Models with a light sterile neutrino: reconciling the 17 keV anomaly with the solar neutrino deficit

NUCLEAR

P H VS I C S B

Nuclear Physics B 375 (1992) 649—664 North-Holland

Models with a light sterile neutrino: reconciling the 17 keV anomaly with the solar neutrino deficit A.Yu. Smirnov

*

and J.W.F. Valle

* *

Inst ituto de Fisica Corpuscular - C.SI. C., Departament de FIsica Te~rica,Universitat de València, 46100 Burjassot, València, Spain Received 17 October 1991 (Revised 20 January 1992) Accepted for publication 21 January 1992

35S, 14C and 63Ni beta decays are The recently reported anomalies in tritium, consistent with the simplestspectral explanation of the observed solar neutrino deficit as well as all other observations in particle physics, nuclear physics, cosmology and astrophysics. To show this we present simple SU(2)®U(1) models (with and without heavy leptons) where the and v,. merge to form the 17 keV quasi-Dirac neutrino ~s. The squared-mass difference between the light neutrinos can naturally lie in the range 104_10b0 eV2, thus explaining the solar neutrino data through v~—~ n conversion, where n is a sterile lepton. The corresponding predictions for solar neutrinos are testable at upcoming installations. Improved laboratory searches for v,~ conversion can test the consistency of the model. In our scheme the possibility that the mass of the r’e is measurable experimentally may still be viable. The ~s decays invisibly via Majoron emission, ~ ~ ~ +Majoron, with a lifetime that can easily be as short as i0~s.

1. Introduction Recent interest in neutrino physics [1] has been prompted by (i) the continued discrepancy between measured [2—4]and theoretically predicted [5] solar neutrino fluxes which can be naturally explained through resonant transitions [6]; (ii) the /3-decay anomalies indicated by recent /3-decay studies involving tritium, 35S, t4C, 7tGe and 63Ni [7,8]. While these are still controversial [9] they provide a hint for the possible existence of a 17 keV neutrino. In the simplest models for the 17 keV neutrino with just three light neutrinos [10] it is not possible to reconcile the /3-decay observations with the MSW solution * **

E-mail 16444::SMIRNOV. On leave of absence from INR, Moscow. E-mail VALLE at EVALUN1I or 16444::VALLE.

0550-3213/92/$05.00 © 1992

—

Elsevier Science Publishers B.V. All rights reserved

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to the solar neutrino deficit. The latter would suggest a tiny mass difference between 1e and some other neutrino species into which 1~e could oscillate in the interior of the sun. For this to happen the squared-mass difference has to be in the range i0~—i0’°eV2 [6]. The compatibility between these two observations has been addressed in many recent papers and a few models have been suggested [11,121.An essential common feature of these models is the need for the existence of a heavy 17 keV sterile neutrino and the fact that the solar neutrino deficit is explained via resonant flavour oscillations of the type Pe~V~.There are two main types of models. The simplest is that which only involves four lepton states and where neutrino masses are generated radiatively in the absence of heavy leptons [13]. The second class involves an incomplete seesaw model [14]. In all cases the 17 keV neutrino v 5 must not be stable, for otherwise the relic ~ will overcontribute to the present density of the universe. This requires the spontaneous violation of lepton number, that generates fast v~ decays via Majoron emission [1,15,16]. Models are further restricted by other cosmological and astrophysical observations which disfavour the existence of a heavy 17 keV sterile neutrino. These potential clashes involve on the one hand the observations of the neutrino burst from SN87A [17], and the limit on the effective number of light neutrinos from nucleosynthesis [181 on the other. Although the nucleosynthesis limit could be avoided due to additional neutrino— Majoron interactions [13,19], the supernova limit, if true, would constrain both models. These potential problems would be avoided altogether if there were no 17 keV sterile neutrino and the solar neutrino deficit were explained through resonant ye n conversions in the sun, where n is a light sterile neutrino [20]. In this paper we suggest models with a sterile neutrino n, lighter than 10 eV in which the 17 keV neutrino is quasi-Dirac type [21], formed by the active 1’e and v~components. The solar deficit may is explained resonant conversions in the sun. Theneutrino light neutrinos either bethrough superlight or otherwise —‘

