XQC and CSR constraints on strongly interacting dark matter with spin and velocity dependent cross sections

Dark matter that interacts strongly with baryons can avoid the stringent dark matter direct detection constraints, because, like baryons, they are likely to be absorbed when traversing the rocks, leading to a suppressed flux in deep underground labs. Such strongly interacting dark matter, however, can be probed by dark matter experiments or other experiments operated on the ground level or in the atmosphere. In this paper we carry out systematic analysis of two of these experiments, XQC and CSR, to compute the experimental constraints on the strongly interacting dark matter in the following three scenarios: (1) spin-independent and spin-dependent interactions; (2) different velocity dependent cross sections; (3) different dark matter mass fractions. Some of the scenarios are first analyzed in the literature. We find that the XQC exclusion region has some non-trivial dependencies on the various parameters and the limits in the spin-dependent case is quite different from the spin-independent case. A peculiar region in the parameter space, where the XQC constraint disappears, is also found in our Monte Carlo simulations. This occurs in the case where the interaction cross section is proportional to the square of the velocity. We further compare our XQC and CSR limits to other experimental constraints, and find that a large parameter space is allowed by various experiments if the dark matter mass fraction is sufficiently small, $f_\chi\lesssim 10^{-4}$.