Neutrino decay and the supernova relic neutrino background

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Neutrino decay and the supernova relic neutrino
background

• Based on
• G.L. Fogli, E. Lisi, A. Mirizzi, D. M.
• Phys. Rev. D 70 013001 (2004)
• hep-ph/0401227

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Introduction

• We have now a striking evidence for neutrino
  oscillations
• What about other non standard neutrino properties?

• magnetic moment

• VLI, VEP

• non standard interactions

• extra dimensions

• quantum decoherence

• sterile neutrinos

• CPT violations

• decay

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Framework

• We stick in the current phenomenology of three
  generations of massive neutrinos. We do not
  consider
• heavy active neutrinos evading the LEP limit
  (m??45GeV)
• light or heavy sterile neutrinos
• We also assume that m??O(1eV)

As of Neutrino04
?m2?8.2?10-5eV2
?m2?2.4?10-3eV2
sin2?12?0.28 sin2?13lt0.07
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Probing neutrino decay
At the moment there are not experimental
evidences in favour of ? decay. In order to leave
unperturbed the current phenomenology, the
decay lifetime should be sufficiently long.
Roughly speaking, for a neutrino with mass m and
energy E must be (in unit c1)
where ? is the proper (rest frame) neutrino
lifetime, E/m is the Lorentz time-dilatation
factor and L is the decay path length. For a
given neutrino energy and decay path length a
bound on ?/m can be fixed.
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Types of neutrino decay
For light neutrinos we have only two possible
decays

• visible (or radiative)
• ?H ? ?L ?

• invisible
• ?H ? ?L X or
• ?H ? 3?L
• where X is massless (or a light) weak
  interacting particle (e.g., a Majoron)

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The Majoron Model
In some models of neutrino mass generation (see
e.g., Gelmini Roncadelli, Phys. Lett. B 99,
411, 1981), neutrinos are coupled with a massless
Nambu-Goldstone boson, used called Majoron
through a renormalizabe coupling
where the ?i,j are the Majorana neutrino mass
eigenstates. If mjgtmi the decays
are possible.
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Neutrino decay into Majoron was also invoked by
Barger et al. (Phys. Rev. Lett. 82, 2640, 1999)
as an alternative explanation of the atmospheric
neutrino anomaly. However, this model is now
strongly disfavoured by the observation of a
dip in the L/E distribution of events in SuperK.
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The intrinsic ? decay rate in vacuum has been
calculated by Kim Lam, Mod. Phys. Lett. A 5,
297, 1980. We consider only the two limiting
cases
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we define ?j as the total decay rate of the state
?j
we define also the branching ratios
From the previous formulae we observe that
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The proper decay lifetime (divided by the mass)
in the Majoron model can be written, in general
as
for the higher (atmospheric) ?m2 we obtain
From solar neutrinos phenomenology we have
?/mO(5?10-4)s/eV. From this limit we infer
gijO(10-4). For diagonal couplings the limits
can be weaker, giiO(10-2). Supernova cooling
arguments may limit the values of gij in a strip
around 10-6?7.
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In order to fix stronger limits on the coupling
constants gij, or equivalently, the decay time
?/m we need a longer baseline (since lowering the
neutrino energy is not admissible from an
experimental point of view)
In particular we can use

• Galactic Supernova neutrinos (L102?5pc)

From SN1987A we can infer a naïve limit
?/mO(105) s/eV, but this limit should be taken
with caution, since it depends on many
assumptions.

• Relic Supernova Neutrinos (L1/H0, H070 km
  Mpc-1s-1)

These neutrinos have also a strong advantage
they constitutes a continuous signal.
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Supernova Relic Neutrinos (SRN)
There is 1type II SN explosion per second
somewhere in the universe
This gives rise to a diffuse neutrino background
of energy E10MeV
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The total flux of SRNs of a given flavour ? is
easily calculated
H(z)H0(1?mz)(1z)2-??z(2z)1/2 is the Hubble
constant as function of the redshift z,
Y?(E)?L?(E,t)dt is the total yield (total time
integrated luminosity) for a typical supernova of
the specie ??, and RSN(z) is the Supernova rate
per comoving volume.
RSN(z)
adapted from Porciani Madau astro-ph/0008249 (f
or ?m1, ??0 and H070kmMpc-1s-1)
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SRNs are thus suitable to probe neutrino decay
lifetimes of cosmological interest. In particular
we expect to prove lifetimes of the order
where E10MeV with a gain of about 14 order of
magnitude with respect to the present limit. In
this way, we can prove neutrino-Majoron couplings
(or, at least, the non-diagonal ones) up to
gij?O(10-10)
But, of course, this is not so easy since the
measure of the SRN flux is extremely difficult
and affected by a number of theoretical
uncertainties (on RSN, the initial ? spectra,
etc.). Moreover, as we will see, in certain
scenarios the effect of decay is almost
unobservable.
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The general framework
The equation governing the evolution of the
number density ni(E,t) (per comoving volume) of
the mass eigenstate ?i is the Boltzmann equation
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• The mass yields Yi(E) are a combination of the
  initial flavor yields Y?(E). We consider only the
  two limiting cases
• adiabatic transitions
• PH0 or sin2?13gt10-2
• strongly non adiabatic transitions
• PH1 or sin2?13lt10-5
• where PH is the higher crossing probability
  between mass eigenstates in matter (the lower
  crossing probability PL is always zero within the
  present phenomenology).
• Any other intermediate choice for PH(E) does not
  affect drastically our conclusions.

