The low-energy constant $L_{10}$ in a two-representation lattice theory.

We calculate the low-energy constant $L_{10}$ in a two-representation SU(4) lattice gauge theory that is close to a composite-Higgs model. From this we obtain the contribution of the new strong sector to the $S$ parameter. This leads to an upper bound on the vacuum misalignment parameter $\xi$ which is similar to current estimates of this bound. Our result agrees with large-$N_c$ scaling expectations, within large systematic uncertainties.