on the 17 kev mass neutrino

Volume 263, number 3,4 PHYSICS LETTERS B 18 July 1991

On the 17 keV mass neutrino

S.M. Bi lenky a, A. Masiero b and S.T. Petcov c a Laboratory of Theoretical Physics, Joint Institute of Nuclear Research, Dubna, SU- 101 000 Moscow, USSR b lstituto Nazionale di Fisica Nucleare, Sezione di Padova, 1-35131 Padua, Italy c Scuola Internazionale Superiore di Studi Avanzati, 1-34014 Trieste, Italy

and 1NFN, Sezione di Trieste, Trieste, Italy and Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria

Received 26 April 1991

The phenomenological implications ofa 17 keV mass neutrino coupled to the electron in the weak charged lepton current with a constant ~ 0.1 are analysed. The possible nature of the heavy neutrino and the related phenomenological, astrophysical and cosmological constraints on its properties and couplings are discussed. Transitions of ~ 92 leading to a reduction by ( 1-2)% of the ~7~ ) fluxes from reactors and accelerators, independent of the source-detector distance and neutrino moment, are predicted to take place. In most cases the transitions of tg~ are into ~,~ which practically coincides with the heavy neutrino. The v, can "weigh" 17 keV or more than 85 keV. The problem of the heavy neutrino decay modes is briefly discussed.

In 1985 Simpson published [ 1 ] the results of an

experiment in which the 13-spectrum of 3H far from

the end point was measured with a semiconductor

detector. A kink was observed in the measured spec-

t rum and it was interpreted by Simpson as being due

to the emission of a "heavy" neutr ino with mass ap-

proximately equal to 17 keV, coupled, in addit ion to

a zero (or very small) mass neutrino, to the electron

in the weak charged lepton current with a constant

~ 0.1. This experiment stimulated the performance

of several other experiments searching for a heavy

neutr ino with 13-spectrometers by measuring the spectra of electrons originating in the ~l-decays of 35S

[ 2 ] and 63Ni [ 3 ]. No indications for the existence of

a heavy neutr ino were found in these experiments. At

the same time the authors of the experiments meas-

uring the fl-spectra with semiconductor detectors

continued to find evidence for emission in the 13-decay of 3H and 35S of a heavy neutr ino with mass ~ 17

keV [4].

The interest in the 17 keV mass neutr ino problem

undoubtedly increased recently. The first results of

three new [3-spectrum experiments, whose authors

also claim to have observed evidence for the exis-

tence ofa 17 keV mass neutrino, were published [ 5 ].

New high precision 13-spectrum measurements, aim-

ing to check these results are in preparation at present [6].

In the present note we shall discuss the possibilities of searching for the heavy neutr ino in experiments aimed at the detection of possible effects of mixing and oscillations [7] of neutr inos produced at reactors, accelerators and meson factories. We shall make also a few comments concerning the possible properties and coupling of the suggested 17 keV mass neutrino and the general phenomenological implications

associated with it. So, let us assume that neutr ino mixing takes place

indeed and

v~L(x) = ~ Uo'eL(x) , (1) i=1

where V~L(X ) is the field of the left-handed (LH) flavour neutr ino v~, UiL(X) is the LH component of the field of a neutr ino vi with definite mass m~, and U~ is an element of a unitary matrix - the lepton mixing matrix U ~L. According to the results [9 ] obtained at LEP, the index ~ in eq. ( 1 ) takes three values: ~ = e, la, x. Ifeq. ( 1 ) is valid, there should exist at least three ( two-component) neutrinos with definite mass: n >/3.

at For a detailed discussion of the neutrino mixing and its possible physical implications see, e.g., ref. [8 ].

448 0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)


The massive neutrinos can be Dirac or Majorana particles [ 8 ]. We shall postpone the discussion of the possible nature of the neutrinos v~ and shall assume only that n >t 3 in eq. ( 1 ).

