where
is the number density of nuclei of species
t
in the detector. The local number density of WIMP particles is
, where
is the WIMP mass and
is the assumed local cold dark matter density. The WIMP velocity
distribution and the cross-section both have a wide range of
uncertainty, which makes accurate predictions impossible. The
preferred range for
in the context of the lightest stable neutralino within minimal
MSSM is 20 to 200
[110,
111], and Han and Hempfling [66] quote a lower mass limit from LEP data as
. In the simplest models the dark matter density distribution in
the halo of the Galaxy is taken to be a spherical
(at least for large
r) distribution with a local density, at the position of the solar
system, of
. The velocity distribution is taken to be a Maxwellian,
consistent with a virialised system but truncated above the
Galactic escape velocity. Models involving non-spherical density
distributions [73
], rotating halos [44,
73], and/or non-virial velocity distributions, such as Galactic
in-fall components with cusps [116] or bound Solar-System Earth-crossing components [40], can individually give factor-of-two differences in the
predicted scattering rates. The WIMP velocity distribution as
seen by a terrestrial detector has a bias imposed by the Earth's
velocity through the halo and its spin. This produces a temporal
modulation of the apparent WIMP velocity distribution, which
results in an annual modulation of the WIMP scattering rate and
recoil spectrum, and daily and annual modulations in the
directional distributions.
The scattering cross-section itself has a very wide range of
possible values [45]. Different neutralino models, within MSSM or SUGRA
(supergravity), exhibit an enormous range of interaction
strengths that can be pure axial in nature (coupling only to
nuclei with non-zero spin), pure coherent (coupling to all
nucleons), or any combination of the two. Figure
6
shows the allowed range of parameter space for the scattering
cross-sections. The plot [79
] has been produced using output from the DarkSusy [58] code, using up to 65 free parameters. Even in this plot some
`reasonable' assumptions have been made in allowing the
parameters to vary; Ellis [45] relaxes some of these and, not surprisingly, finds a wider
range of resulting cross-sections. The cross-sections are
normalised to one nucleon; to calculate the total cross-section
for a target nucleus with
N
neutrons and nuclear spin
J
requires a scaling as
for the coherent spin-independent part of the cross-section and
for the spin-dependent part. The value of
depends on the target material [60].
Form factor effects, which arise due to the finite size of the
nucleus, are significant for the heavier target nuclei, are
different for axial and coherent scattering, and again have
uncertainties [47,
107]. Predicted event rates typically range from
to 10 events/day/kg. To achieve sensitivity to such rare events
requires low-background instruments operating in well shielded
underground environments.
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Experimental Searches for Dark Matter
Timothy J. Sumner http://www.livingreviews.org/lrr-2002-4 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |