  We report the results of lattice numerical studies of the Sp(4) gauge theory
coupled to fermions (hyperquarks) transforming in the fundamental and two-index
antisymmetric representations of the gauge group. This strongly-coupled theory
is the minimal candidate for the ultraviolet completion of composite Higgs
models that facilitate the mechanism of partial compositeness for generating
the top-quark mass. We measure the spectrum of the low-lying, half-integer
spin, bound states composed of two fundamental and one antisymmetric
hyperquarks, dubbed chimera baryons, in the quenched approximation. In this
first systematic, non-perturbative study, we focus on the three lightest
parity-even chimera-baryon states, in analogy with QCD, denoted as
$\Lambda_{\rm CB}$, $\Sigma_{\rm CB}$ (both with spin 1/2), and $\Sigma_{\rm
CB}^\ast$(with spin 3/2). The spin-1/2 such states are candidates of the top
partners. The extrapolation of our results to the continuum and
massless-hyperquark limit is performed using formulae inspired by QCD
heavy-baryon Wilson chiral perturbation theory. Within the range of hyperquark
masses in our simulations, we find that $\Sigma_{\mathrm{CB}}$ is not heavier
than $\Lambda_{\mathrm{CB}}$.
