A neutrino decay model, solar antineutrinos and atmospheric neutrinos

Physics Letters B 285 (1992) 371-375 North-Holland

P H Y$1C $ k ET T ER S B

A neutrino decay model, solar antineutrinos and atmospheric neutrinos Andy Acker a Anjan J0shipura b and Sandip Pakvasa a Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA b Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India Received 26 April 1992

The neutrino decay solution to the solar neutrino problem calls for large mixing and a short lifetime for the decaying neutrino. We propose a model for neutrino masses which has these features and furthermore leads to decays into antineutrinos. The resulting fluxes of%'s are detectable in future solar neutrino detectors. The large v~-v, mixing can account for the atmospheric neutrino anomaly at the same time.

I. Introduction

There is now a well established discrepancy between the solar neutrino flux in the standard solar model and the observation o f solar neutrinos in several detectors: the 37C1radiochemical H o m e s t a k e detector o f Davis, the K a m i o k a n d e - I I ( K - I I ) water Cherenkov detector and the 7~Ga radiochemical detector ( S A G E ) [ 1 ]. Decay in f i g h t o f neutrinos enroute as a possible solution is an old proposal [2]. This proposal, including the constraints from SN1987A observations, was re-examined in depth recently [ 3] and confronted with the recent data on solar neutrinos. The p a r a m e t e r range in mixing and lifetime that would account for the solar neutrino p r o b l e m and be consistent with SN1987A was identified. These results can be s u m m a r i z e d as follows. Let Ve be expressed as a mixture o f mass eigenstates vi (masses mi); ve= Z,UeiV~ and one o f these, say v2 is unstable with a rest-frame lifetime to. The solar neutrino flux is depleted and the spectrum distorted as given by

qb(v., E ) = qb0 ( E ) I Ue212 ( 1 - I Ue212 )

• (v~, E ) = 4 o ( E ) X{(1-IUe212)2+]U~2Iaexp[-t/r(E)]},

about 480 s and q)o ( E ) is the flux o f solar Ve'S as predicted by the standard solar model ( S S M ) [4]. Note that this modification is independent of the n u m b e r of mass eigenstates present in Ve and depends only on the element I ~21 and the lifetime %. F o r short lifetimes an i m p o r t a n t b o u n d on mixing comes from the fact that the signal o f 9e's observed from SN 1987A is consistent with expectations [ 5 ]. F o r neutrinos from SN1987A the factor e x p [ - t / r ( E ) ] is vanishing and in the limit o f only two flavors (re, v , ) mixing substantially, it can be shown that the supernova 9c signal is m o d i f i e d by a factor 1 - I U¢214 (in the a p p r o x i m a t i o n that Nv, -~ ½Nve and Tv, -~ 2 T~e ). Allowing for a factor o f 2 - 3 uncertainty in the model expectation o f supernova 9e fluxes then leads to a b o u n d on I ~21 o f [ Ue21 < 0.9 [ 5,6 ]. As shown in fig. 1, the solar neutrino data from K-II, Homestake 37C1 and SAGE can be accounted for if r ( E ) is in the range 100-2000s for I Ue2l < 0.9. In this calculation, the contribution o f v, (from Ve conversion) to the K-II signal is taken into account; the v, flux is given by

(1)

where r ( E ) is the lifetime ~o at energy E ( r ( E ) = ( E / m 2 ) r o ) , t is the S u n - E a r t h flight-time, which is

×{ l + e x p [ - t / r ( E )

l}

(2)

in the limit o f two-flavor mixing. As discussed previously [3,6] for the decay solu-

0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

371

Volume 285, number 4

09

PHYSICS LETTERS B

~

7

L

400/~

[5~oo/yF

2o/~ laB0o/y~l

0 7 7

06

'

. . . . . . . . .

i

i

-

i

i

500

- -.