As is well known, eq. ( 1 ) implies the existence of oscillations (transitions) between the flavour eigen- state (anti)neutrinos ~9~ ), ~)~ and ~9~. The amplitude of the probability of the v~--,v~, transition in vacuum at time t, if the neutrino v~ has been produced at time to = 0, is given by [ 8 ]

A(v~--*v~; t) = ~ U ~ , ~ e x p ( - i E d ) U ~ . (2) i = 1

Here E ~ = ~ and p is the neutrino momentum. Let us enumerate the neutrino masses in such a way that m l ~< m2 ~<... ~< mn. Using the unitarity of the neutrino mixing matrix we can rewrite the amplitude of the v~--,v~, transition in the form

A (v~ ~v~, ; t) =exp( - iEl t)

{ ~ [ ( m 2 m 2 ) 1 } • i - - 1 .

X i , U~,i exp - 1 ~p R - 1 U~i+J~,~ ,

(3)

where R is the distance between the neutrino source and the neutrino detector, p = IPl, and we have made use of the standard assumption p >> mi, i-- 1, 2, ..., n, ineq. (3).

We shall assume first that, under the conditions of the experiments performed with neutrinos from reactors, accelerators and meson factories, one has

1 - - , , , , , 2 p ( m ~ - m 2 ) R < < l , i= 1, 2, n - 1 (4a)

1 2p ( m 2 - m Z ) R > 1 . (4b)

In other words, we shall assume that there exists only one relatively heavy neutrino, all other massive neutrinos having rather small masses, and that only the differences of the squares of masses of the heavy and any of the light neutrinos can be relevant in terres- trial experiments with neutrinos from artificial sources (reactors, etc. ). The differences of the squares of masses of the light neutrinos can lie in the rangel0-4-10 -8 eV 2 for which resonance conver- sion [ 10] of the solar neutrinos (into, e.g., v, and/or v~) is possible. Given the existing experimental situ-

ation (including the solar neutrino observations), the assumptions (4) seem rather natural to us. From eqs. ( 3 ) and (4) we get the following expressions for the (anti) neutrino transition probabilities:

P(v~ --*v~, ; t) =P(9~ --.9~, ; t)

= 2 1 G ~ I 2 1 G . . I 1 - c o S ~ - p R , £ # £ ' ,

P(v~ --*vG t) =P(9~ --.9~; t)

Am 2 \ = I - 2 1 U ~ , I 2 ( 1 - I U ~ , I 2) 1 - c o s ~ - p R ) , (5)

where Am 2 = m 2 _ m 12. Thus, if conditions (4) hold, the neutrino transition probabilities under discussion are determined by the squares of the absolute values of the elements forming the nth column of the lepton mixing matrix U. Let emphasize also that all possible types of vacuum neutrino oscillations in question depend on one oscillation length:

L = 4 n p Am 2 . (6)

In the case of a heavy neutrino with mass m , - 17 keV, one has for the vacuum oscillation length

L - ~ 10 -8 (E / I M e V ) m . (7)

So, i fa heavy neutrino does exist, in all cases of prac- tical interest the vacuum oscillation length will be much smaller than the distance between the source and the detector of the neutrinos and the dimensions of the neutrino source (e.g., the core of a reactor, the n- and K- meson decay tunnel, etc. ). This means that the term c o s ( A m 2 R / 2 p ) in the expressions for the probabilities (5) will be strongly suppressed and therefore negligible as a result of the averaging over the dimensions of the region of neutrino production, the neutrino spectrum, etc. As a result, one has for the averaged probabilities

P(v~--,v~, )=fi(9~-.9~,)=21U~,,,IZlU~,,I 2, £' ~ £ ,

/5(v~ --.v~ ) =/~(9~ -*90

=I-2[U~, ,12(1 - IU~, , I 2) . (8)

Consequently, if light neutrinos are mixed with only one heavy neutrino, only the effects of the neutrino mixing can be observed in experiments with beams of neutrinos from reactors, accelerators and meson

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factories: the neutrino transition probabilities in vacuum do not depend on the neutrino momentum and on the source-detector distance.

