MAA instability
large, the unstable region shifts to larger !-values [17]as
shown in Fig. 1 for all three cases. We have usedblackbody-like
zenith distribution (uniform on 0!u!1)where q bimodal ¼ 1=2þ 1=
ffiffiffi3
p$ 1:077, qMZA¼1=2%
1=ffiffiffi3
p$%0:077 and qMAA ¼ %1=2. On the horizontal
axis in Fig. 1, we use !j as a variable, so the physical !range
is very different for the 3 cases.
Numerically it appears that for large !", the instabilityoccurs
for #j!& !", where #j is a coefficient different foreach case.
It also appears that for the bimodal and MZAcases, actually #j
& jq jj and we roughly have !"& j!jj.Note that !" ¼ $!þ
"& jqMZAj! ¼ 0:077!, so that, forreasonable values of $, the
matter density " would have tobe negative—the MZA instability is
self-suppressed by theunavoidable effect of neutrinos themselves,
and plays norole in a realistic SN situation. On the other hand, we
findthe new MAA instability the least sensitive to mattereffects,
as the instability region shifts only for much largerinteraction
strength (#MAA & 6jqMAAj).
Schematic SN example.—During the SN accretionphase, the matter
effect can be so large as to suppresscollective flavor conversions
[18,33,34]. In Fig. 2 wejuxtapose the instability regions for the
IH bimodal andthe new NH MAA instabilities for a simplified SN
model.We use single energy and blackbody-like emission at
theneutrino sphere, ignoring the halo flux [35]. We choosephysical
parameters R, !ðRÞ, and $ that mimic the morerealistic 15M)
accretion-phase model used in our previousstudy [18,35]. We show
the region where %r > 1, i.e.,where the growth rate is deemed
‘‘dangerous.’’ We alsoshow "ðrÞ, where the shock wave is seen at 70
km.
The matter profile never intersects the bimodal instabil-ity
region; i.e., this instability is suppressed everywhere inthis
specific SN example. On the other hand, "ðrÞ intersectsthe MAA
instability region just outside the shock wave.This simplified case
illustrates that the MAA instabilitycan arise in SN models where
the bimodal instability issuppressed. It also shows that the
‘‘danger spots’’ are in
very different places, although it remains to be seen if
thisfinding is generic.Conclusions.—All previous studies of
self-induced
neutrino conversion in SNe or the early universe were basedon
the false premise that solutions of the equations of motionwould
inherit the symmetries of the initial or boundaryconditions. We
have shown that azimuth-angle instabilitiesare a generic phenomenon
of collective neutrino oscillations.Every single case in the
previous literature with enforcedaxial symmetry may have missed the
dominant effect.We have linearized the equations of motion around
the
initial state of neutrinos in flavor eigenstates. The systemthen
shows either the bimodal or the MAA instability, butnot both. (For
more complicated spectra that would lead tomultiple spectral splits
[14], the bimodal instability occursfor positive spectral
crossings, the MAA instability fornegative ones.) However, evolved
bimodal solutions,where the off diagonal % entries are not small,
may stillbecome ’-unstable, and the other way round.Both
instabilities can be suppressed by matter, but the
required density is larger for MAA. Therefore, it is
notnecessarily clear if collective flavor conversions are
ge-nerically suppressed during the SN accretion phase, animportant
question for possible neutrino mass hierarchydetermination [5]. For
those cases where suppression is noteffective, dedicated numerical
studies are needed.
NH
IHne m
NYe
10 9g cm 3
10 11
10 10
10 8
10 7
10 6
10 5
100 100050 300 5000.1
1
10
102
103
104
103 102 10 1 0.1
r km
km1
km 1
FIG. 2 (color online). Region where %r > 1 for IH (blue)
andNH (red), depending on radius r and multiangle matter potential"
for our simplified SN model. Thick black line: SN densityprofile.
Thin dashed lines: Contours of constant electron density,where Ye
is the electron abundance per baryon. (The IH casecorresponds to
Fig. 4 of Ref. [18], except for the simplifiedspectrum used
here.)
0 20 40 60 80 100 120 1400
1
2
3
4
5
j 0
0
0MZ A
Bim odal
MAA
FIG. 1 (color online). Growth rate % for blackbody-like
zenithdistribution, single energy *!0, and $ ¼ 1=2. Black line:
Allcases for !" ¼ "þ $! ¼ 0 (no matter effect). Other
lines:Indicated unstable cases for !" ¼ 300j!0j.