form a quasi-Dirac neutrino whose mass could still be detectable in /3-decay studies, a possibility suggested in ref. [22]. These models are consistent with all of physics, including astrophysical and cosmological observations. We consider the phenomenological aspects of the models, including neutrino masses and oscillations, as well as the nonobservation of total-lepton-number-violating neutrinoless double-/3-decay processes (A, Z) (A, Z + 2) + 2e. We show that the explanation of the solar neutrino deficit through resonant ~‘e n conversions in the sun leads to new signatures testable in the upcoming generation of solar neutrino experiments. Our results highlight the importance of experiments such as Superkamiokande, BOREX and SNO, which should be sensitive enough to detect and/or separate neutral current neutrino interactions. We briefly describe the related signatures. —*

—~

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2. Minimal structure and phenomenological constraints Here we identify the minimal structure of the neutrino mass matrix which can fit the main phenomenological restrictions. This structure will be embedded in a full SU(2) ® U(1) gauge-theoretic scheme in sect. 3. There we present concrete models that also incorporate the spontaneous violation of lepton number required in order to generate fast r’5-decays [1]. 2.1. MASS MATRIX

In order to satisfy the existing constraints we consider the simplest generalization of the matrix discussed in ref. [10] that includes a sterile neutrino n. In the basis defined by n, (with i 1, 2, 3 denoting the family index), this mass matrix takes on the following form: i.’1,

i.’2,

i.’3

=

,a

M=

a

a 0 Om b 0

Oh m 0 0 M MO

(1)

The part of this matrix corresponding to the active neutrinos embodies the symmetry L1 L2 + L3 postulated in ref. [10]. The element b induces a mixing between active and sterile neutrino necessary to produce neutrino decay, while the parameters a determine the masses of the light neutrinos, ye, n, responsible for solar neutrino conversion. To describe the solar neutrino data and the 17 keV anomaly we need to assume a, b <
ji,

jL,

—*

=

—

p2

p~

—‘

2.2. NEUTRINO MASSES

We start by diagonalizing the neutrino mass matrix. It is instructive to make a rotation between and by an angle 0 defined by p1

p3

*

tan U *

=

rn/M.

(2)

This rotation corresponds to the one introduced in the three-neutrino model of ref. [10] in order to identify the massless state.

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This gives the mass matrix the form

M~0=

p.

a9

a0

0

o

b0

o 0

0 0

o

b0 0 M0

M0

0

‘

(3)

where a0=acosO—bsinO,

(4)

b0=a sin O+b cos 0,

(5) (6)

M0=Vm2+M2.

In the limit where p. 0 the four neutrino states combine exactly to form 2 andtwo is slightly mixed Dirac neutrinos. The heavy one has a mass M9 = ~/m2 + M identified with the 17 keV neutrino z~.The light one has mass a 0 and must be identified as the neutrino dominantly emitted in /3-decay. From the Los Alamos experiment one has —

a0 ~ 9.4 eV.

(7)

Due to the nonzero value of p. both the heavy 17 keV neutrinos and the light ones split in mass. The splitting of the heavy components is given by (8) and is very small on the 17 keV mass scale. This implies a negligibly small neutrinoless double-beta decay rate, in agreement with observation [1]. The splitting corresponding to the light sector is ~1m=p..

(9)

The generation of the total-lepton-number-violating entry p. is crucial in this picture. It is needed in order to generate the ~e n oscillations that can explain the solar neutrino deficit. The value of p. may be either large or small when compared with the value of a0. In the first case the two light neutrinos are very light Majorana-type neutrinos. In the second, they form a quasi-Dirac neutrino whose mass a9 may be as large as 9.4 eV. Finally, the SN87A restriction is automatically satisfied due to the lightness of the sterile neutrino, eq. (7). Moreover, the big-bang-nucleosynthesis constraints will be obeyed due to the smallness of the splitting needed to explain the solar neutrino data. —‘

