Phenomenology of nuclear scattering for a WIMP of arbitrary spin
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_{χ} . To this aim we obtain constraints from a representative sample of present direct detection experiments assuming the WIMPnucleus scattering process to be driven by each one of the 44 effective couplings that arise for j_{χ}≤2 . We find that a high value of the multipolarity s ≤2 j_{χ} 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 ≤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 spinindependent 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}≳100 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 highmultipole 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.
 Publication:

Physical Review D
 Pub Date:
 September 2021
 DOI:
 10.1103/PhysRevD.104.063018
 arXiv:
 arXiv:2102.09778
 Bibcode:
 2021PhRvD.104f3018G
 Keywords:

 High Energy Physics  Phenomenology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 33 pages, 8 figures, 2 tables