Astronomical observations of SN1987A, such as the light curve, spectral intensities of lines, the X-ray emissions, etc., constrain the lifetime for the decay of a heavy neutrino 1 MeV less than or equivalent to m sub nu H less than or equal to 50 MeV through nu sub H yields nu sub 1+e(+)+e(-) exceeds 4 x 10 to the 15th exp(-m sub nuH/5MeV) seconds. Otherwise. resulting ionization energy deposits and stronger X-ray emission would have been observed. This coupled with traditional cosmological considerations argues that the lifetime of tau-neutrinos probably exceeds the age of the universe. This in turn would imply the standard cosmological mass bound does apply to nu sub tau, namely m sub nu sub tau less than or equivalent to 100 h squared eV (where h is the Hubble constant in units of 100 km/sec/mpc). The only significant loophole for these latter arguments would be if nu sub tau primarily decays rapidly into particles having very weak interactions

Cowsik, R.

Hoflicn, P

Schramm, D. N.

English

NASA Technical Reports Server

* Fermi Natiorfal Accelerator Laboratory v P ~ I L A B - P u b - 8 8 / 1 3 1 - A  k 
September 1988 
Lower Bound on  e+e- Decay of Massive Neutr inos 
ORIGINAL PAGE 1s 
OF POOR  QUAL^^ 
)J/7 i / i"  
J / d  -72-22/ ' 
1 
R. Cowsik("lb), D. N. Schramm(e*d*c), and P. HGfli~n(~) 
a) McDonnell Center for The Space Sciences, Washington University, St. Louis MO 
63130. 
b) Tata Institute of Fundamental Research, Bombay-400 005, INDIA. 
c) The University of Chicago, Chicago, IL 60637. 
d) NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, 
Batavia, IL 60510. 
e) Max Planck Institute fur Physik und Astrophysik, 8046 Garching, FRG. 
Y89-16458 (NU&-CZl-l82953) 
7 F  
L C Y E B  EOUEC C %  e+- DECAY 
CI BALSSIIVB IYBUTLIlCS (UashiagtcP UfiYe) 
CSCL 208 
tlnclas 
~ 3 / n  o 189849 
ABSTRACT 
Astronomical observations of SN1987A, such as the light curve, spectral intensities of 
lines, the X-ray emission etc., constrain the lifetime for the decay of a heavy neutrino 
lMeV 5 mu,, 5 50MeV through VH 4 y + e + + e -  exceeds 4~1015exp(-m,,H/5MeV) 
seconds. Otherwise, resulting ionization energy deposits and stronger x-ray emission 
would have been observed. This coupled with traditional cosmological considerations 
argues that the lifetime of .r-neutrinos probably exceeds the age of the universe. This 
in turn would imply the standard cosmological mass bound does apply to v7, namely 
m, 5, lOOh2eV (where h is the Hubble constant in units of 100 km/sec/mpc). The 
only significant loophole for these latter arguments would be if v7 primarily decays 
rapidly into particles having very weak interactions. 
Operated by Universities Research Association Inc. under contract with the United States Department of Energy 
https://ntrs.nasa.gov/search.jsp?R=19890007087 2020-03-20T03:41:19+00:00Z
ORIGINAL PAGE IS I 4 . 
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The standard model of weak interactions demands that individual lepton numbers 
be conserved. On the other hand almost every extention of the model envisages 
the possibility of the nonconservation of lepton numbers, thereby allowing neutrinos 
of one type to decay into others. It has been recognized, for more than a decade 
now, that astrophysical and cosmological considerations can provide rather stringent 
bounds on the decay rates of neutrinos through various  channel^(^*^). Among these 
the most stringently constrained mode is the radiative one: UH + u1 + y. However, 
theoretically, this channel is expected to be suppressed'. Alternative modes of decay 
are those with scalars, pseudo scalars, Nambu-Goldstone bosons or e+e- pairs in the 
final state('). Since the decay products are directly observable the last of these modes 
is of particular interest, especially for the T neutrino whose mass is constrained by 
laboratory measurements to be m, c 35 MeV, thus allowing in principle, for above 
the threshold decay into e+e- pairs. The supernova 1987A which exploded in the 
LMC provides a sensitive and direct way of looking for decays of neutrinos without 
the uncertainties caused by assumptions about the cosmological density parameter 
and the supernova rate which go into the earlier discussions. Previous examinations 
