5.2 Expected Energy DepositNeutralino Detection Principles and TechniquesNeutralino Detection Principles and Techniques

5.1 Expected Scattering Rates 

The scattering rate per unit detector volume tex2html_wrap_inline1995 depends on the local density of dark matter particles tex2html_wrap_inline1997 ; their velocity distribution relative to a detector in a terrestrial laboratory tex2html_wrap_inline1999, and the velocity dependent scattering cross-section tex2html_wrap_inline2001, via the usual equation

  equation349

where tex2html_wrap_inline2003 is the number density of nuclei of species t in the detector. The local number density of WIMP particles is tex2html_wrap_inline2007, where tex2html_wrap_inline2009 is the WIMP mass and tex2html_wrap_inline2011 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 tex2html_wrap_inline2009 in the context of the lightest stable neutralino within minimal MSSM is 20 to 200  tex2html_wrap_inline1973  [110, 111], and Han and Hempfling [66] quote a lower mass limit from LEP data as tex2html_wrap_inline2017 . In the simplest models the dark matter density distribution in the halo of the Galaxy is taken to be a spherical tex2html_wrap_inline2019 (at least for large r) distribution with a local density, at the position of the solar system, of tex2html_wrap_inline1933 . 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 [73Jump To The Next Citation Point In The Article], 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 [45Jump To The Next Citation Point In The Article]. 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 [79Jump To The Next Citation Point In The Article] 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 tex2html_wrap_inline2029 for the coherent spin-independent part of the cross-section and tex2html_wrap_inline2031 for the spin-dependent part. The value of tex2html_wrap_inline2033 depends on the target material [60].

  

Click on thumbnail to view image

Figure 6: Total neutralino elastic scattering cross-section normalised to one nucleon for a range of neutralino models within MSSM and mSUGRA, taken from [79]. The pink area corresponds to a neutralino in a dominantly bino state, the green bounded area is dominantly higgsino. The cross-section includes both spin-independent and spin-dependent contributions, and in general the spin-dependent part is likely to be larger.

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 tex2html_wrap_inline2035 to 10 events/day/kg. To achieve sensitivity to such rare events requires low-background instruments operating in well shielded underground environments.



5.2 Expected Energy DepositNeutralino Detection Principles and TechniquesNeutralino Detection Principles and Techniques

image 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