cdms-ii - CDMS Experiment - University of California, Berkeley

1.3. DIRECT DETECTION OF DARK MATTER 17
matter. The second contribution,
of the neutralinos in our galaxy.
ρ
m χ
vf(v) deals with the astrophysical distribution
Interaction of Neutralinos with Matter
Determining the differential neutralino-nucleus cross section involves calculating the
neutralino-nucleon cross section and then summing this cross section over the structure
of the nucleus. The neutralino-nucleon cross section contains all of the dependence
on the particle physics model. Since the scattering is non-relativistic, the neutralino
coupling to matter breaks down into two components. The first component is
an effective scalar interaction which couples to nucleon number and the second component
couples to the nucleon spin. This decomposition is a general one, appropriate
for any particle in the non-relativistic limit [36].
Since, the majority of the nuclei in the CDMS detectors have no net nuclear
spin, the CDMS experiment is less sensitive to the spin dependent component of the
interaction.
For this reason, I will only discuss the consequences of the scalar or
spin-independent interaction.
The scalar neutralino-nucleon cross section is dominated by two processes: interactions
with quarks in the nucleon through Higgs and squark exchange, and interactions
with gluons in the nucleon through quark and squark loops. Fig. 1.9 shows some of
the Feynman diagrams contributing to the scalar cross section. Direct evaluation of
the Feynman diagrams and nucleon matrix elements give the matrix elements for the
scattering of the neutralino off of protons, f p , and neutrons, f n . If we assume that all
the nucleons in the nucleus add coherently, the differential neutralino-nucleus cross
section is given by Fermi’s Golden rule
dσ
dq 2 = 1
πv 2 (Zf p + (A − Z)f n ) 2 (1.10)
where A is the total number of nucleons and Z is the number of protons. In most
models, f = f p ≃ f n which gives
dσ
dq 2 = 1
πv 2 A2 f 2 (1.11)