Flavor physics with generalized ALP-quark couplings

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A light axionlike particle or an axionlike particle (ALP) not just gives rise to interesting and spectacular signals of new physics as final states in meson decays, it necessarily leaves tell-tale signatures in processes that involve standard model (SM) fields only (i.e., SM processes). These effects result in the violation of the Gell-Mann-Okubo mass relation, modified form factors, altered integrated and differential rates for various SM transitions etc. This suggests that in the presence of a low lying state, such as an ALP, extraction of masses, mixing angles, and form factors in an entirely data-driven way from meson-physics observables is a highly nontrivial exercise. However, once done correctly, these same observables may, in turn, provide important (indirect) bounds on ALP physics, which remain robust even in the limits where new physics effects conspire to weaken the bounds from direct searches. Starting with a generalized ALP-quark Lagrangian (where restrictions due to parity are removed) we demonstrate this approach by focusing on ${K}_{{\ensuremath{\ell}}_{3}}^{+}$ decays, where we derive (indirect) bounds on ALP physics using $\mathrm{NA}48/2$ data and lattice results. We also find sum rules that not just show deviations in the presence of an ALP but also give hints towards the specific nature of the ALP physics itself.