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With this position we have simply
NH, PH0
IH NH, PH1
IH, PH0
NH IH, PH1
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where the last relation comes from the fact that
Ue3sin?13 is small and thus the state ?3 is
(almost) unobservable.
From this fact we draw a first general conclusion
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3? decay schemes
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The decay spectrum ??j??i(Ej,Ei)Prob(?j(Ej)??i(E
i) for ultra relativistic ?s normalized to
unity, ?dEi?(Ej,Ei)1 can be written as follows
Ei?Ej
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Results NH, QD case
As expected, in this case we have an enhancement
of the signal. In particular, in the case of
complete (or fast) decay (i.e., when
?/mltlt1010s/eV) the number of events in a
water-Cherenkov detector is increased of a factor
2.3 with respect to the no decay case. We have
chosen ?/m7?1010s/eV as intermediate case.
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Results NH, SH case
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Results IH, any case
In this case we have a depletion of the signal.
In particular, in the case of complete decay we
have the complete disappearance of the signal.
This case is sensitive to the value of the PH.
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Total number of events (normalized to the
no-decay case and PH1) for a water-Cherenkov
detector in the positron energy window
Epos?10,20MeV.
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Conclusions
One of the next frontier of the neutrino physics
is to prove (or bound) non-standard neutrino
properties, in particular, neutrino decay.
In particular invisible decays (such as, Majoron
decays) can be proved through the observation of
the diffuse background of neutrinos coming from
all past supernovae which will be possible with
the next generation of water-Cherekov detectors.
Unfortunately, in NH with m3gtgtm2gtgtm1 the effects
of decay are almost unobservable. For this
reason, the absolute neutrino masses as well the
correct mass hierarchy should be known from other
experiments.
However, if we are not in the previous unlucky
case, by simply requiring that the number of
events does not deviate more than a factor 2 from
the expected one, one can fix a naïve limit,
?/m?5?1010s/eV, which is 14
order of magnitude stronger than the present
limit.
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Appendix Radiative decay
In principle is possible also in the Standard
Model
However the decay amplitude is extremely small
(see e.g. Pal Wolfenstein, Phys. Rev. D 25,
766, 1982)
where xm2/m1. A shorter decay lifetime is thus a
signal for non standard interactions.
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Radiative neutrino decays was invoked by Sciama
et al. to explain the high degree of ionized
hydrogen in the universe. However, the Sciama
model is now ruled out.
Limits on radiative decay lifetime can be derived
from a variety of astrophysical and cosmological
arguments. The most stringent limit comes from
the observation of O(TeV) photons coming from
distant sources. In fact, if a diffuse infrared
background of photons coming from the decay of
Big Bang relic neutrinos would fill the
intergalactic space, this would be opaque for TeV
?s, due to the reaction ?(TeV)?(background)?ee
-
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Limits on radiative decay
SRNs can be used also to limit the ?/m in the
hypothesis of radiative ? decay, although this
limit is not competitive with those coming from
cosmology.
We consider only the case of NH in the SH case.
In this case the decay spectrum of the photon is
the following
where E? is the photon energy and ? is a
parameter which quantifies the amount of parity
violation in the process (??-1,1 for Dirac
neutrinos, ?0 for Majorana neutrinos).
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In the hypothesis of very large ?/m the neutrinos
can be considered, in firs approximation,
undecayed. In the hypothesis of the same ?/m for
each decay channel, the flux of photons on Earth
coming from the ? decay can be easily calculated
where n0j(E,z) is the undecayed number of
neutrinos ?j per comoving volume as function of
the redshift z.
The flux J? should be compared with the
observations of the diffuse background of gamma
rays at E?O(MeV).
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