arXiv:hep-ph/0501184v2 6 May 2005
Supernova neutrinos can tell us the neutrino mass
hierarchy independently of flux models
V. Barger1, Patrick Huber1and Danny Marfatia2
1Department of Physics, University of Wisconsin, Madison, WI 53706
2Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045
We demonstrate that the detection of shock modulations of the neutrino spectra
from a galactic core-collapse supernova is sufficient to obtain a high significance de-
termination of the neutrino mass hierarchy if the supernova event is observed in both
a Mton-class water Cherenkov detector and a 100 kton-class liquid argon detector.
Neither detailed supernova neutrino flux modelling nor observation of Earth matter
effects is needed for this determination. As a corollary, a nonzero value of θxwill be
The current status of neutrino oscillation parameter estimations can be very briefly sum-
marized  as follows: Atmospheric (solar) neutrinos oscillate with |δm2
a| ∼ 0.002 eV2and
θa∼ π/4  (δm2
s∼ 8 × 10−5eV2, θs∼ π/6 )1. All we presently know about θxis that
sin2θx<∼0.05 at the 2σ C. L. . A long-standing hope is that neutrinos from a core-collapse
supernova (SN) may shed light on two of the unknown oscillation parameters, sgn(δm2
Only a handful of neutrinos from a Type II SN have ever been detected. The detection
of 11 neutrinos from SN 1987A in Kamiokande II  and 8 neutrinos in the Irvine Michigan
Brookhaven experiment  have been of great importance for understanding core-collapse .
It is evident that the physics potential offered by a future galactic SN event is immense.
With cognizance of this potential, experiments dedicated to SN neutrino detection have
been proposed  even though only a few galactic SN are expected per century.
Attempts have been made to extract neutrino oscillation parameters from the 19 SN
1987A events. However, conclusions drawn from such analyses are highly dependent on
the neutrino flux model adopted and are far from robust. For example (and within the
context of this paper), it was claimed that the data favor the normal hierarchy (δm2
over the inverted hierarchy (δm2
a< 0) provided sin2θx>∼10−4, but this conclusion was
contradicted in Ref. .
Neutrinos from a galactic SN could in principle provide a wealth of information on neu-
trino oscillations. A determination of θxand the neutrino mass hierarchy from SN neutrinos
is unique in that ambiguities [11, 12] arising from the unknown CP phase δ and the devia-
tion of atmospheric neutrino mixing from maximality do not corrupt it. The absence of the
eight-fold parameter degeneracies that are inherent in long baseline experiments  results
because (i) nonelectron neutrino fluxes2do not depend on δ independently of neutrino con-
version , and so SN neutrinos directly probe θx, and (ii) whether atmospheric mixing is
1In our notation, δm2
a) is the solar (atmospheric) mass-squared difference and θs, θxand θaare the
mixing angles conventionally denoted by θ12, θ13and θ23, respectively .
2We focus on detection via charged current νeand ¯ νeinteractions, which cannot distinguish between the
different nonelectron neutrino species (that we denote by νxwith x = µ,τ, ¯ µ, ¯ τ).
maximal or not is immaterial since θadoes not affect the oscillation dynamics.
Investigations of the effect of neutrino oscillations on SN neutrinos in the context of a
static density profile (i.e., neglecting shock effects) have been made in Refs. [14, 15, 16].
Whether or not the mass hierarchy can be determined and θxbe constrained depends sensi-
tively on the strength of the hierarchy between ?E¯ νe? and ?Eνx?. The higher ?Eνx?/?E¯ νe?
is above unity, the better the possible determinations .Unfortunately, modern SN
models that include all relevant neutrino interaction effects like nuclear recoil and nucleon
bremsstrahlung indicate that the hierarchy of average energies is likely smaller than ex-
pected from traditional predictions; ?Eνx?/?E¯ νe? is expected to be about 1.1, and no larger
than 1.2  as opposed to ratios above 1.5 from older SN codes . Another relevant
uncertainty is that different SN models predict different degrees to which equipartitioning
of energy between νe, ¯ νe and νx is violated. For example, in Ref.  an almost perfect
equipartitioning is obtained while according to Refs. [20, 21], equipartitioning holds only to
within a factor of 2.
Given these uncertainties, it is not a simple task to determine θxand the mass hierarchy
simultaneously from SN data . A significant improvement would be a determination of
the mass hierarchy independently of predictions for ?Eνx?/?E¯ νe? and equipartitioning from
SN models. In this paper we propose a new method using SN neutrinos to determine the
mass hierarchy that exploits recent advances in the understanding of shock propagation in
At densities ∼ 103g/cm3, neutrino oscillations are governed by δm2
aand sin2θx .
Neutrinos (antineutrinos) pass through a resonance if δm2
a> 0 (δm2
a< 0). As the shock tra-
verses the resonance, adiabaticity is severely affected causing oscillations to be temporarily
suppressed, as first pointed out in Ref. . After the shock moves beyond the resonance,
oscillations are restored. Then one expects a dip in the time evolution of the average neutrino
energy and the number of events3. This modulation is visible in the neutrino (antineutrino)
3Recently, this idea was taken one step further in Ref. . A reverse shock caused by the collision
between a neutrino-driven baryonic wind and the more slowly moving primary ejecta may also form. The
direct and reverse shocks yield a “double dip” signature . In the present work we restrict our attention
to the effects of the forward shock which is a generic feature of SN models and whose existence is better
established than that of the reverse shock.
Figure 2: (a) R(νe,Ar) vs. R(¯ νe,H2O) for SN models spanned by Eqs. (6,7) and tan2θx=
0.01 assuming ?Ei? = ?E0
i?. R is the ratio of the mean energy of the events occuring between
4 and 10 seconds to the mean energy of the events occuring in the first 4 seconds. The
red squares (green triangles) correspond to the normal (inverted) hierarchy. The blue dots
are for θx = 0. Each contour contains 95% of the 105νe and ¯ νe spectra generated for
the corresponding case. We have plotted only 103triangles, squares and dots so as to not
overwhelm the figure. (b) is the analog of (a) but for the case in which ?Ei? falls linearly
with time 5 secs after bounce. The separation of the clusters is a measure of the significance
with which the hierarchy can be determined.
0.96 0.97 0.98 0.9911.01 1.02
0.95 0.96 0.97 0.98 0.99
Figure 3: (a) The dashed red curve shows the fraction of spectra corresponding to the normal
hierarchy and tan2θx= 0.01 with R(νe,Ar) below a given value (use the y-scale on the left).
The solid blue curve shows the number of spectra with θx= 0 and R(νe,Ar) below a given
value divided by the number for the normal hierarchy and tan2θx = 0.01 with R(νe,Ar)
below the same value (use the y-scale on the right). (b) is the analog of (a) but for the
inverted hierarchy. Spectra with ?Ei? = ?E0
i? were assumed. See Eq. (9) for the definition