We shall analyse next the results of the experiments searching for effects of mixing and oscillations of neutrinos, from the point o f view of the possibility of the existence o f a heavy neutrino. Our analysis will be based on the fact that, according to the data obtained in refs. [ 1,4,5 ], the heavy neutrino (vn) cou- ples to the electron in the weak charged lepton current and

I U~o 12-~0.01, (9)

Ue, being, obviously, the element o f the lepton mixing matrix U multiplying the term formed by the electron and the heavy neutrino fields in the weak charged lepton current ~2. We shall assume first that either sterile neutrinos do not exist or if they exist and they mix (due to, e.g., mass terms which are non- diagonal in the neutrino fields) with the ordinary flavour neutrinos, the total lepton charge L is conserved and the neutrinos with definite mass v~ are Dirac particles (see, e.g., ref. [ 8 ] ). The unitarity of the lepton mixing matrix U implies in this case

I Ue~ 12+ I Uv,,12+IU~,,I 2= 1 . (10)

A rather stringent upper bound on the probability o f the v,--'Ve transition was obtained for "large" values of Am 2 from the data of an experiment performed at BNL [11]:

/~(v,~v~) < 1.7X 10 -3 . ( 11 )

From (8), (9) and ( 11 ) we get

I Uu~I/<0.1 . (12)

Using (9) and (12), one can find with the help o f the unitarity condition (10) the allowed interval of values of I U~, 12:

0.9~< I U~,I2< 1 . (13)

Next we shall take into account the existing data on the v ,~v~ transition. The following experimental limit on the probability P(v~--.v~; t) for "large" values of Am 2 was found in ref. [ 12]:

/5(v~--,v~) <2)< 10 -3 . (14)

#2 The value of I U~, [ ~ found, e.g., by Hime and Jelly [ 5 ] reads I U~,I2= (8.5 +0.6 +0.5) x 10 -3.

From (8), using ( 13 ) and (14), we get a stronger restriction on I U~n 12 than (12):

I Uunl2< 10 -3 . (15)

The unitarity condition (10), together with eq. (9) and the limit ( 15 ), leads to

I U~nl 2~- 1--{Ue~1220.99. (16)

Thus, under the rather general assumptions made, the results o f the experiments searching for effects of neutrino mixing imply that I Us, 12 = 0.99. Obviously, in this case v~ practically coincides with v, ,3

Consider next the transition Ve----~V x (Ve----~gx). The corresponding probability is given by the expression

P(Ve-- .VO=P(Ve-- ,VO=21U~,,I21U,,~I 2 . (17)

I f follows from (9), (16) and ( 17 ) that the probability o f the VerY, (9~--,9~) transition can be predicted. One has

/~(ve--,v~) =/5(9~ ~ v , ) = 1.5 × 10 -2 . (18)

Note that (18) ~4 does not contradict the existing data obtained in the experiments performed with neutrino beams ( / ~ ( 9 ~ V ~ ) < 8 × 1 0 -2 [13] and / 5 ( v ~ v , ) < 3.5 × 10 -2 [14] ) .

The check of the prediction (18) would constitute one of the important independent tests o f evidence for the existence o f a heavy neutrino found in refs. [ 1,4,5 ]. The experiments with beams of tagged electron neutrinos (antineutrinos) originating in the decay K ÷ - - - ~ ° e + V e (K---*x°e-ge) provide a possibility to perform the indicated test. Such experiments are in progress at present at the accelerator in Protvino [ 15 ]. It is planned to reach a sensitivity o f the order of 2.5% in the measurements of the ve~v~ transition probability in these experiments.

Our conclusions are based on a phenomenological analysis of the existing experimental data. A non-ob- servation of transitions t ~ -~ ~ ~ at the level corre-

,3 More precisely, the state -.~2tor ofv, is the dominant component in the linear superposition of the massive neutrino state vectors, which represents the state vector of v, in the case under consideration.

,4 Our estimate ( 18 ) of P( ¢ v~ __, ~ ~ ) is conservative. If one takes into account the errors in the value of I Uen I 2 quoted, e.g., by Hime and Jelly [ 5 ], one finds that P( < ~2 --, ¢,7~ ) can actually be somewhat larger.

