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.