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We present the spectrum of baryons in a new SU(4) gauge theory withfundamental fermion constituents. The spectrum of these bosonic baryons is ofsignificant interest for composite dark matter theories. Here, we compare thespectrum and properties of SU(3) and SU(4) baryons, and then compute thedark-matter direct detection cross section via Higgs boson exchange forTeV-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 ofthe constituent-fermion mass that may arise from electroweak symmetry breaking.Lattice calculations of the dark matter mass spectrum and the Higgs-dark mattercoupling are performed on quenched $16^{3} \times 32$, $32^{3} \times 64$,$48^{3} \times 96$, and $64^{3} \times128$ lattices with three differentlattice spacings, using Wilson fermions with moderate to heavy pseudoscalarmeson masses. Our results lay a foundation for future analytic and numericalstudy of composite baryonic dark matter.

Composite bosonic baryon dark matter on the lattice: SU(4) baryon spectrum and the effective Higgs interaction