  We present the spectrum of baryons in a new SU(4) gauge theory with
fundamental fermion constituents. The spectrum of these bosonic baryons is of
significant interest for composite dark matter theories. Here, we compare the
spectrum and properties of SU(3) and SU(4) baryons, and then compute the
dark-matter direct detection cross section via Higgs boson exchange for
TeV-scale composite dark matter arising from a confining SU(4) gauge sector.
Comparison with the latest LUX results leads to tight bounds on the fraction of
the constituent-fermion mass that may arise from electroweak symmetry breaking.
Lattice calculations of the dark matter mass spectrum and the Higgs-dark matter
coupling are performed on quenched $16^{3} \times 32$, $32^{3} \times 64$,
$48^{3} \times 96$, and $64^{3} \times128$ lattices with three different
lattice spacings, using Wilson fermions with moderate to heavy pseudoscalar
meson masses. Our results lay a foundation for future analytic and numerical
study of composite baryonic dark matter.
