Form factors for dark matter capture by the Sun in effective theories

Abstract

In the effective theory of isoscalar and isovector dark matter-nucleon interactions mediated by a heavy spin-1 or spin-0 particle, 8 isotope-dependent nuclear response functions can be generated in the dark matter scattering by nuclei. We compute the 8 nuclear response functions for the 16 most abundant elements in the Sun, Ni, through numerical shell model calculations. We use our response functions to compute the rate of dark matter capture by the Sun for all isoscalar and isovector dark matter-nucleon effective interactions, including several operators previously considered for dark matter direct detection only. We study in detail the dependence of the capture rate on specific dark matter-nucleon interaction operators, and on the different elements in the Sun. We find that a so far neglected momentum dependent dark matter coupling to the nuclear vector charge gives a larger contribution to the capture rate than the constant spin-dependent interaction commonly included in dark matter searches at neutrino telescopes. Our investigation lays the foundations for model independent analyses of dark matter induced neutrino signals from the Sun. The nuclear response functions obtained in this study are listed in analytic form in an appendix, ready to be used in other projects.

A review of the discovery reach of directional Dark Matter detection

“…Refs. [162,163]. NR operators which are typically studied lead to nuclear response functions proportional to (v ⊥ ) 0 (which is the standard case) or proportional to (v ⊥ )…”

Ab initio nuclear response functions for dark matter searches

“…In the simplest treatment, only spin-independent interactions are considered and phenomenological nuclear response functions-so-called "Helm form factors"-are used. More recently, many additional responses have been considered and more sophisticated nuclear-structure calculations have been performed using the shell model (SM) [11][12][13][22][23][24][25]. The SM is arguably a very successful phenomenological model for nuclear structure; see e.g.…”

Aspects of WIMP Dark Matter Searches at Colliders and Other Probes

“…(9.14) and Table 9.2, for a generic angle θ the DM-nucleon scattering is mediated by a linear combination of O 4 , O 8 and O 9 , with coefficients similar in magnitude. The contributions from O 8 and O 9 can be safely ignored for IceCube: given the composition of the solar environment, their nuclear form factors are between 100 and 1000 times smaller than the one for O 4 [518]. This is not the case for DD experiments, where the three operators give a similar contribution, and the scattering cross section is not exactly σ SD χp , which is defined as being given by the operator O 4 alone.…”

“…[518], the bounds on Γ ann can be interpreted as a bound on σ pχ for the operator O NR 6 = ( s χ · q)( s N · q). This operator originates in the non-relativistic limit in the case in which the DM is a Dirac fermion χ.…”