(cf. ref. 5,6) have focused on lifetime limits from the pure radiative mode implied 
by the lack of observed ?-coincidences with the u-burst. In this letter we derive 
the constraints placed by the observations in the vicinity of SN1987A on the decay 
UE + u1+ e+ + e-. 
The idea on which these discussions are based is that the electrons and positrons 
that emerge from the decay will lead to observable effects through their interaction 
with the supernova debris and the circumstellar material. These effects are listed 
below: 
1. Deposition of energy in the material through coulomb interactions. 
2. Ionization. 
3. Generation of X-rays through bremsstrahlung. 
4. Generation of X-rays through annihilation of the positrons. 
5.  Acceleration of the material by the gradients in the pressure of electrons and 
positrons. 
Limits on neutrinos come from the fact that in gravitational collapse the neutron star 
binding energy, - 3 x 1053ergs, is radiated in neutrinos. Via neutral currents, all 
ORIGINAL PAGE IS 
OF POOR QUALITY 
species of neutrinos are radiated. The arguments below will apply to all neutrinos 
with mu 2 1.1 MeV so that e+e- pairs can be produced. 
In calculating the bounds we make several simplifying assumptions; more exact 
calculations will not qualitatively alter the limits presented here. These assumptions 
are the following: 
1. The total energy radiated per neutrino species (neutrino plus antineutrino) is 
independent of its flavor7 and is given by 
Q - 10S3ergs x 6 x 1OS8MeV for mu kT, - 5 MeV 
[A temperature of 5 MeV is a conservative estimate for p and r neutrinos. 
Mayle etaL7 find kT,, - 6 MeV. Only v, and have lower temperatures, 
due to their charged current interactions altering the radii of their respective 
neutrino spheres7 .] 
2. The kinematics of the three body decay are not included in the calculations but 
it is assumed that about a third of the energy of the neutrino is carried away 
by each of the decay products. 
3. We assume that the electrons and positrons that arise in the decay have negli- 
gible spatial diffusion. In the Large Magellanic Cloud, with its high density of 
interstellar gas, the magnetic fields are expected to be somewhat higher than 
the 3p Gauss fields of our Galaxy, say - 5p Gauss; the circumstellar fields may 
even be larger. In any case the gyroradii of the electrons and positrons with 
typical energies of - 5 MeV in such fields is 10'ocm. Since the scattering 
meanfree path of particles in a magnetised plasma is about the same as their 
gyroradii the spatial diffusion can be neglected over the length scales of interest 
here. 
With these assumptions we now proceed to calculate the effects. The energy 
radiated in neutrinos is given by 
Q = los3 f ( m )  erg 
f ( m )  = 1 f o r m s k T  
f ( m )  = (m/kT)eap - (m/kT) for m > kT. 
ORIGINAL PAGE 13 
POOR QUALITY 
The number of neutrinos emitted in the supernova is given by 
< where < E,, > x  3kT for m N kT - 6 MeV and < E, > x  m for m >> kT. The 
number of positrons or electrons generated per unit volume at a distance T is given 
bv 
N 
x x-  
N N 
n(r) x 
47rr17pcr 4 1 r ~ ~ c r  kT47r~~m (3) 
where r is the lifetime for the neutrino decay. Since we are considering neutrinos of 
mass above the decay-threshold of N 1.1 MeV, setting 7 x 1 and p M 1 in eq. 3 does 
not lead to serious error in our estimates. 
Each electron and positron arising from the decay will have an energy of several 
MeV in the laboratory frame and will deposit energy in the surrounding material at 
the rate of ( x 4 MeV g " n 2  x 4.10-e erg g-' cm2. This will heat up the debris 
and will contribute to the luminosity of the supernova, in a manner quite similar 
to the energy deposited there by 5 6 C ~  decay, for example. The contribution to the 
luminosity due to this process is given by 
2Q(r0 4 - 1053e-mfkT 
x erg 8-l (4) 2Q L = / % n c ( p  d3r = - ( p  dr = -
1 3 k T r  3kTr 7- 
Here ro x 10 gm-' is the optical depth of the matter surrounding the supernova 
at present. Now, the present luminosity of the supernova is N 1039*5erg 8-l  and the 
light-curve fits a 5 6 C ~  decay lifetime of 114 days excellently('). Study of the light 
curve shows that an additional contribution from any hypothetical process cannot 
