On the sbottom resonance in dark matter scattering
  A resonance in the neutralino-nucleus elastic scattering cross section is
usually purported when the neutralino-sbottom mass difference m_sbottom-m_chi
is equal to the bottom quark mass m_b ~ 4 GeV. Such a scenario has been
discussed as a viable model for light (~ 10 GeV) neutralino dark matter as
explanation of possible DAMA and CoGeNT direct detection signals. Here we give
physical and analytical arguments showing that the sbottom resonance may
actually not be there. In particular, we show analytically that the one-loop
gluon-neutralino scattering amplitude has no pole at m_sbottom=m_chi+m_b, while
by analytic continuation to the regime m_sbottom<m_chi, it develops a pole at
m_sbottom=m_chi-m_b. In the limit of vanishing gluon momenta, this pole
corresponds to the only cut of the neutralino self-energy diagram with a quark
and a squark running in the loop, when the decay process chi->squark+quark
becomes kinematically allowed. The pole can be interpreted as the formation of
a sbottom-antibottom-qqq or antisbottom-bottom qqq resonant state (where qqq
are the nucleon valence quarks), which is kinematically not accessible if the
neutralino is the LSP. Our analysis shows that the common practice of
estimating the neutralino-nucleon cross section by introducing an ad-hoc pole
at m_sbottom=m_chi+m_b into the effective four-fermion interaction (including
higher-twist effects) should be discouraged, since it corresponds to adding a
spurious pole to the scattering process at the center-of-mass energy sqrt(s)
m_chi m_sbottom-m_b. Our considerations can be extended from the specific case
of supersymmetry to other cases in which the dark matter particle scatters off
nucleons through the exchange of a b-flavored state almost degenerate to its
mass, such as in theories with extra dimensions and in other mass-degenerate
dark matter scenarios recently discussed in the literature.
