Low-energy flavour probes of light vector bosons

In this work, we construct the chiral Lagrangian for a light spin-1 boson $X$ possessing both vectorial and axial couplings to the light Standard Model quarks $u,d,s$. We then use it in order to describe the tree-level, model-independent contributions to the $\mathrm{\Delta }S=1$ transition $K^{\pm }\to {\pi }^{\pm }X$, which is induced by Standard Model charged currents and is possibly enhanced by the emission of a longitudinally polarized $X$ boson. Such a flavour observable is then shown to set the best model-independent bounds on the diagonal axial couplings of $X$ to light quarks in the mass range allowed by the decay kinematics, improving the currently available constraints from beam-dump experiments and collider searches.