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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 weobtain the contribution of the new strong sector to the $S$ parameter. Thisleads to an upper bound on the vacuum misalignment parameter $\xi$ which issimilar to current estimates of this bound. Our result agrees with large-$N_c$scaling expectations, within large systematic uncertainties.

Low-energy constant $L_{10}$ in a two-representation lattice theory