content_image/364299.jpg content_image/364297.jpg content_image/364296.jpg content_image/364295.jpg content_image/364294.jpg content_image/364292.jpg content_image/364293.jpg content_image/364290.jpg content_image/364291.jpg
## Appendix B: The Bino/Higgsino and Wino/Higgsino Limits 

In the limit of large M$_{1}$ ( M$_{2}$ ) the neutralino is dominantly a Wino/Higgsino (Bino/Higgsino) admixture. We can explore this effective 3 state system using the SDM defined as (see Eq. (27) above): 

The resulting lightest eigenstate ( χ ) is specified by 

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Following [9], it is useful to write this system in a basis defined by S and D$_{±}$ ≡ 1 √ 2 ( D ± ¯ D ). Note that the labels ± have nothing to do with electric charge. The mass matrix is then, in the ( S, D$_{+}$, D$_{−}$ ) basis, 

with the resulting lightest eigenstate, 

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Since we are interested in the SD DD cross section, our goal is to extract the coupling of χ to the Z $^{0}$. The coefficient of the operator O SD q of Eq. (11) is given by 

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Note that | 2 Z$_{D}$$_{+}$ Z$_{D}$$_{−}$ | ≡ | Z$_{D}$ | 2 − | Z ¯ $_{D}$| $^{2}$. One can find analytic expressions for the mass eigenstates and the combination | 2 Z$_{D}$$_{+}$ Z$_{D}$$_{−}$ | in various useful limits. To second order in v , for | µ$_{D}$ | , | µ$_{S}$ | , ( | µ$_{D}$ | − | µ$_{S}$ | ) ≫ λ v, λ ′ v 

and for | µ$_{D}$ | = | µ$_{S}$ | ≫ λ v, λ ′ v , 

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