PRL 111, 091101 (2013) P HY S I CA L R EV I EW LE T T E R Sweek
ending
30 AUGUST 2013
091101-4
by the MAA instability in case A is consistent with whatwas
presented in [34], where an ordered behavior in thefinal ν spectra
under MAA effects was found for largeflavor asymmetries (ε≳ 1).
Moreover, the symmetrybetween the effects of the bimodal
instability in IH andthe MAA one in NH has been recently pointed
out with asimple toy model in [32].Finally, in Fig. 5, we show the
initial (dashed curves) and
final fluxes (continuous curves) for e (black curves) and
x(light curves) flavors and for neutrinos (left panels)
andantineutrinos (right panels). We consider both MZA andMAA
effects. The upper panels show the NH, while thelower panels refer
to IH. We realize that the final spectra areremarkably similar in
both hierarchies. In particular,neutrino spectra present a split at
E ≃ 12 MeV. The splitis sharper in IH where it is driven by the
bimodal instability.The ν̄ spectra are swapped with respect to the
initial ones.In particular, as expected from the swap function of
Fig. 3,the swap is more complete in IH, where deviations from
acomplete swap are confined to low energies (E ≲ 2 MeV).
C. Case C
The gω spectrum for case C (Fig. 1 lower panel) has beenwidely
studied in the axial symmetric case as representativeof energy
spectra with a flux ordering Nνx ≳ Nνe ≳ N ν̄e and
energy spectra with multiple crossing points leading tomultiple
splits around these points (see, e.g., [22–26]).Remarkably, with
spectra of type C, one expects both thehierarchies to be unstable
under MAA and bimodal effects,since spectra present both positive
(unstable in NH forMAA effects and in IH for the bimodal ones) and
negative(unstable in IH for MAA effects and in NH for the
bimodalones) crossings. In Fig. 6, we show the radial evolution
ofthe function κobtained solving Eqs. (6) and (7). The leftpanels
refer to NH, while the right ones to IH. Differentfrom case A,
these two equations will have simultaneoussolutions in both
hierarchies. Therefore, in the upperpanels, we show the solutions
of Eq. (6) (bimodal insta-bility), while in lower panels, we refer
to Eq. (7) (MAAinstability). As in Fig. 3, continuous curves refer
to MZA,while dashed ones are for SZA.We remark that Eq. (6) havea
couple of solutions ðγ;κÞ corresponding to positive andnegative γ,
respectively (see, e.g., [35]). However, in thefollowing, we will
show only the case with the larger κ.Starting from the NH case, we
see that in the SZA situation,both bimodal and MAA effects produce
a sharp rise in κaround r≃ 40 km. Therefore, low-radii conversions
wouldbe possible in these cases. Since both instabilities
arecomparable (peak value of κ≃ 1.2), one expects that bothwould
equally contribute to the further flavor evolution.Passing now to
the MZA case, as expected from [35], the
FIG. 5 (color online). Case A. MZA and MAA flavor evolution for
ν’s (left panel) and ν̄’s (right panel) in NH (upper panels) and
IH(lower panels). Energy spectra initially for νe (black dashed
curves) and νx (light dashed curves) and after collective
oscillations for νe(black continuous curves) and νx (light
continuous curves).
MULTI-AZIMUTHAL-ANGLE INSTABILITY FOR … PHYSICAL REVIEW D 90,
033004 (2014)
033004-7
Bimodal MAA
→
(Raffelt+ 2013) 11(Chakraborty+ 2014)
⌫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⌫e +
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ARsG9Cg8+rgCwILmO7qDHmsSejd4EjJJkbcpbgDI3RMp/7HBVi1Oa4XtOP2AZ3MXl7zBzFOD3SDb3SA93SM338WasW1aj/pcq33uAKt9h/PLzx/i/L4jvAwRerCUPnn2kcC2Y01xaghNlIk2SNboTU1RqNPpXD09eN+fXx2gRd0QvrvKQnumelduXNuF4T6xdI8qCyP8fy21GnMnMZWptO5xbjiSUwgjFM8lhmkMMyVqFyW4kTnOFcGVRmlQUl10hVWmLOEL6ZsvIJy4iTSw==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
⌫̄e +
⌫̄µ/⌧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
⌫̄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
18
MSW resonance
![SuperIso v3.0: A program for calculating flavor physics ... · arXiv:0808.3144v3 [hep-ph] 10 Sep 2009 SuperIso v3.0: A program for calculating flavor physics observables in 2HDM](https://img.pdfslide.us/doc/110x75/60d92156ffe186446e1e2fcb/superiso-v30-a-program-for-calculating-iavor-physics-arxiv08083144v3-hep-ph.jpg)
