Breaking the Grossman-Nir bound in kaon decays

Xiao Gang He, Xiao Dong Ma, Jusak Tandean, German Valencia

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16 Citations (Scopus)


The ratio ℬ(KL→π0vv¯)/ℬ(K+→π+vv¯) of the branching fractions of kaon decays KL→ πvv¯ and K+→ π+vv¯ has a maximum of about 4.3 under the assumption that the underlying interactions change isospin by ∆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 ℬ (KL→ πvv¯) could be much larger, by nearly two orders of magnitude, than that predicted in the SM. In this work we study the possibility of violating the GN bound in an effective field theory approach with only SM fields. We show that the bound holds, in addition to the original GN scenarios, whether or not the kaon decays conserve lepton number. We demonstrate that the inclusion of ∆I = 3/2 operators can lead to a violation of the GN bound and illustrate with an example of how the KOTO numbers may be reached with a new physics scale of order tens of GeV.

Original languageEnglish
Article number57
Number of pages15
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - 1 Apr 2020


  • Beyond Standard Model
  • CP violation
  • Kaon Physics
  • Neutrino Physics

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