On the sbottom resonance in dark matter scattering

초록

A resonance in the neutralino-nucleus elastic scattering cross section is usually purported when the neutralino-sbottom mass difference m((b) over tilde) - m(X) is equal to the bottom quark mass m(b) similar to 4 GeV. Such a scenario has been discussed as a viable model for light (similar to 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 m((b) over tilde) + m(X) + m(b), while by analytic continuation to the regime m((b) over tilde) < m(X), it develops a pole at m(<(b)over tilde>) = m(x) - 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 x -> (Q) over tilde + Q becomes kinematically allowed. The pole can be interpreted as the formation of a (b) over tilde(b) over bar qqq or (b) over tilde *bqqq resonant state (where qqq are the nucleon valence quarks), which is however 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 n((b) over tilde) = m(X) + m(b) into the effective four-fermion interaction (also 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 root s similar or equal to m(X) similar or equal to m((b) over tilde) - m(b). Our considerations can be extended from the specific case of supersymmetry to other similar cases in which the dark matter particle scatters off nucleons through the exchange of a b-flavored state almost degenerate in mass with the dark matter particle, such as for instance in theories with extra dimensions and in other mass-degenerate dark matter scenarios recently discussed in the literature.

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