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2.3. FLAVOUR MIXING AND NEUTRINO OSCILLATIONS

In order to determine the structure of lepton mixing one needs to diagonalize also the charged lepton mass matrix which should also obey the L1 L2 + L3 —

symmetry. This introduces an angle Oe that rotates between first and third charged lepton generation. At the end we get the following form for the charged current leptonic weak interaction g

e~y KiaPaL

—

+

h.c.,

(10)

i—i a—O

where ~aL are two-component mass eigenstate neutrinos, two light ones (a = 0, 1) and two heavy ones (-~ 17 keV) corresponding to a = 2, 3. The mixing matrix K is given as

K~

Cm

Sm

~C~Sm

C8Cm

b0

b0

S8Sm

~S8Cm

/~b0/M0 ~/~b9/M9 ~

~—

(11)

~

—

5m = sin 0m’ cm = cos 9m refers to the mixing angle °m that arises from the where diagonalization of the 2 x 2 light (-~ iO~ eV) mass matrix ~.

tan 20m= —2a 0/p., and sa

=

(12)

sin 60, where 60 defined as 6O=O~0e,

(13)

is the difference between the angles characterizing the rotations performed between the first and third families of neutrinos and charged leptons, respectively. It must be identified with the angle indicated by the beta decay measurements, 2ôO = 0.008—0.010. (14) sin The first row of the matrix K gives the sterile neutrino n, while the second row gives 1.’e’ the third row v~, and the fourth r’~. *

Strictly speaking, there is another angle characterizing the diagonalization of the heavy sector, We have taken

6M

=

~

which is a good approximation.

0M

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TABLE 1 Channels of neutrino oscillation in the approximation b

9 ~ M9

Channel

Scale

Strength 26O sin sin2260 ~5ifl22Om sin2260 ~sin226O cos26O Sifl22Om cos2öO 5~fl220msin2~O

-4

(l7keV)2 c5M2 5M2 n n

~

With the help of the matrix K one may compute all relevant neutrino oscillation probabilities. There are three main scales of squared-mass differences which determine the oscillation lengths in this model: (i) the (17 keV)2 scale characterizing the nearly identical splittings between the masses of light and heavy sector; (ii) the scale ~ responsible for the explanation of the solar neutrino deficit, 6rn~~=p./p.2+4a~

~ i0~ eVa;

(15)

(iii) the scale characterizing the splitting in the heavy sector, 6M2=p. 2b~/M 9.

(16)

2. In table 1 we As will be shown later, this is expected to be less than iO~ eV summarize the spectrum and strength of oscillations for the various channels possible in our model. Small contributions proportional to b 0/M0 are neglected. Note that in this limit the only scale characterizing the ~e n and ~T n channels is ~ with a correspondingly very long oscillation length. The channels involving v~,v~ v.1. and are also by a absent. very long oscillation length 2. v~ The channel v.,~characterized n is completely The richest pattern scale set by 1/6M of oscillations is that corresponding to the ~e ~ ~ channel, where all three scales —

—p

—‘

p~

—~

—~

are present. As far as laboratory experiments are concerned, the only relevant oscillation channel that is predicted is ~~‘e~ si~, also present in the models considered in refs. [13,14]. The strength of this transition is directly related to the mixing angle measured in the /3-decay experiments. However, no modulations [13] of the v~ transition are expected, in contrast to the case of the models of refs. [13,14], since the splitting of eq. (16) is much smaller than in refs. [13,14]. An improvement in the sensitivity of the ~ r~,. searches at the laboratory by about an order of magnitude should suffice to check consistency of this scheme. ~-

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655

If mixings proportional to b0/M0 are taken into account new modes of oscillation appear. All of them have a strength of order b~/M~.Moreover, the only channel with fast 17 keV scale oscillations is n, characterized by a strength i.’.~ —p

7. (17) 4b~/M~1O This channel may be responsible for producing the sterile neutrino state in the early universe. Using eq. (17) and the cosmological restrictions from nucleosynthesis [24] one obtains b 9/M0 ~ 5

X

iO~,

(18)

which corresponds to b0 < 10 eV. Other oscillation channels which may produce the sterile state are ~e n and n. They can also avoid the cosmological restrictions. Moreover, r’~ n is less efficient than v~ n in producing the sterile states (see table 1). The latter channel will be considered in the next section. —p

p~ —*

—~

—~

2.4. SOLAR NEUTRINO OSCILLATIONS

2—sin22Om can be found for the case of Regions of neutrino parameters 6rn the data of Homestake, Kamiokande and sterile neutrino oscillations [23] in which SAGE experiments are simultaneously accounted for. The favored region can be parametrized by 6rn2

(2.0 ±0.5)

x

108

sin22Om,

6rn2

~

3

X

10—6 eV2.

