Form factors for dark matter capture by the Sun in effective theories
  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, i.e. H, $^{3}$He, $^{4}$He, $^{12}$C, $^{14}$N, $^{16}$O,
$^{20}$Ne, $^{23}$Na, $^{24}$Mg, $^{27}$Al, $^{28}$Si, $^{32}$S, $^{40}$Ar,
$^{40}$Ca, $^{56}$Fe, and $^{58}$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.
