ experiments LSND and KARMEN in the decay scenario is at the sa into account the energy distribution of the decay products, prediction for the spectralof shape the of the spectrum. LSNDthat signal, the Comparing with fit this mo of( prediction the with decay the is spectra slightly worse than for oscillatio allow to distinguish between decay and oscillations. reactor and accelerator oscillation experiments. The agre superposition of light neutrino massof eigenstates. the If ¯ this fi LSND experiment. On the way to the LSND detector the 0 the decay of aassume heavy a sterile small neutrino mixing of into the a heavy light neutrino scalar mass part eigenstate form, instead of theas usual the decoupling form Universe ofFor evolves, weak instance, which interacti if may alike have a light some delayed scalar effects matter-radiation couples equalityhigher in to and later enhanced neutrinos e damp before t guarantee that these scatterings are out of equilibrium for scenario. Moreover, if onefree-streaming, or a more uniform neutrinos are shift of scattering the CMB peaks to larger not give rise toarguments a [66]. neutrinoless Universe [65], which is disfa 8. Summary and conclusions We have presented an explanation for the LSND evidence for ¯ neutrino-Majoron interactions [63], or by2 assuming a low re e.g. through a large lepton asymmetry of order 10 scalars as far as they are slower than the expansion rate at BB BBN, by suppressing the initial production of obtained. Let us mention also the possibility to avoid the th non-trivial way on model parameters, and values of τ hence limit on extra relativistic degrees of freedom becomes much BBN considerations a more detailedmight analysis is play required, a si role. For example, in the presence of a small chem JHEP09(2005)048 µ ν ]. SND and all (2001) 112007 Curie Intra-European hep-ex/0203021 n the upcoming Mini- oes not find a positive ent baselines. However, n scenario. In addition, atory bounds and have nimal decay model it is ov, H. Ray, R. Scherrer, gramme”. MEN) and disappearance sit during which this work -0151 and by the Spanish D 64 e find PG = 55% for decay R. and S.P. are grateful to ture neutrino experiments. r scenario, which may allow B observations. del is in complete agreement g for the antineutrino signal inos. so-called parameter goodness ]; terference term between decay y of the same order as seen in tality during part of this work. e decay exponential depends on with masses in the 1 keV–1 MeV Evidence for oscillation of atmospheric (2002) 112001 [ Phys. Rev. , Upper limits for neutrino oscillations anti- D 65 beam µ hep-ex/9807003 ν 6% for decay, which is slightly better than the . – 19 – Evidence for neutrino oscillations from the Phys. Rev. , (1998) 1562 [ 81 . This can lead to a suppression of the signal in MiniBooNE 2 collaboration, Y. Fukuda et al., appearance in a anti- e ν 1 eV ]. ∼ 025% for (3+1) oscillations. Testing the compatibility of L . collaboration, B. Armbruster et al., 2 54 from muon decay at rest Phys. Rev. Lett. m , e ν collaboration, A. Aguilar et al., 1% obtained in ref. [18] for a (3+2) five-neutrino oscillatio . anti- , which allows us to reconcile the two results due to the differ hep-ex/0104049 → Super-Kamiokande neutrinos LSND observation of anti- KARMEN [ ν In the minimal version of the decay model we predict a signal i [3] [1] [2] case of oscillations. MuchL/E as the oscillation phase,unlike also the th case of (3+1)with four-neutrino the schemes, constraints our from decayof mo disappearance fit results. (PG) to Using test(Bugey, the the CHOOZ, CDHS, compatibility of atmospheric neutrino) appearancebut experiments, (LSND, w only KAR PG = 0 the null-result experiments, we findPG PG =2 = 4 we have shown thatdiscussed implications our for model supernova evolution, is BBN consistent and CM withBooNE present experiment labor corresponding toLSND, a and transition we probabilit haveto discussed distinguish characteristic signatures it ofFurthermore, from ou we oscillations have in shownpossible MiniBooNE that to within introduce or CP an other violation in extensionand fu the oscillations of decay of through the two an nearly mi in range degenerate heavy and neutrinos, ∆ running in the neutrino mode, and simultaneously accountin in LSND. Hence, thissignal model either can in only the be neutrino excluded mode if or MiniBooNE running d with antineutr Acknowledgments We thank J. Beacom,M. B. Sorel, Louis, R. S. Tomas Pakvasa, andthe S. W. Theoretical Pastor, Winter Astrophysics S.T. for Group Petc usefulT.S. for acknowledges kind discussions. support hospi from S.P. the CERNwas Theory initiated. group for S.P.R. a is vi Grant supported FPA2002-00612 by of NASA the GrantFellowship MCT. ATP02-0000 within T.S. the is 6th supported European by Community Framework a Pro “Marie References JHEP09(2005)048 , , ]. 89 ]. to 2 B 520 3 eV . (2001) 117303 , 0 nd 95-meters from olation or . . . ? hep-ph/0207157 D 64 Phys. Rev. Lett. ]. Phys. Lett. ]. range , hep-ex/0404034 , 2 M (2005) 112005 (2005) 081801 ∆ e SNO data set oscillations in the NOMAD 94 Phys. Rev. (2002) 321 [ ]. D 71 e observatory , ν ]; ]. Status of global fits to neutrino Ruling out four-neutrino oscillation (1993) 3259. → (1995) 503. (2004) 101801 [ hep-ex/0411038 hep-ph/0306226 µ Evidence for an oscillatory signature in A measurement of atmospheric neutrino Status of the cpt violating interpretations B 643 ν 93 Reconciling dark matter and solar D 48 ]; Phys. 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