(19)

It corresponds to the nonadiabatic (NAD) region. At large mixing (large mixing solution) the allowed region is rather marginal. Moreover, this region is probably disfavoured by cosmological considerations related to effect of sterile oscillations in nucleosynthesis [241(see, however, ref. [19]). The region of eq. (19) lies lower in 6rn2 scale than the corresponding one for the case of flavour conversion (for which also large mixings are allowed). This difference is related to the fact that in the flavour case there is an additional contribution to the Kamiokande signal arising from converted or v~scattering on electrons via the neutral current. The allowed region is determined mainly by the relation between the total suppressions of signals in the chlorine experiment (RAr) and Kamiokande (Rye) experiments, as well as by the upper limit of Ga production rate in the gallium experiment. In the NAD region one predicts the following ratio of suppression factors r = Rye/RAr: r 1.3 in the model of ref. [251 and r 1.45 in the model of ref. [261. This value agrees with the experimental value r = 1.6 ±0.4 and is somewhat smaller than in the flavour case. Finally we note that in the large mixing angle region one expects r 1. —

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Eq. (19) gives the preferred solution to the solar neutrino problem. However, keeping in mind the astrophysical uncertainties, we will also regard the large mixing solution with 6rn2 10-6 eV2 as unexcluded. Consider now the constraints on the mass matrix parameters arising from solar neutrino data. For the case of small mixing, p.2>> 4a~,one finds from eq. (12) and eq. (15), p.2 6m2 and a~ 6rn2 sin2 20m or, from eq. (19), qualitatively, p.

(0.3—2.0)

x i0~ eV,

a 0

(1.0—1.5) x iO~ eV.

(20)

For the large mixing angle region p. ~ 2a0 ~ iO~ eV. Finally, in the quasi-Dirac case, <
Therefore the upper limit for p. varies from 5 x 10_8 to i0’ eV as a0 decreases from 9.4 to 5 x iO~eV. So, in all cases one has p. ~ 2

x iO~ eV,

(22)

while a0 is fixed in the favoured NAD solution and may be as large as 9.4 eV in the region of maximal mixing. Alternatively, also have the vacuum just-so 2 10— 10 one eV2may values. oscillation case at even smaller 6rn 2.5. NEUTRINO DECAY

The cosmological density constraint on the

i.’

lifetime may be written as [27]

5

2 T10’

l7keV rn~

2

s.

(23)

If the lifetime is close to the limit given in eq. (23) the universe is expected to have been radiation-dominated by the relativistic s.’ 5 decay products, ever since the decay occurred, a situation that seems problematic for structure formation. Requiring that the universe should have become matter-dominated by a redshift of at least 1000 one gets a much shorter lifetime limit [28], 7

rn~ l7keV

2

s.

(24)

T10

However, given our ignorance of the details of galaxy formation theory we consider this limit to be less safe than that of eq. (23).

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In order to satisfy the cosmological constraints in eq. (23) and eq. (24) we assume the existence of the neutrino decay [1,15,29]

(25)

Ps~*i/1ight+J,

where J denotes the massless pseudoscalar Majoron, arising from the spontaneous violation of lepton number [161. Moreover, the astrophysical limits on photons 1.’Iight + y can be easily satisfied since in these models produced in the decay “s the dominant mode of decay is by far the one given in eq. (25) which does not produce photons the v~ decays invisibly. We stress that the nondiagonal Majoron couplings responsible for the decay in eq. (25) are strongly model-dependent. Therefore we consider separately the implications of the limits in eq. (23) and eq. (24) for each of the models of interest. —