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sponding to a transition probability of 1.5× 10 -2 would be evidence that:

(i) more than one length of oscillation is relevant under the conditions o f the experiments with neutrino beams and the corresponding neutrino transition probabilities have a more complicated structure than (8);

(ii) there exist sterile neutrinos which mix with the flavour neutrinos in such a way that the total lepton charge L is not conserved [ 16 ]. In this case the uni- rarity of the lepton mixing matrix U implies

IUenl2+lU~,nl2+lGnl2+~ I U ~ n l 2 = l , (19)

where the elements U~ of U are determined as follows:

O,~R(x) )c__ calR(x) = Y u~,v,~(x), (20) i

V~R (X) being the field of a right-handed sterile neutrino (C is the charge conjugation matrix).

(iii) the question about the existence o f the heavy neutrino remains open.

So far we have discussed only "appearance" neutrino oscillations experiments in which the heavy neutrino could manifest itself. Let us consider briefly the possibility to search for effects o f the heavy neutrino in experiments with reactor antineutrinos which are of the inclusive (i.e., "disappearance" ) type. We have

Ivy(E) =_/5(9 e --*ge)I°o(E). (21 )

Here / 6 ( 9 ~ 9 e ) = 1-21U~,12-~0.985, L,o(E) is the flux o f % with energy E at some distance (practically, outside the core) of the reactor and I°, (E) is the expected flux of % in the absence of oscillations (or transitions). Thus, if a heavy neutrino exists, the spectrum of the % produced in a reactor will coincide in form with the spectrum expected in the absence of neutrino oscillations, but will differ from the latter in magnitude by 1.5%. The determination of the initial flux of reactor antineutrinos with such a precision seems to us rather problematic.

Evidently, eq. ( 1 ) implies that the additive lepton charges L~, L , and L~ are not conserved. In this case the lepton flavour nonconserving decays g-+ --.e -+ +7, g-+ --.e ± + e + + e - , x -+ --,IU +7, x~ --'~-+ + I~' + +12'-, ~, ~' =e , g, etc., are allowed. Let us note, however, that the standard weak interaction contributions (due to

diagrams with exchange of virtual W -+-bosons) to the rates o f these decays for mn-~ 17 keV are suppressed at least by the factor [ 17] (rn, , /Mw)4~ 10 -27.

We shall discuss next the possible nature of the suggested heavy neutrino. Depending on the symmetries that the neutrino mass term and the leptonic sector o f the underlying theory as a whole have, a massive neutrino can be [ 8 ] a "s tandard" or "nons tandard" (i.e., Zeldovich-Kanopinsky-Mahmoud- l ike) Dirac neutrino, or a pseudo-Dirac [ 18 ] or a Majorana par- ticle. The most stringent direct constraint on the nature of the heavy neutrino follows from the data on

the neutrinoless double 13-((1313)ov-) decay: (A, Z)--, (A, Z + 2 ) + e - + e - . As is well known, this lepton charge nonconserving process is allowed in the Ma- jorana [19] and pseudo-Dirac [201 neutrino cases. It has not been observed and the best upper limit on the effective neutrino mass parameter ( m y ) , infor- mation about which is extracted from the (1313)or-decay data (see ref. [8 ] ), was obtained in experiments with 76Ge [ 21 ]:

I ( m v ) l < 1 - 2 e V . (22)

Suppose tlrst that only three LH massive neutrino fields giL(X) enter into the expression for the weak charged lepton current, i.e., that n = 3 in eq. ( 1 ). The massive neutrinos vi, i = 1, 2, 3, (including the heavy neutrino) will be "s tandard" Dirac neutrinos and the (1313)or-decay will be forbidden if the total lepton charge L is conserved (Dirac neutrino mass term). Together with a heavy neutrino such a scheme can accommodate a solution of the solar neutrino problem in terms of matter-enhanced solar neutrino transitions ~5 and is perfectly acceptable from a phenomenological point o f view. However, it seems rather difficult ( if not impossible) to satisfy the cosmolog-

~5 For m 3 --~ 17 keV >> m~, m2, there can exist only one resonance layer of matter on the path of solar neutrinos from the central part of the Sun, where they are produced, to the surface of the Sun. As can be shown using the results of the analysis performed in ref. [22], the three-neutrino oscillations of solar neutrinos in the Sun reduce in this case effectively to two-neutrino transitions (which can be matter-enhanced provided 10-8<m~-m~ ~< 10 -4 eV 2 and if the relevant vacuum mixing angle ~012 satisfies sin22qh2 > 10-4).

