What question did this study set out to answer?

This research aims to calculate the branching ratios of K_L and K^+ decays using Chiral Perturbation Theory.

March 5, 2026Open Access

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

Key Points

This research aims to calculate the branching ratios of K_L and K^+ decays using Chiral Perturbation Theory.
Calculated branching ratios for K_L→π^+π^-e^+e^- and K^+→π^+π^0e^+e^- decays.
Used recent experimental results to determine weak low-energy couplings from the chiral Lagrangian.
Compared obtained values to theoretical models to assess weak coupling distinctions.
Predicted branching ratio of K^+ decay based on weak low-energy coupling assumptions.
Identified two possible values for the weak low-energy coupling combination (N_16^r - N_17).
Provided predictions for the branching ratio of K^+ decay based on weak coupling models.
Derived decay width for K^+ decay using specific models for low-energy couplings.

Abstract

In this paper the branching ratios of the measured decay KL→π^+π^-e^+e^- and of the still unmeasured decay K^+→π^+π⁰e^+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 (N₁6ʳ - N₁7) of weak low-energy couplings (LEC) from the O (p⁴) 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 (N₁6ʳ - N₁7) 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 (N₁4ʳ+ 2N₁5ʳ) 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.

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