Light scalar beyond the Higgs mixing limit

We explore the possibility that the interactions of a light scalar singlet, which mixes with the Standard Model~(SM) Higgs, also receive other UV contributions of comparable size. We focus, in particular, on the flavor aligned limit, where couplings of the light scalar to the SM are almost flavor diagonal, but not necessarily proportional to the Higgs Yukawa couplings. The phenomenology of such a general flavor aligned light scalar differs from both the Higgs-mixed scalar, as well as from a general axion-like particle. We explore this for light scalar masses below a few hundred MeV, such that they can be produced in kaon decays, and in decays of $\eta$ and $\eta'$ mesons, and the transitions described using chiral perturbation theory. We then derive constraints on the light scalar interactions, assuming that light scalar decays are either just into photons or are invisible. We also discuss several UV examples of such light scalar models: a two-Higgs doublet model extended by a light scalar, a light dilaton from the dark sector, and a SM extended by heavy vector-like quarks and a light scalar. For the latter we also performed matching onto low energy theory at one-loop.