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ical constraints on the heavy neutrino properties within it (see further) ~6

The heavy neutrino can be a "nonstandard" Dirac neutrino if instead of the total lepton charge L, the lepton charge L' =L~-Lo+L~, L~, £=e, Ix, x, being the ordinary additive lepton charges, is conserved [ 20 ]. This is possible only if the neutrino mass term is of Majorana type [23]. As can be shown [20], in this case the neutrino v~ is massless, ml = 0, the fields U2L(X) and//3L(X) are mass-degenerate, m2 = m3 = m, U2L(X) = ~UL(X), U3L(X) = C(~R)T(x), ~'(X) being the field of the nonstandard Dirac neutrino ~, which should be identified with the heavy neutrino, and

\f cos0 sin0 i ) U = | 0 0 ,

- s i n 0 cos 0 (23)

where 0 is a mixing angle. Eqs. ( 1 ) and (23) imply that /YlaL(.X')=C(~//R)T(.x'), i.e., that the muon neutrino should also weigh ~ 17 keV. The prediction ( 18 ) for the t 92 -* ~ 9~ ) transition probability remains valid. Obviously, the neutrino mass spectrum does not allow for a MSW solution of the solar neutrino problem based on the neutrino mass and mixing hypoth- esis. However, since the discussed scheme is associated with a neutrino mass term of Majorana type, it can be possible to incorporate it in some form in a self-consistent theory, containing a majoron [24] coupled in a proper manner to the massive neutrinos, so that the cosmological constraints on the heavy neutrino instability could be satisfied ,7

Massive pseudo-Dirac neutrinos can exist if neutrinos possess a mass term exhibiting a global symmetry which is not a symmetry of the weak interaction [18,20,23]. In the simplest case we are considering ( n = 3 in eq. (1) ) , the neutrino mass spectrum in a scheme with a pseudo-Dirac neutrino is practically the same as that in the scheme with a "nonstandard" Dirac neutrino discussed above, but the lepton mixing matrix U has the most general form possible for a real matrix (unlike (23)) [20]. More

~6 As long as the total lepton charge L is conserved this conclusion does not depend on the number of right-handed (RH) sterile neutrinos present in the theory.

~7 For examples of theories incorporating "fast" massive neutrino decay into a majoron and a lighter neutrino see, e.g., ref. [251.

specifically, Ue2 and Ue3 can both be different from zero and the field ~,(x) (~Ue(X) = V2L(X), C~R(X) = V3e (X)) is now the field of a pseudo-Dirac neutrino to be identified with the heavy neutrino. All possible types of neutrino oscillations are allowed and the averaged transition probabilities are given by expressions which can formally be obtained from those in eq. (8) by the substitution U~n-,U~1, U~.n---,U~,~, 2, 2' =e, IX, x. The (f3fl)ov-decay is not forbidden and the effective neutrino mass parameter has the form [ 20 ]

( m,~)pD=2mUe2U~3 (24)

(m = m2 = m3 ). It follows from the data obtained in refs. [ 1,4,5] that

[Ue212"~ I Ue312"0.01 . (25)

Thus, for m-~ 17 keV, I (mv)pD I can satisfy the bound (22) only provided lug21 or IUe31 is very small: for instance, if I Ue21 -~ 0.1, then I Ue31 < 5 × 10 -4. Analysis of the constraints following from the neutrino oscillation data (eqs. ( 11 ) and (14) ) leads to the conclusion that the prediction (18) is valid and that v, should "weigh" ~ 17 keV ( I U,I 12 < 10- 3 ). The 9 ~ (9~ transitions are strongly suppressed:/~((9,) --.

