WIMP neutrinos from the Sun and the Earth

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PoS(idm2008)116
WIMP neutrinos from the Sun and the Earth (15’+5’)
MATTIAS BLENNOW∗
Max-Planck-Institut für Physik
E-mail: blennow@mppmu.mpg.de
JOAKIM EDSJÖ
Department of Physics, Stockholm University
E-mail: edsjo@physto.se
TOMMY OHLSSON
Department of Theoretical Physics, Royal Institute of Technology
E-mail: tommy@theophys.kth.se
We discuss the propagation treatment of the indirect dark matter detection using WIMP annihi-
lations in the Sun and the Earth. In particular, we focus on treating neutrino interactions and
oscillations in a consistent framework, including tau neutrino regeneration and a full three-flavor
neutrino oscillation framework. We also discuss the equivalence of using a Monte Carlo approach
- suited for inclusion in neutrino telescope Monte Carlos - and the density matrix formalism.
Identification of dark matter 2008
August 18-22, 2008
Stockholm, Sweden
∗Speaker.
c
Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/

PoS(idm2008)116
WIMP neutrinos from the Sun and the Earth (15’+5’) MATTIAS BLENNOW
1. Introduction
When weakly massive interactive particles (WIMPs) from the galactic halo passes through the
Sun, there is a possibility that they scatter and lose enough energy to be gravitationally trapped.
Following subsequent scatterings in the Sun, the WIMPs sink to the solar core and thermalize.
The accreted WIMPs can then undergo co-annihilation into different channels depending on the
particular WIMP model. Regardless of the model, the only particles which interact weakly enough
to escape from the Sun are neutrinos, which can be produced either directly or through the subse-
quent decays of the co-annihilation products. Here, we will present an event based Monte Carlo
for computing the neutrino flux at Earth given the co-annihilation rate and branching fractions into
the different channels. We will also comment on the equivalence between this Monte Carlo and the
density matrix formalism usually used to treat this phenomenon analytically.
2. Density matrix formalism
When treating the neutrino propagation analytically, it is customary to use the density matrix
formalism in which the neutrino evolution is given by
˙
ρ
(r,E) = −i[H,
ρ
]−1
2{Γ,
ρ
}+˙
ρ
reg,(2.1)
where
ρ
(r,E)is describing the flavor and energy distribution of neutrinos, the first term on the
right-hand side describes neutrino oscillations, the second describes the degrading of the neutrino
flux due to interactions, and the last term is a regeneration term describing the gain in neutrinos
from the same interactions (a neutral-current interaction simply degrades the neutrino energy, while
a charged-current interaction may produce new neutrinos if the neutrino interacts as a
ντ
). This
approach has been used in a number of papers in order to study the impact of neutrino oscillations
and interactions in a consistent framework [2, 3, 4].
3. Monte Carlo treatment
In our Monte Carlo, we instead use an event based approach, where every neutrino is described
by a vector in flavor space as well as an energy. We then compute if and when the neutrino will
interact. If the neutrino does not interact, then we simply evolve its flavor state any desired point.
However, if it does interact, it is treated differently depending on the type of interaction. For neutral
current interactions, we simply remove the neutrino from our simulation and create a new neutrino
with the same flavor vector but degraded energy due to the energy loss in the interaction. If the
interaction is due to a charged-current, then the neutrino is completely lost unless it interacts as
a
ντ
. In this latter case, the resulting
τ
will decay before it loses energy due to interactions, and
thus, produce new neutrinos. We then simulate this interaction and subsequent decay and add the
resulting neutrinos to our computation.
It is fairly straightforward to show that this Monte Carlo treatment is equivalent to the usual
density matrix formalism on a statistical level. The simplest way of doing this is to start from
the fact that the evolution of the density matrix is linear (this is no longer true if one considers the
evolution where neutrino-neutrino interactions become important, such as above the neurino sphere
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PoS(idm2008)116
WIMP neutrinos from the Sun and the Earth (15’+5’) MATTIAS BLENNOW
Annihilation
channel
Neutrino
parameters
WIMP
parameters
Model parameters
Detector
latitude
Time
interval
Target
material
Experimental definitions
Neutrino
flux (det.)
Lepton
flux
Hadronic
showers
Neutrino
flux (1 AU)
Output
DarkSUSY
Nusigma
Pythia
External software
WimpAnn WimpEvent
1 AU
events
ν
param.
WimpSim package
Figure 1: A flowchart of how the WimpSim package operates, including input, output and dependencies on
external programs.
in a supernova). Then one can construct the density matrix corresponding to a single neutrino in the
Monte Carlo and deduce how it is propagated. This readily gives back the density matrix evolution
when one considers the statistical average. For details, see the Appendix of Ref. [1].
Our Monte Carlo has been written in a very general format and is easy to implement together
with DarkSUSY or into neutrino telescope Monte Carlos. The code, as well as the results of our
simulations are publically available [5]. Essentially, the code is built up of two main programs,
WimpAnn and WimpEvent, which together form the program package WimpSim. WimpAnn is
responsible for the treatment from the WIMP annihilations up to the propagation of the resulting
neutrinos to a distance of 1 AU. Essentially, this is the part which needs no input on the experi-
mental setup. From 1 AU, WimpEvent takes over and propagates the neutrinos to the detector and
computes the final neutrino fluxes and other data that could be of interest. For a schematic view on
how the WimpSim package operates, see Fig. 1. Further information can be found at Ref. [5].
4. Results
As our main example in Ref. [1], we present the results for annihilations of m
χ
=250 GeV
WIMPs into
τ
+
τ
−pairs, simply because this channel will give a relatively large difference in the
initial fluxes of different neutrino flavors. The difference between the simulations with and without
neutrino oscillations included are shown in Fig. 2. Essentially, the results arise in the following
manner: On the way out of the Sun,
νµ
↔
ντ
oscillations due to the mass squared splitting ∆m2
31
more or less equilibrates the
νµ
and
ντ
fluxes, although the oscillation pattern can still be seen in
the energy spectrum. When propagated to a distance of 1 AU, also the mass squared splitting ∆m2
21
has started to affect the oscillations and also produced an increased flux of
ν
eat the expense of
the other neutrino flavors. The
νµ
↔
ντ
oscillations are now so fast that they are no longer seen
in the energy spectrum, while there remains an oscillation pattern for the oscillations into
ν
eat
higher energies. Finally, the propagation to a detector (in this case a detector located at the South
3