9 ~ cL

F -

J

i

-

40

i

,

1000 Lifetime

at

i

tO

MeV

I

sNt

i 1500

~

i

i

i 0000

,

i

i

,

2500

(see)

Fig. 1. Contour plot of the parameter region allowed by solar neutrino observations and expected counting rates for various solar neutrino detectors. The dotted lines bound the regions allowed at the 68% and 95% CL, the dash-dolled lines are the expected counting rate in SAGE, and the solid lines are the expected annual counting rates for v¢'s in Borexino (SuperKamiokande ). lion for solar neutrinos, the most interesting range of 5 m ~ = m 2 - m 2 is 1 0 - 2 - 1 0 - 4 eV 2. For 6m2~ in this range and I U~2I in the range 0.9-0.7 large effects are expected in the v J v c ratio of low energy ( < ~ 1 GeV) atmospheric neutrinos, just of the kind recently reported by Kamiokande and IMB [7,8]. The expected flux ratio r = vo/ve at low energies is about 2.2 and the expected zenith angle distribution flat. For sufficiently low energies (Ev< 1 GeV) and sufficiently long paths when sin 2 5 m 2 L / 4 E averages to ½ the probability for v e r y , is given by P=2IL~2I 2 X ( 1 -- ] ee2[ 2 ) and the ratio of ratios R = (v~/Vc)obs./ (VJVe)e,p will be given by [9] R=

1 - ( 1 - 1/r)P 1+ ( r - 1)P

"

the range 500-1500 s is also a favored region for accounting for the solar neutrino observations. In ref. [ 3 ] we has assumed Dirac neutrinos and the coupling responsible for neutrino decay was g2~ v~] C - ~VR2Z where Z is a light iso-singlet scalar. This coupling leads to a decay in flight of v2: v2 ~ 9~R + X where 9~ R is a right-handed singlet. Hence the decay products are unobservable, and there are no distinctive signatures of the decay itself. There are, of course, predictions for the suppressed counting rates for solar Ve'S in various detectors as well as a distorted spectrum for 8B re'S; these have been discussed in detail elsewhere [ 3 ]. Here we consider Majorana neutrinos and the corresponding decay coupling to be given by g2~ X VITLC--I VZLJ; where J is a majoron. In this case, in the decay in flight of v2: v2~gj + J , the final state contains a 9~ which interacts as a % with a probability I L~] 2. Even moderate fluxes of 9~, in spite of the energy degradation, can give detectable signals because of the large cross-section for 9 e + p ~ n + e +. Such decays were considered before [ 5,6 ] but fell into disfavor when the LEP results on invisible width of the Z [ 11 ] ruled out the simplest models of this type [ 12 ]. The simple Gelmini-Roncadelli [ 12 ] model with one scalar triplet furthermore does not have flavor changing neutrino-Majoron coupling at tree level [ 13 ], and thus does not permit fast neutrino decay. Models which permit fast decays were discussed by Valle and Gelmini [ 14]. Below we present a model for Majorana neutrino masses which is (a) consistent with the Z decay properties as measured at LEP, (b) has non-vanishing neutrino decay vertex at the tree level, thus permitting fast neutrino decay and (c) has 5m 2 and mixings in the range described above.

(3)

For values of I Ue2l between 0.75 and 0.9 we expect R to lie between 0.46 and 0.6. R is reported by Kamiokande to be 0 . 5 4 + 0 . 0 9 and by IMB to be 0.61 + 0.11 in the lowest available m o m e n t u m interval ( p = 3 0 0 - 7 0 0 MeV) [ 10] where the approximation of < s i n 2 8 m 2 L / 4 E ) = ½ should be reasonable, and indeed the zenith angle distributions bear this out. Detailed fits reported by Kamiokande [ 7 ] also favor a region of Sin 2 between 5 × 10 - 3 and 10 -2 eV 2 and I U~2I between 0.7 and 0.9. As seen in fig. 1 the region for IU~2I in the range 0.75-0.9 and r (10 MeV) in 372

16 July 1992

2. T h e model

We extend the standard model by a global U(1 )Lo-L~ which is broken spontaneously. The new scalar fields are T~ (3, - 1, 0), T2 (3, - 1, - 2) and ~/(1, 0, 2) where (x, y, z) describe their properties under S U ( 2 ) × U ( I ) × U ( 1 ) L o L,. The Yukawa couplings o f the neutrinos are: - Y~ = ½9L(F, T o +12 T °) v~. + b . c . ,

where

(4)