~9~)=2XIUo~Ie lU~I[2<2×10 -5. In general, for ] Ue3 [ << [ Ue2 ] the predictions of the schemes with "nonstandard" Dirac and with pseudo-Dirac neutrinos that we have considered are very similar, except in the following point. Since the global symmetry of the neutrino mass term is not a symmetry of the leptonic weak interactions, the latter generate correc- tions of Majorana type to the mass of the pseudo- Dirac neutrino [ 18,20 ]. These split the pseudo-Dirac neutrino into two Majorana neutrinos having different but very close masses. For a pseudo-Dirac neutrino mass of 17 keV the generated mass splitting and the relevant lepton mixing angles can have values for which the MSW effect takes place for a small fraction of the solar neutrinos.

Let us add that nonstandard Dirac (and pseudo- Dirac) neutrinos arise as a rule in theories with ex- tended Higgs sector [26,27]. Such neutrinos typi- cally have large magnetic moments which are generated (at one loop level) by the neutrino couplings to the Higgs bosons [26 ]. A 17 keV mass neutrino can easily have a magnetic moment of the order of /t~,~ 5 × 10- ~ ~/zB, where #B is the Bohr magneton. In

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the scheme with nonstandard Dirac neutrino that we have discussed above, #~, is, in fact, a u,--* (Or cos 0

- #e sin 0) (#~--. (u~ cos 0 - ue sin 0) ) transition moment of magnetic dipole type, with sin20= 0.01. The lepton-Higgs boson interactions can mediate also flavour changing decays of la +- and/or x +- with branching ratios close to the existing experimental upper limits [26], the particular type of the decay being model dependent.

Finally, UiL(X), i= 1, 2, 3, can be the LH compo- nents of the fields of three massive Majorana neutrinos Zi, having different masses. Assuming that the weak interaction of leptons conserves CP-parity, we have (see ref. [ 8 ] )

1 L ( m ~ ) = _ Igekl2qCemk, (26) 1 k=l

where qcP = + i is the CP-parity of the neutrino Zk" I f m3 "~ 17 keV, then I Ue3 ] 2 ~ 0.01 and the contribution due to the heavy neutrino in ( m y ) is approximately equal to 170 eV. Obviously, in this case a second heavy neutrino, say g2, possessing an opposite CP- parity qcP = _ r/3ce, whose contribution in (m~) compensates that of Z3, should exist ~8. The form of eq. (26) indicates that Z2 should have a mass greater than 170 eV. There are basically two possibilities compatible with the neutrino data. The first corre- sponds to the existence of two almost mass-degenerate heavy Majorana neutrinos ~9: m2-~ m3. It follows from eqs. (22), (25) and (26) that in this case IUe212~_ I U o 3 1 2 - 5 x 1 0 -3 and one practically re- covers the scheme with a pseudo-Dirac (or nonstandard Dirac) neutrino. For I 2 2 m3 --m2[ > 100 e g 2

the neutrino mass measurements, the neutrino oscillation data [13,14] and the unitarity of the lepton mixing matrix U imply: I U¢,12>_-0.99, I U. l l2< 1.8X 10 -3, [ Ura2[ 2> 0.83 and I UeZI2<2X 10 -3. Con- sequently, the experimental limit (22) can be satisfied only provided ml < 2 eV and m2> 85 keV. Thus, v, should "weigh" more than 85 keV if this second possibility is realized.

How can these results change if there exist RH ster-

#8 The upper limit on the ve mass obtained in the tritium I~-decay experiments implies mt < 9 eV.

