  We perform the first comprehensive analysis of the prospects for direct
detection of dark matter with future ton-scale detectors in the general
11-dimensional effective theory of isoscalar dark matter-nucleon interactions
mediated by a heavy spin-1 or spin-0 particle. The theory includes 8 momentum
and velocity dependent dark matter-nucleon interaction operators, besides the
familiar spin-independent and spin-dependent operators. From a variegated
sample of 27 benchmark points selected in the parameter space of the theory, we
simulate independent sets of synthetic data for ton-scale Germanium and Xenon
detectors. From the synthetic data, we then extract the marginal posterior
probability density functions and the profile likelihoods of the model
parameters. The associated Bayesian credible regions and frequentist confidence
intervals allow us to assess the prospects for direct detection of dark matter
at the 27 benchmark points. First, we analyze the data assuming the knowledge
of the correct dark matter nucleon-interaction type, as it is commonly done for
the familiar spin-independent and spin-dependent interactions. Then, we analyze
the simulations extracting the dark matter-nucleon interaction type from the
data directly, in contrast to standard analyses. This second approach requires
an extensive exploration of the full 11-dimensional parameter space of the dark
matter-nucleon effective theory. Interestingly, we identify 5 scenarios where
the dark matter mass and the dark matter-nucleon interaction type can be
reconstructed from the data simultaneously. We stress the importance of
extracting the dark matter nucleon-interaction type from the data directly,
discussing the main challenges found addressing this complex 11-dimensional
problem.