3. Models We will now consider models which reproduce the minimal structure discussed given in eq. (1) and consequently all the phenomenological features considered above. The models are all based on the simplest SU(2) 0 U(1) gauge structure, broken spontaneously by the nonzero vevs (/) of standard isodoublet 4~’and ~H) of isotriplet H. The latter, originally used in ref. [30], contains both a doubly and a singly charged component and is used mainly to induce the 17 keV neutrino mass. The requirement that the 17 keV neutrino s.’~must not be stable, makes us only consider models in which the full lagrangian, including the Higgs potential, is also invariant under a U(1)G global lepton-number symmetry (see table 2). This global U(l)G lepton-number symmetry is violated spontaneously through nonzero vev

TABLE 2 SU(2)®U(1)yOU(1)G assignments of the leptons and Higgs scalars. The number in parenthesis is the U(l)G assignment of the sterile lepton n in the model of subsect. 3.2. In this case there are two other isosinglets with G ±1. Quarks are U(1)G singlets

T 3

G

0

—1 —1 —2

1 —11 1

0 0 0

—2 —2 0

—1 1 —1(—3)

1 0

1 2 0

‘Li 1L3 elR

V

e 2~ e3R

n H U

0 0 2

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Light sterile neutrino and solar deficit

Ku) of an additional SU(2) 0 U(1) isosinglet Higgs scalar field u. It maybe written as u=(u)+~(p+iJ).

(26)

Spontaneous breaking of U(1)G results in the existence of the Majoron J responsible for the fast neutrino decay eq. (25). Since the Majoron is an SU(2) 0 U(1) singlet, we naturally avoid the invisible Z-decay channel Z p + J. Therefore there is no conflict with the recent LEP measurements of the Z invisible width. Note that the Higgs scalar sector of these models retains most of the simplicity of the SU(2) 0 U(1) theory, except for the canonical value p = 1 for the ratio of neutral to charged current strengths, which is modified by O(KH)2/Kt~)2). As for the fermions, the models we will consider here have a completely standard quark sector, while the lepton sector is minimally enlarged. We consider models with one and with three isosinglet leptons. They acquire masses through the combined electroweak and lepton number symmetry breaking effects discussed above. In order to comply with our basic requirements above, there must be four light neutrino species —*

~.

3.1. SIMPLEST MODEL

We first consider a model where the lepton sector is extended through the addition of a single SU(2) 0 U(1) singlet lepton, rather than three [30]. This model is the simplest in the sense that it does not invoke the existence of any heavy leptons and the structure of the neutrino mass matrix is precisely the one discussed in subsect. 2.1 The lepton Yukawa interactions are given by ~

h~~l~4e~ +f1J1TCiT2H11 1

+

hjlTT24*n + ~AnTCnu + h.c.,

(27)

and satisfy the SU(2) o U(1)~0 U(1)G symmetry given in table 2. The first term is the canonical one responsible for generating the charged lepton masses. The U(l)G symmetry imposes the following restrictions on the couplings in eq. (27):

*

**

f11=0=f13,

(28)

h12=h21=h23=h32=O,

(29)

h2=0

(30)

The existence of four light neutrino species as introduced here is perfectly consistent with recent LEP results, since the fourth neutrino is sterile. As for nucleosynthesis, we deal with the corresponding limits explicitly as seen above. The number of isosinglet neutrinos is completely arbitrary since they do not carry any anomaly. In addition, in many extensions of the electroweak theory such as string models, the number of isosinglets is not equal to that of isodoublets [31,321. For simplicity we assume that all of the Yukawa coupling constants are real.

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for i = 1, 2, 3. Moreover, the f~ couplings form a symmetric matrix in generation space. The resulting neutrino mass matrix takes on the form given in eq. (1), where M=f23(H), a

=

h1(4i),

rn =f12KH),

(31)

b

(32)

=

h3K~),

(33)

p.=AKcr).

Note that the different entries of eq. (1) have different SU(2) 0 U(1) transformation properties. In principle this might explain the required neutrino mass hierarchy with, e.g., the 17 keV mass scale arising from the triplet Higgs scalar vev. Barring a strong cancellation in the quantity a0 so that a a0 and b a0/sin 80 we obtain from the above equations and eq. (20) 6, h 5, (34) h1~3x10~ 3~3x10’ which implies a new scale for Yukawa couplings (note that the smallest Yukawa coupling for charged leptons is 10—6). Although technically consistent, this may be regarded as unaesthetic. This is the price we have to pay for minimality, both in the fermion (we have only one additional lepton, n) as well as in the scalar sector (we have only two additional Higgs multiplets, H and a-, needed for the neutrino mass generation). Consider now the question of neutrino decay via eq. (25). The couplings of the neutrinos to the Majoron in this model are described by a 4 X 4 matrix which, due to the U(1)G assignments of table 2, has only one nonzero entry, given by ‘~

ip.