PoS(idm2008)116
WIMP neutrinos from the Sun and the Earth (15’+5’) MATTIAS BLENNOW
10 6
10 7
10 8
10 9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
νe (std. osc.)
νµ (std. osc.)
ντ (std. osc.)
νe (no osc.)
νµ (no osc.)
ντ (no osc.)
z = Eν / mχ
dNν/dz (10-35 cm-2 ann-1)
Neutrino yields at detector
Mass: 250 GeV
Channel: τ+τ-
M. Blennow, J. Edsjö and T. Ohlsson, 2007
Figure 2: The result for annihilations of a m
χ
=250 GeV WIMP into
τ
+
τ
−, both in the case when neutrino
oscillations are included (std osc.) and for the case when they are not (no osc.). Figure from Ref. [1].
Pole) and making a time-average over half a year essentially erases all of the remaining oscillation
features (see Ref. [1] for details).
Acknowledgments
This work was supported by the Royal Swedish Academy of Sciences (KVA) [TO] and the
Swedish Research Council (Vetenskapsrådet) through Contract Nos. 623-2007-8066 [MB], 622-
2003-6025 [JE] and 621-2005-3588 [TO].
References
[1] M. Blennow, J. Edsjö, and T. Ohlsson, Neutrinos from WIMP Annihilations Using a Full
Three-Flavor Monte Carlo.JCAP 01 (2008) 021 [0709.3898].
[2] M. Cirelli et al., Spectra of neutrinos from dark matter annihilations,Nucl. Phys. B727 (2005) 99
[hep-ph/0506298].
[3] R. Lehnert and T. J. Weiler, Neutrino flavor ratios as diagnostic of solar WIMP annihilation,
Phys. Rev. D77 (2008) 125004 [0708.1035].
[4] V. Barger, W.-Y. Keung, G. Shaughnessy, and A. Tregre, High energy neutrinos from neutralino
annihilations in the Sun,Phys. Rev. D76 (2007) 095008 [0708.1325].
[5] http://www.physto.se/˜edsjo/wimpsim, WimpSim homepage.
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