K→ππe^+e^- Decays and Chiral low-energy Constants

In this paper the branching ratios of the measured decay K_L→π^+π^-e^+e^- and of the still unmeasured decay K^+→π^+π^0e^+e^- are calculated to next-to-leading order in Chiral Perturbation Theory (CHPT). Recent experimental results are used to determine two possible values of the combination (N_16^r - N_17) of weak low-energy couplings (LEC) from the O(p^4) chiral Lagrangian. Furthermore, the obtained values are compared to theoretical models of weak counter-term couplings to distinguish between the two possibilities. Using the favoured value of the combination (N_16^r - N_17) and taking into account additional assumptions suggested by these models, one can predict the branching ratio of the second decay as a function of the numerically unknown combination (N_14^r+ 2N_15^r) of weak low-energy couplings. Finally, making use of a particular model for the individual LECs, one predicts the decay width of the K^+ decay in question.