(35)

~flfl~/~).

The fact that the Majoron coupling matrix and M~in eq. (1) are not simultaneously diagonalizable implies the existence of nondiagonal couplings of the two 17 keV neutrinos to the light ones, specified by the effective 2 x 2 matrix ip.b 9

[Cm

Cm\

2M0(a-)~~m Sm)’

36

( )

These couplings are responsible for the decays of the two heavy (mass-eigenstate) neutrinos contained in the 17 keV s~with a decay width 2 + = 647r (37) 1 M(u)2 b~p. —~

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The cosmological limit of eq. (23) gives the following restriction ~5X10b0eV and for b0

b

(38)

iO~eV we obtain a stringent limit on the value of Ku) ~ iO~eV.

Ku), (39)

The corresponding late phase transition might have interesting cosmological consequences Let us now consider the possibility of strong cancellation in a0. In this case one can reconcile a small value for a0 with large a and b values and therefore increase the corresponding Yukawa couplings as well as the value of Ku). Using our upper bound on b0 we obtain (a-) 0.1—1 GeV and, at a b, h 10h1. Such a cancellation may follow from some horizontal symmetry between the first and third generations. Indeed, the condition a0 0 implies a/b = rn/M. In this connection let us remark that if we restrict the model by imposing a discrete permutation symmetry D between the first and third generations, 1 3, we have (i) massless v~ (ii) massless electron and (iii) 60 = 0. Nonzero values of these masses and angle would arise from D-breaking effects. ~.

~-*

3.2. MODEL WITH A HEAVY QUASI-DIRAC LEPTON

This model has the same particle content of the simplest model, except for the addition of two new SU(2) 0 U(1) isosinglet leptons n2 and n3. Thus the number of isosinglet leptons is also 3, as the number of isodoublet neutrinos. Here we assign the same U(1)G lepton numbers of table 2 for all particles, except n1, which has G(n1)= —3. The two new isosinglets have G(n2)= 1 and G(n3)= —1. The allowed lepton Yukawa interactions are now given as h~Jl~4eRJ +f~~lTCi’r2Hl1 + g13l~r2~*n3 + g22l~r24,* n2 +

~A12nTCn2u + ~A22n~Cn2u*

+

+

~A33n~Cn3cr+ h.c.

g33l~T2~*n3 (40)

The first two terms in eq. (41) coincide with the corresponding ones of the simplest *

Since (U) <1 MeV this phase transition would take place after the epoch of primordial nucleosynthesis. At nucleosynthesis and before, one has (U> = 0 so that the global lepton-number symmetry is unbroken. As a result, there is no splitting in the lightdisappears neutrino sector no —~region n oscillations 2 [24,19] and anand additional of 6m2are io5—io4 mixing becomes possible. In eV2 this with case large the constraint on bm possible for the solar neutrino conversions. Correspondingly the restriction on ~ of eq. (21) becomes weaker (10—6 is replaced by iOn). Note that sterile neutrino production through scattering processes is negligibly small.

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:~

a. .

14

~

‘~)4~3 fl

3

6)

£~.

~ fl1

I

~

ni

fl2

~>

~(i5)

Mn I

M~

~x,

i—i—.

n2 ri3n3 ~art1

~P) ~ ~) M~ M~ I *K~ 54)(Ip i.—4..

I

,-

I

~3

~a~2

~3

Fig. 1. Typical diagrams generating lepton number violating neutrino masses and/or decays in the model of subsect. 3.2.

model. In addition, there is a bare mass term, invariant under SU(2) U(1)G ~M~n~Cn3

+

h.c.