exceed - 2.5% or 103'erg 8-l. Substituting this in eq. (4) we get 
Note that even for m, > kT, - 5 MeV this still yields a restrictive limit. 
A sizable fraction of the energy transferred to the debris through Coulomb inter- 
actions of the electrons and positrons goes into ionization of the hydrogenic material. 
At larger distances (101s*5-17m) the particle densities are sufficiently low and the 
velocities are sufficiently large, that Lyman-a photons escape relatively freely from 
the material. Under these circumstances a fraction of about 30 % of the ionization 
energy is converted into Lyman-a photons. Thus the luminosity in Ly-a is about a 
ORIGINAL PAGE IS 
OF POOR QBsAsrTY 
third of the energy transfer rate given in eq. 4 
2Q(r0 1063e-m1kT 
9kTr 7 
L, x -x erg 5-l  
Noting that a luminosity of - 2.103' in Lyman-a would have been detected, even if 
interstellar absorption is taken into account, one gets as before the limit 
The limits obtained from the rest of the considerations 3-5 are less stringent; we 
therefore discuss them only briefly. The X-ray luminosity of the supernova is less 
than - 103serg 5-l now@). The expected X-ray flux is estimated simply by assuming 
that the electrons and positrons radiate e-l of their energy within a radiation length 
x IOOgCm-'. 
The inequality (8) translates into r > lOI3 f(m) s. The gamma-ray data has been 
obtained with telescopes with very large angular response and yield far less stringent 
limits. The dynamical effects of the electrons and positrons on the debris could be 
used to preclude very short decay times for the massive neutrinos by noting that the 
kinetic energy in the debris is a small fraction of the energy emitted in neutrinos. 
The dynamical effects for relatively large r are subtle and need further study. 
It is interesting to consider the implications of the limits derived here. Among 
these the most stringent is the one derived from the observations of the light curve in 
eq. 5. Let us focus on discussions on the r-neutrinos whose mass is constrained by 
laboratory studiess to be less than 35 MeV and thus may be in a regime where these 
limits are relevant. Depending on the actual value of its mass the lifetime for the 
decay into electrons and positrons the r must satisfy the following set of conditions 
< r > 4.10"s for 1.1 < rn x 5MeV I 
r > 4 10"s for m x lOMeV > (9) 
r > 4 1 0 ' ~ ~  for m M 35MeV I 
This means that the .r-neutrinos generated in the big bang will survive without sub- 
stantial decay up to redshifts (1 + zd) M (~ , , / r ) ' /~  i.e. up to redshifts of 100 to 
1000 depending upon their mass. That is the decay will occur after the decoupling 
of the cosmological background radiation. And, if their decay lifetime should be as 
short as indicated by the limits then there would be several important cosmological 
consequences3, distortion of the relic microwave background and the effect on the 
cosmological expansion, to name only two of them. The latter effect is discussed in 
detail by Dicus, Kolb and Teplitz who derive the constraint 
From equation (10) one can see that either the mass of the r-neutrino is below the 
1.1 MeV threshold for ve* decay or that its lifetime is longer than the age of the 
universe. Keeping in mind the theoretical and experimental constraints on radiative 
decays this long lived option would mean that the r-neutrino is also very light and 
should satisfy the constraint 
Ern, < 100 h' eV (11) 
unless, of course, it can decay rapidly into particles having only very weak interactions 
with matter. 
We wish to thank Gene Parker for the discussions on the relative strengths of 
the magnetic fields in our galaxy and the LMC, as also Professor J. Trumper for 
discussion on the X-ray observations of SN1987A. We would also like to acknowledge 
useful discussions with Michael Turner and Rocky Kolb. This work was supported in 
part by NSF at The University of Chicago and by The NASA/Fermilab Astrophysics 
Group. One of us (DNS) would like to thank the Humboldt Foundation for his stay 
at the Max Planck Institute where some of this work was carried out. 
ORIGINAL PAGE !S 
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Lower bound on e+e- decay of massive neutrinos

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