Volume 285, number 4

FI =

0 0

PHYSICS LETTERS B

, F2= g3

g2 0

(5,6)

m

0

00)

(7)

,

The Gr disappears after the SSB while a combination of Gr and GL orthogonal to Gr remains as massless majoron. This is given by

J=Nj(GL+sin ysin a s i n f l G r ) •

in the flavor basis. After the SSB of U( 1 )L~-Z, the neutrino mass matrix is

•/Iv =

where M=gl ( T o ), m = g 2 ( T ° ) and m 3= g3 ( T° ). If the matrix U diagonalizes ~#~, i.e., (8)

T21 = - Nj sin ? J

+0((T°'2) (q)

(-0°) ]

UT=

1

,

where c=cos 0 and s=sin 0. The mixing angle is given by

tan20=-2M/rn=-2

mx/-m~m2/(mz-m~),

8m21 = m 2 / c o s 20.

(10) ( 11)

Define 1 ~1= ( ~ ) "~- 7 : ~ (/']R + ? h ) ,

(12)

then the Nambu-Goldstone boson ("majoron") is predominantly given by q~ if ( T o )<< ( q ) . To see this explicitly, note that the states associated with two broken U(1 ) symmetries, namely the hypercharge and the L~_., are respectively given by, G r = c o s c~ 01 +sin o~(cos 3 T . +sinfl T21) , GL = -- sin ? ~ . + cos 7 r/i,

( 13 )

where (T°> tanfl= ( T O ) ,

( T O> tan 7= - -

(o)

tana=

2(T ° ) (0O)sinfl,

"

The lifetime of v2 for energy E2 in the laboratory frame is given by z=

Em ~ g~ ( m ~ - m ~ ) ( m 2 + m ~ ) 2" 16~z ,

(18)

To satisfy the experimental constraints from solar neutrinos and supernova observations, as given in fig. 1 for 8m22~ in the range 1 0 - 2 - 5 × 10 -3 eV z, we find that me is in the range 0.02-0.12 eV, rn2 in the range 0.07-0.16 eV, sin 0= I Uczl in the range 0.75-0.9. The r(10) is in the range 500-2000 s and gz~ ~ (0.73.3) X 10 -4. (r/) is in the range 25-250 eV. In the case of the triplet majoron model, the Z could directly decay into the majoron and the associated scalar with the width = 330 MeV [ 13 ]. This is grossly in conflict with the LEP data [ 11 ] on the Z width into invisible channels. The presence of r/avoids this conflict [15] if ( 0 ) >> ( T ° ) . The Z width into the majoron and the associated scalar is now suppressed because ofeq. (16) by a factor sin 2 y. For (q)

Here T|,21(t~l) are properly normalized imaginary parts of the triplet (doublet) fields defined in analogy with ql.

~

(17)

sin?= (T°~) <0.2,

(14)

(16)

"

m2 --m~

(~1) m-~-+m---2N/

(9)

0

(~1)

Upon transforming the Yukawa couplings to the neutrino mass eigenstate basis and using eq. ( 16 ), we obtain ig2~91 v2J where

&,=csm/~(~D--

C

(T°) J

'(T°,2)J -

U r can be written as

(ii s

(15)

The Nj is a normalization constant. It follows from eqs. ( 1 3 ) - ( 1 5 ) that

m3

U.ggvUX=diag(ml, m2, m3) .

16 July 1992

(19)

the said width is less than about 14 MeV which is consistent with the LEP measurements at the 2alevel ill]. In our model, there is no 0v-[3[3 decay expected because of the vanishing of the mee element of the mass matrix. For the same reason the effective coupling 373

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PHYSICS LETTERS B

(gB) for the Ov-majoron 1313decay is also vanishing [161.