~9 This possibility was exploited in ref. [28 ], where a see-saw model of neutrino mass generation with massive Majorana neutrinos, incorporating the 17 keV mass neutrino, was suggested. Prediction (18) is valid also in the model [28].

ile neutrinos which mix with the ordinary flavour neutrinos and the total lepton charge L is not conserved (Dirac-Majorana neutrino mass term [ 16 ] )? Obviously, in this case n > 3 in eq. ( 1 ), and eqs. (19) and (20) will be valid. First, instead of oscillating into t9~), ~%) can oscillate into a sterile neutrino with a probability ~ 1.5 X 10 -2, which could be detectable only in tV~) oscillation experiments of disappearance type, capable of registering a reduction of the initial ~9~) flux by 1-2% independent of the source-detector distance and of the neutrino momentum. Second, v~ may not "weigh"~ 17 keV or more than 85 keV, but rather the dominant component in U,L(X) in eq. ( 1 ) can be a field of a neutrino having a small mass.

We conclude with a few remarks concerning the astrophysical and cosmological constraints on the 17 keV neutrino.

It is well known that for a stable neutrino with mass < 1 MeV the requirement that its energy density does not lead to a Universe younger than 101° yr yields an upper bound on its mass in the range 50-100 eV. Hence, the 17 keV neutrino must decay and, indeed, its decay should take place early enough to allow for an efficient redshift of the energy of its relativistic decay products. This amounts to the bound

Zv~ 1012-1013 S , (27)

independently from the specific nature of the decay mode.

However, it is not enough to ask for the redshift of the decay products to ensure that their contribution to the energy density of the Universe is sufficiently small. The point [29] is that the presence of these light relativistic particles coming from the decay of the 17 keV neutrino would lead to a period of radia- tion domination, hence reducing the time the Uni- verse has been dominated by matter energy. This would shorten the time at disposal for energy density fluctuations, i.e., such fluctuations could be too small to originate the observed galaxy structures. To pre- vent that, the 17 keV neutrino must decay early enough to allow for a consistent period of matter domination. This requirement yields the bound

rv<3X 107 s ~ 1 y r , (28)

again independently from the decay modes. Given the stringent bound (28), what are the

available decay modes for the 17 keV neutrino? First,

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we can readi ly rule out the rad ia t ive decay mode , i.e.,

v-- ,v ' + y . Indeed , the e m i t t e d y 's wou ld p roduce an

excess ive d i s to r t ion o f the cosmic m i c r o w a v e back-

g round rad ia t ion dur ing the in te rva l 106 < "t'< 3 × 107

s, whilst r ad ia t ive decays wi th z < 106 s wou ld cont ra-

d ic t the absence o f a 7 burs t in assoc ia t ion wi th the

neu t r ino burs t f r o m the s u p e r n o v a SN 1987A. To be sure, this b o u n d f r o m S N 1 9 8 7 A yields zv> 4 × 1013 s

for the rad ia t ive decay o f a neu t r ino wi th a mass o f

17 keV, hence rul ing ou t a l ready by i tse l f any possi-

b i l i ty o f such a decay mode .

The decay o f the 17 keV neu t r ino into three l ighter

neu t r inos is cer ta in ly m u c h less ha rmfu l than the ra-

d i a t ive mode . Never the less , the fu l f i lment o f the

condi t ion (28) surely calls for drast ic depar tures f rom

s tandard physics. The decay cons tan t should be

roughly three orders o f m a g n i t u d e larger t han the or-

d inary F e r m i cons tan t GF: s o m e new very l ight scalar

coupled to neu t r inos a n d / o r s o m e new re la t ively

s t rong in te rac t ions in the neu t r i no sector should be

invoked to p roduce such a large e n h a n c e m e n t wi th

respect to the o rd ina ry weak in terac t ions . It is no t the

purpose o f this pape r to p rov ide any specif ic mode l ,

bu t the p rev ious cons ide ra t ions seem to po in t in fa-

v o u r o f solut ions where m a j o r o n s are present , hence

a l lowing for a fast decay o f the 17 keV neut r ino .

We wou ld like to thank M. Baldo-Ceol in , S. Bono-

met to , G. Confo r to and A. M a r c h i o n n i for useful

discussions.

Note added. Whi le the text o f ou r pape r was be ing

typed we r ece ived several art icles in which mode l s

i nco rpora t ing the 17 keV mass neu t r ino are sug-

gested and the i r p h e n o m e n o l o g i c a l p red ic t ions are

s tud ied [ 30 ].

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