190
Supersymmetric dark matter
be detected in asttophysical neutrino detectors on earth. The most promising
technique for detection is via the observation of upward-moving muons produced
by charged-current interactions of the muonic neutrinos with the rock below the
detector. Neutralinos annihilate almost always to two-body final states, each
carrying energy m x' and the decays of these can produce muonic neutrinos with
energies between m x /3 and m x /2. The lower bound on the neutralino mass is
conservatively 40 GeV, so the energy of the muonic neutrinos is several GeV.
The only background is from atmospheric neutrinos produced by cosmic-ray
spallation. This is a well-modelled and easily subtracted background.
The first step in calculating the WIMP-induced neutrino rate is to determine
the annihilation rate r A in the sun (or earth). This is given by
rA = !CAN 2
(6.64)
where N is the number of WIMPs in the sun (or earth) and
V2
CA = (uAlvl)2"
(6.65)
VI
(UA Ivl) is the annihilation cross section multiplied by the relative velocity in the
limit of zero relative velocity, i.e. the a term of (6.53), and VI,2 are effective
volumes
Vj == (3~~T )3 / 2
(6.66)
2}m x p
where T and p are the core temperature and density respectively. The time
evolution of N is given by
N=C-CAN 2
(6.67)
where C is the WIMP accretion rate and the second term arises because of the
depletion caused by annihilations. The two processes equilibriate when N = 0
and then
rA = !C.
(6.68)
In other words, the annihilation rate is entirely determined by the accretion rate.
One might wonder whether enough time has elapsed for equilibrium to become
established but, in all cases of interest, it turns out that there has been [29].
Thus the next step is to calculate the capture rate C, which is, in turn,
determined by the elastic scattering of the WIMPs with the nuclei of the sun
(or earth). We have already noted that there are just two channels for elastic
scattering: axial (spin-dependent) and scalar (spin-independent). The former
contributes only to WIMP capture by the sun, since a negligible fraction of the
earth's mass is in nuclei with spin. The latter contributes to capture by both the
sun and the earth.
It is beyond our scope to give any details of these calculations. We merely
note that it is relatively straightforward to estimate the axial contribution in terms
Supersymmetric dark matter
be detected in asttophysical neutrino detectors on earth. The most promising
technique for detection is via the observation of upward-moving muons produced
by charged-current interactions of the muonic neutrinos with the rock below the
detector. Neutralinos annihilate almost always to two-body final states, each
carrying energy m x' and the decays of these can produce muonic neutrinos with
energies between m x /3 and m x /2. The lower bound on the neutralino mass is
conservatively 40 GeV, so the energy of the muonic neutrinos is several GeV.
The only background is from atmospheric neutrinos produced by cosmic-ray
spallation. This is a well-modelled and easily subtracted background.
The first step in calculating the WIMP-induced neutrino rate is to determine
the annihilation rate r A in the sun (or earth). This is given by
rA = !CAN 2
(6.64)
where N is the number of WIMPs in the sun (or earth) and
V2
CA = (uAlvl)2"
(6.65)
VI
(UA Ivl) is the annihilation cross section multiplied by the relative velocity in the
limit of zero relative velocity, i.e. the a term of (6.53), and VI,2 are effective
volumes
Vj == (3~~T )3 / 2
(6.66)
2}m x p
where T and p are the core temperature and density respectively. The time
evolution of N is given by
N=C-CAN 2
(6.67)
where C is the WIMP accretion rate and the second term arises because of the
depletion caused by annihilations. The two processes equilibriate when N = 0
and then
rA = !C.
(6.68)
In other words, the annihilation rate is entirely determined by the accretion rate.
One might wonder whether enough time has elapsed for equilibrium to become
established but, in all cases of interest, it turns out that there has been [29].
Thus the next step is to calculate the capture rate C, which is, in turn,
determined by the elastic scattering of the WIMPs with the nuclei of the sun
(or earth). We have already noted that there are just two channels for elastic
scattering: axial (spin-dependent) and scalar (spin-independent). The former
contributes only to WIMP capture by the sun, since a negligible fraction of the
earth's mass is in nuclei with spin. The latter contributes to capture by both the
sun and the earth.
It is beyond our scope to give any details of these calculations. We merely
note that it is relatively straightforward to estimate the axial contribution in terms