3. The

9~ s i g n a l

The flux and energy spectrum of antineutrinos produced by the decays is given by ~(9~,E)=

[Uc, [2[ U¢212

× J dE' ~o(E') E

X {1 - e x p [ -

2(E'-E) E,2

t/r(E') ]},

(20)

where E ' is the parent neutrino energy and E is the 9~ energy. Note that the %'s are degraded in energy from the parent neutrino as the decay is backward peaked. The counting rate ofge + p--, n + e + events in a detector is given by

C=Np f ~(%,E)a(ge+p--,n+e+)dE,

(21)

where Np is the number of protons in the detector and a(9~ + p - , n + e + ) -~ 8.5 × 1 0 - 4 4 ( E - 1.8 M e V ) 2 c m 2. The event spectrum is plotted in fig. 2 for the range

. . . .

[

. . . .

I

. . . .

I

'

500

400

2 M -

800

200

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o f neutrino lifetime and mixing that solve the solar neutrino problem. The e + spectrum Te+ = E - 1 . 8 MeV yields the 9e spectrum (the "visible" energy is T~+ + 1 MeV). In fig. 1 the counting rates for %% for one year of running in Borexino (Super-Kamiokande) are given. The Super-Kamiokande detector [ 17 ] is designed to contain ~ 22 000 tons of H 2 0 in the fiducial volume. The Borexino detector [ 18 ] will contain 100 tons of the scintillant trimethyl boroxine ( T M B ) in the fiducial volume. We have assumed a cut-offfor T~+ of about 3.2 MeV corresponding to E~o of 5 MeV for both detectors. For Kamiokande-II, with a fiducial volume o f 680 tons and a cut-off for T~+ at 7.5 MeV, we estimate a rate ~ 310 times smaller than that predicted for Super-Kamiokande. Although the event rate in Borexino is rather small ( < 6 0 / y r ) these events are easily detectable by their unique signature. The ~°B in the scintillator absorbs the neutron with a large cross-section and emits a 0.48 MeV 7-ray, setting up a e + - n delayed coincidence tag for the % with negligible internal background (at levels of radio-purity of 10 -~5 g/g already achieved). The external background is mainly from nearby nuclear power reactors and is estimated at 2 - 3 / y r with the same cuts. In water Cherenkov detectors such as SuperKamiokande the above tag is not available and the angular distribution of events is flat rather than forward peaked. Hence they will be part of the general background after directional events due to solar neutrinos are picked out. We have also calculated the signal in SNO [19 ] from the reaction % + d - , n + n + e +, where d is the deuteron. With 1000 tons of D 2 0 in the fiducial volume and an Evo cut-off at 6 MeV we find the SNO event rate to be ~ 1.3 times that predicted for Borexino. With these cuts the external background from nearby nuclear power reactors is estimated at ~ 5/yr.

100

4. Conclusion

0 10

15

E v MeV

Fig. 2. The inverse beta decay event rate for various values of INe21 and rio. Solid line: I Ue2l=0.77, r~o=500 s; dash-dotted line: I Ueel =0.87, rw=500 s; dashed line: IUe2l=0.77, r~o= 1000 s; dotted line: ] Ue21=0.87, rio= 1000 s. 374

We have re-examined the decay solution to the solar neutrino problem with substantial mixing to accommodate the S N I 9 8 7 A observations. We have given examples of models where neutrinos have

Volume 285, number 4

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M a j o r a n a masses a n d large m i x i n g s w i t h short lifet i m e s w i t h decays into m a j o r o n s . We stress that in this case the low energy a t m o s p h e r i c n e u t r i n o a n o m aly is a u t o m a t i c a l l y a c c o u n t e d for by v e ~ % mixing. T h e r e is a sizeable solar 9e signal d e t e c t a b l e in several future detectors, n o t a b l y B o r e x i n o , S N O a n d SuperK a m i o k a n d e . N e u t r i n o l e s s d o u b l e b e t a decay is not e x p e c t e d to take place, w i t h or w i t h o u t m a j o r o n e m i s s i o n . We e x p e c t v, to m i x little with ve or %, to be stable a n d possibly with a mass in the range o f a few eV. T h e e x p e c t a t i o n for solar ve's h a v e b e e n discussed before; to recapitulate, we expect a b o u t 1 0 - 3 0 S N U S in the g a l l i u m e x p e r i m e n t s , neutral c u r r e n t s to be suppressed by a b o u t 0.6, the 7Be line v - e scattering s u p p r e s s e d by a b o u t 0.1 a n d a d i s t o r t i o n o f the v~ energy s p e c t r u m f r o m 8B.

