Breaking the Grossman-Nir Bound in Kaon Decays

Understand

The ratio $\mathcal{B}(K_L\to\pi^0\nu\bar\nu)/\mathcal{B}(K^+\to\pi^+\nu\bar\nu)$ of the branching fractions of kaon decays $K_L\to\pi^0\nu\bar\nu$ and $K^+\to\pi^+\nu\bar\nu$ has a maximum of about 4.3 under the assumption that the underlying interactions change isospin by $\Delta I=1/2$.

• This is referred to as the Grossman-Nir (GN) bound, which is respected by the standard model (SM) and by many scenarios beyond it.
• Recent preliminary results of the KOTO and NA62 Collaborations searching for these kaon modes seem to imply a violation of this bound.
• The KOTO findings also suggest that $\mathcal{B}(K_L\to\pi^0\nu\bar\nu)$ could be much larger, by nearly two orders of magnitude, than that predicted in the SM.