Closing in on the radiative weak chiral couplings

We point out that, given the current experimental status of radiative kaon decays, a subclass of the \(\mathcal{O} (p^4)\) counterterms of the weak chiral lagrangian can be determined in closed form. This involves in a decisive way the decay \(K^\pm \rightarrow \pi ^\pm \pi ^0 l^+ l^-\), currently being measured at CERN by the NA48/2 and NA62 collaborations. We show that consistency with other radiative kaon decay measurements leads to a rather clean prediction for the \(\mathcal{{O}}(p^4)\) weak couplings entering this decay mode. This results in a characteristic pattern for the interference Dalitz plot, susceptible to be tested already with the limited statistics available at NA48/2. We also provide the first analysis of \(K_S\rightarrow \pi ^+\pi ^-\gamma ^*\), which will be measured by LHCb and will help reduce (together with the related \(K_L\) decay) the experimental uncertainty on the radiative weak chiral couplings. A precise experimental determination of the \(\mathcal{{O}}(p^4)\) weak couplings is important in order to assess the validity of the existing theoretical models in a conclusive way. We briefly comment on the current theoretical situation and discuss the merits of the different theoretical approaches.