Flavor physics with generalized ALP-quark couplings

A light axionlike particle or an (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 processes that involve standard model (SM) fields only (i.e., SM processes). These effects result the violation Gell-Mann-Okubo mass relation, modified form factors, altered integrated differential rates for various transitions etc. This suggests presence a low lying state, such ALP, extraction masses, mixing angles, factors entirely data-driven way from meson-physics observables is highly nontrivial exercise. However, once done correctly, these same may, turn, provide important (indirect) bounds on ALP physics, which remain robust even limits where conspire weaken direct searches. Starting with generalized ALP-quark Lagrangian (where restrictions due parity are removed) we demonstrate this approach by focusing ${K}_{{\ensuremath{\ell}}_{3}}^{+}$ derive using $\mathrm{NA}48/2$ data lattice results. We also find sum rules show deviations but give hints towards specific nature itself.