Abstract
We provide a first systematic and quantitative discussion of the phenomenology of the nonrelativistic effective Hamiltonian describing the nuclear scattering process for a weakly interacting massive particle (WIMP) of arbitrary spin ${j}_{\ensuremath{\chi}}$. To this aim we obtain constraints from a representative sample of present direct detection experiments assuming the WIMP-nucleus scattering process to be driven by each one of the 44 effective couplings that arise for ${j}_{\ensuremath{\chi}}\ensuremath{\le}2$. We find that a high value of the multipolarity $s\ensuremath{\le}2{j}_{\ensuremath{\chi}}$ of the coupling, related to the power of the momentum transfer $q$ appearing in the scattering amplitude, leads to a suppression of the expected rates and pushes the expected differential spectra to large recoil energies ${E}_{R}$. For $s\ensuremath{\le}4$ the effective scales probed by direct detection experiments can be suppressed by up to five orders of magnitude compared to the case of a standard spin-independent interaction. For operators with large $s$ the expected differential spectra can be pushed to recoil energies in the MeV range, with the largest part of the signal concentrated at ${E}_{R}\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{keV}$ and a peculiar structure of peaks and minima arising when both the nuclear target and the WIMPs are heavy. As a consequence the present bounds on the effective operators can be significantly improved by extending the recoil energy intervals to higher recoil energies. Our analysis assumes effective interaction operators that are irreducible under the rotation group. Such operators drive the interactions of high-multipole dark matter candidates, i.e., states that possess only the highest multipole allowed by their spin. As a consequence our analysis represents also the first phenomenological study of the direct detection of quadrupolar, octupolar, and hexadecapolar dark matter.
Highlights
Interacting massive particles (WIMPs) are the most popular particle candidates to provide the invisible halos of Galaxies, including the Milky Way
For operators with large s the expected differential spectra can be pushed to recoil energies in the MeV range, with the largest part of the signal concentrated at ER ≳ 100 keV and a peculiar structure of peaks and minima arising when both the nuclear target and the weakly interacting massive particle (WIMP) are heavy
In the present paper we have provided a first systematic and quantitative discussion of the phenomenology of the nonrelativistic effective Hamiltonian introduced in Ref. [31] to describe the nuclear scattering process for a WIMP of arbitrary spin jχ
Summary
Interacting massive particles (WIMPs) are the most popular particle candidates to provide the invisible halos of Galaxies, including the Milky Way. In case several effective operators contribute to the scattering process, for example in the nonrelativistic limit of a higher energy theory, their interference may weaken the bounds, up to one order of magnitude in the couplings for spin 1=2 [15,32] The details of the procedure followed to obtain the upper bounds is described in the Appendix
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