Volume 200, number 3 PHYSICS LETTERS B 14 January 1988
THE MASS OF THE ELECTRON NEUTRINO:
MONTE CARLO STUDIES OF SN 1987A OBSERVATIONS
David N. SPERGEL and John N. BAHCALL
Institute for Advanced Study, Princeton, NJ 08540, USA
Received 5 October 1987
Monte Carlo s~mulatlons of a wide class of possible neutnno emission models are used to assign statistical s~gmficanceto the
hm~ts set on the mass of the electron neutrino by observations of SN 1987A Using the combined Kamlokande II and IMB data
sets, we reject neutrino masses greater than 16 eV at the 5% significance level.
I. Introductton. The observations of neutrinos from the recent LMC supernova [ 1,2 ] place interesting upper
llmtts on the mass of the electron's neutrino, rnv~. The bastc idea was discussed first by Zatsepm [3], who
pointed out that if neutrinos had a finite mass the higher energy neutrinos from a supernova explosion would
arrive before the more slowly moving, lower energy neutrinos. The extra time, At, that a fimte mass neutrino
requires to reach the earth compared to a zero mass particle ts
/'dlstance'~ (mvL)2{10MeV]2
At,=2.S7s~pc) ~ \ ~,, j , (1)
where E, is the energy of the tth neutnno. A finite mass of the neutrino will cause, according to eq. (1), particles
of different energies to arrive at different times, even if they are emitted simultaneously. This dispersion re-
lation will typically stretch out a burst in nine, with the lowest energy pamcles arriving last unless there are
special cancellations.
One cannot deduce a mass limit without some assumption. All that eq. (1) allows us to compute, for any
assumed value of rnv~, is the emisston time for each of the observed neutrinos. Unless we make a supporting
stattstlcal or physical assumption, we cannot proceed further and, in particular, cannot infer a mass limit.
Bahcall and Glashow [4] and Arnett and Rosner [5] derived an upper hmlt of about 11 eV for rn,,~ by as-
suming that nature was not satamc and therefore that the observed two second half width of the observed neu-
trino pulse was not narrowed by more than a factor of two in flxght. This argument has the advantage of slmphcity,
but does not prowde statisncal confidence levels for the inferred mass hmlt. If the delay time due to finite
neutrino mass becomes comparable to the characteristic w~dth of the pulse, the expected distribution of events
should show a correlation of energy with time. This correlation is not present, which also suggests in a model-
independent way that the observed data do not imply a measurable mass for re. Bahcall and Glashow [ 4 ] pointed
out that more strmgent limits could be referred if one were willing to interpret the observed substructure of
the neutrino burst in terms of specific physical processes.
Other authors have argued for more stringent hmits, or for specific mass values, by assuming that the neu-
trino pulse had dtscernable substructure [6]. Kolb et al. [7] and Schramm [8] have questioned the vali&ty
of all of these limits by noting that nature could be cruel: the supernova could first emit low energy neutrinos
and then later emit more energenc neutrinos m just such a way that the pulse of neutrinos from the LMC is
focussed at the earth. (This possibility is suggested in some models [9 ].) An unfortunate coincidence between
the earth/LMC distance and the mass of the neutrino could sharpen the neutrino pulse. However, Kolb et al.
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