Acknowledgement We t h a n k K. Julio, M. G o o d m a n , J.G. L e a r n e d , M. M o e , J. P a n t a l e o n e , R.S. R a g h a v a n , U R e s v a n i s and X. T a t a for useful discussions. O n e o f us (S.P.) thanks the t h e o r y g r o u p at Physical R e s e a r c h L a b o r a t o r y , A h m e d a b a d for hospitality a n d the I n t e r n a t i o n a l C e n t e r for T h e o r e t i c a l Physics, Trieste, for a Passage to India. T h e w o r k o f A.A. a n d S.P. was s u p p o r t e d in part by the U S D e p a r t m e n t o f Energy u n d e r c o n t r a c t DE-AM03-76SF00235.

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S. Pakvasa and K. Tennakone, Phys. Rev. Lett. 28 (1972) 1415. [3] A. Acker, J. Pantaleone and S. Pakvasa, Phys. Rev. D 43 (1991) 1754. [ 4 ] J.N. Bahcall and M.H. Pinsonneault, preprint IASSNS-AST 92/10 (1992); J.N. Bahcall, Neutrino astrophysics (Cambridge U. P., Cambridge, 1989 ); J.N. Bahcall and R.K. Ulrich, Rev. Mod. Phys. 60 (1988) 297. [5] J.A. Frieman, H.E. Haber and K. Freese, Phys. Lett. B 200 (1988) 115. [6] R.S. Raghavan, X-G. He and S. Pakvasa, Phys. Rev. D 38 (1988) 1317; Z.G. Berezhiani et al., preprint INFN-FE-05-91. [7 ] K.S. Hirata et al., ICRR report-263-92-1 ( 1992); Phys. Len. B 205 (1988) 416. [8] R. Becker-Szendy et al., preprint BUHEP-91-24: D.W. Casper et al., Phys. Rev. Lett. 66 ( 1991 ) 2561. [9] J.G. Learned, S. Pakvasa and T. Weiler, Phys. Lett. B 207 (1988) 79. [ 10] E.W. Beier et al.. Penn. report 1992. [ l l ] J . Carter, in: Proc. 1991 Lepton photon conf. (CERN, Geneva, July 1991 ), to appear; R. Peccei, The Vancouver Meeting: Particles and fields (August 1991 ), eds. D. Axen, D. Bryman and M. Comyn (World Scientific, Singapore, 1992), Vol. 1, p. 3. [ 12] G.B. Gelmini and M. Roncadelli, Phys. Lett. B 99 ( 1981 ) 411. [13] H. Georgi, S.L, Glashow and S. Nussinov, Nucl. Phys. B 193 (1981) 297. [14] J.W.F. Valle, Phys. Lett. B 131 (1983) 87; G.B. Gelmini and J.W.F. Valle, Phys. Lett. B 142 (1984) 181. [ 15 ] A.S. Joshipura, PRL Report-PRL-TH-91/6, Intern. J. Mod. Phys. A, to appear; K. Choi and A. Santamaria, Phys. Lett. B 267 ( 1991 ) 504. [ 16 ] M. Doi, T. Kotani and E. Takasugi, Phys. Rev. D 37 ( 1988 ) 2575. [ 17 ] Y. Totsuka, SUPER-KAMIOKANDE, ICRR-report-227-9020 (December 1990). [ 18 ] C. Arpasella et al., Borexino at Gran Sasso: proposal for a real time detector for low energy solar neutrinos, Vol. l, University of Milan, INFN report (August 1991 ). [19] G.T. Ewan et al., Sudbury neutrino observatory proposal, SNO-87-12 (October 1987).

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