0

U(1) and (41)

Note that due to the U(l)G prescriptions, the n1 has no couplings with active neutrinos nor Majorana-like diagonal coupling to a-. Therefore, to lowest order, the spontaneous SU(2) 0 U(1) and U(l)G breaking gives a = b = p. = 0. We stress that before U(l)G breaking the six two-component neutral leptons form three Dirac leptons: the heaviest one made up of n2 and fl3~ of mass M~,the 17 keV formed by and v3, and a massless one corresponding to and n1. The couplings of n1 with active neutrinos appear at tree level but only as a result of higher order Yukawa interactions, see fig. 1. Nonzero values for the entries a and b are generated after U(l)G breaking by the exchange of the heavy leptons (fig. la), i.e. i-’5

i-’2

i-’1

a=g13(4)~,

b=g33K~)~,

(42)

where (43) can be made as small as we please, by choosing a sufficiently large value for M~. Similarly, one generates small diagonal entries, such as p., responsible for the splitting in the light sector, e.g., 2. (44) p. =A33(u)~

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In contrast with the simplest model, there is a small seesaw-like parameter ~ which makes it possible to realize the required values of a, b, p. parameters needed for the explanation of the solar neutrino data in a natural way. There is no need for having very small Yukawa couplings as in eq. (34). For example, for a a0 iO~ eV [eq. (20)] and for typical first-generation Yukawa couplings g13(4) MeV one obtains from eq. (42) i0~—i0~.

0.1—10

(45)

Thus, all Yukawa couplings may be of the same order of magnitude as those for the charged leptons and quarks. Moreover, we may easily have Ku) in the range 1—100 GeV and M~ 100 GeV. We stress that there is no need to introduce any mass scale above the electroweak scale. Consider now the question of neutrino decay via eq. (25). In this model the nondiagonal couplings of the Majoron responsible for decay arise more directly than in the simplest model, via the fig. la and may be estimated as i-’5

1~Ka-~ (4,) =

(46)

tg33~~

For natural parameter choices they may easily be much larger than required in order to produce a lifetime that obeys the cosmological limits of eq. (23) and eq. (24).

4. Discussion In this paper we have presented simple models that reconcile the existence of a 17 keV neutrino with the explanation of the solar neutrino data via resonant te conversion into a sterile neutrino. Such a reconciliation suggests a substantial departure of the neutrino mixing and mass spectrum from the naive pattern based on quark—lepton analogy and the standard seesaw model. The present models are consistent with all laboratory, astrophysics and cosmological observations, including the constraint on the present-day density of the universe and on the formation of structure in the early universe, the time structure of SN87A neutrino observations and the limit derived from nucleosynthesis on the number of light neutrinos. Since the decay lifetime corresponding to eq. (37) may be short enough that one expects that the s~ produced in a supernova explosion could decay before reaching the earth. This opens the interesting possibility for detecting the decay-produced ~e by observation of delayed charged and/or neutral current events at a neutrino observatory such as Sudbury [33]. The existence of such a massive neutrino ~s

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could also have important consequences for the mechanism of supernova explosion itself [34]. Essential implications of these models for laboratory experiments include: (1) the possibility of having a measurable value of the mass, accessible to further /3-decay searches; (2) the existence of very short wavelength u~ ~ oscillation whose effects lead to a depletion in the ~‘e flux at the 2% level without appreciable modulation; (3) very strong natural suppression of neutrino-less double /3-decay. Future solar neutrino experiments may actually single out the case of sterile solar neutrino conversions. A clear signature is expected in the Sudbury and BOREX experiments, in which one expects to measure separately the effects of NC and CC. For the v~ n case one predicts equal suppression of NC and CC signals, while for the ~e case the NC is unsuppressed. In contrast to the case of astrophysical solutions, n conversions result in a distortion of the neutrino energy spectrum. Moreover, a measurement of the ratio RAr and Ry~ with good accuracy at Super-Kamiokande and at the Baksan chlorine experiments will enable one to distinguish between flavour and sterile channels. We also predict a small difference in the recoil electron energy spectrum for ~e ~ n and si~ v.,~ channels due to the s~e scattering (in the last case the distortion is weaker). This could be measured at Super-Kamiokande. i’~

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This work was supported by CICYT, under grant number AEN-90-0040 and by a Sabbatical grant of the Spanish Ministry of Science (A.S.)

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