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Model Independent Experimental Limits on Spin-dependent WIMPs Franco Giuliani

Model Independent Experimental Limits on Spin-dependent WIMPs Franco Giuliani. Introduction Weak point of “traditional” exclusion plots: WIMP-model dependence How to “get around it”: Without positive signal An experiment is not equally sensitive to all theoretical candidates

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Model Independent Experimental Limits on Spin-dependent WIMPs Franco Giuliani

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  1. Model Independent Experimental Limits on Spin-dependent WIMPsFranco Giuliani • Introduction • Weak point of “traditional” exclusion plots: WIMP-model dependence • How to “get around it”: • Without positive signal An experiment is not equally sensitive to all theoretical candidates • With positive signal: necessity of combining at least 3 experiments

  2. Spin-dependent WIMP-nucleus elastic cross section Effective lagrangian for elastic scattering: • cross sections of a nucleus at 0 momentum transfer: Traditional “Odd Group” Approx.:< Sp>ap  0 or < Sn>an  0 • Justified by rarity or radioactivity of most odd-odd nuclei (except 14N!) • p   A (n   A), at the price of no constraints on  n ( p) • generally, both < Sp> and < Sn> 0, so OGA is also obtained from an or ap = 0 WIMP-model dependence

  3. “EXTREME” EXCLUSION PLOTS: If an = 0 the correct exclusion plots are on the left If ap = 0 the correct exclusion plots are on the right

  4. Spin-dependent exclusion relations [Tovey et al., PLB 488 (2000) 17]: In terms of coupling strengths: • Sign depends on <Sn>/<Sp> ratio • mn mp In terms of cross sections: Sign depends on an<Sn>/ (ap<Sp>) ratio

  5. 3D Spin dependent exclusion plots: Coupling strengths representation

  6. 3D Spin dependent exclusion plots: Cross section representation

  7. cross section formulation coupling strengthformulation Bi-dimensional sections of the exclusion plots

  8. When intersecting the permitted regions of various experiments, much better limits are found survey of experiments

  9. In the coupling strengthformulation, the relative orientation of the various experimental permitted regions can strongly reduce the overall allowed area. From this survey, the limits at M = 50 GeV/c2 are: |ap| ≤ 1.5 |an| ≤ 1.3 Survey in the coupling strengthformulation

  10. Now also lower limits: Extension to the case of a positive signal In terms of coupling strengths: • Sign depends on <Sn>/<Sp> ratio • mn mp In terms of cross sections: Sign depends on an<Sn>/ (ap<Sp>) ratio

  11. Exclusion with positive signal experiments • A single positive signal experiment determines an elliptical ring centered in the origin • Two positive signal experiments intersect in 4 spots, giving 2 possible pairs of nucleon cross sections • Three experiments yield two spots corresponding to a single proton (neutron) cross section. The sign ambiguity in ap,n is partially removed.

  12. Conclusions • Traditional spin-dependent exclusion plots are WIMP-model-dependent, and insufficient to meaningfully compare both odd-Z and odd-N experiments • A model-independent approach allows to overcome these difficulties, at the price of making the exclusion plots 3D • The simplest model-independent exclusion plots are in ap,n • When a positive signal is found, this does not completely determine ap,n: to achieve such result at least three positive signal experiments are needed.

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