  We show that QCD instantons can generate large effects at small length scales
in the ultraviolet in standard composite Higgs models that utilise partial
compositeness. This has important implications for possible solutions of the
strong CP problem in these models. First we show that in the simplest known UV
completions of composite Higgs models, if an axion is also present, it can have
a mass much larger than the usual QCD axion. Even more remarkable is the case
where there are no axions, but the strong CP problem can be solved by
generating the up quark mass entirely from the contribution of instantons thus
reviving the massless up-quark solution for these models. In both cases no
additional field content is required apart from what is required to realise
partial compositeness.

High Energy Physics - Phenomenology;High Energy Physics - Theory