Breaking the Grossman-Nir Bound in Kaon Decays

Abstract

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. 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 $\Delta I=3/2$ 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.

arXiv comment15 pages, 2 figures, minor changes for typos

References in corpus (7)

• $K_L\to {\pi }^0\nu \bar{\nu }$ Beyond the Standard Model
• Constraints on scalar leptoquarks from lepton and kaon physics
• New physics implications of recent search for $K_L\to {\pi }^0\nu \bar{\nu }$ at KOTO
• The CP Conserving Contribution to $K_L\to {\pi }^0\nu \bar{\nu }$
• Long Distance Contribution to $K^{+}\to {\pi }^{+}\nu \bar{\nu }$
• Loophole in K --> pi nu nubar Search and New Weak Leptonic Forces
• Constraints on new physics from $K\to \pi \nu \bar{\nu }$

Cited by in corpus (11)

• Explaining $(g-2{)}_{\mu ,e}$, the KOTO anomaly and the MiniBooNE excess in an extended Higgs model with sterile neutrinos
• Study of the $K_L\to {\pi }^0\nu \overline{\nu }$ Decay at the J-PARC KOTO Experiment
• 2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
• Looking forward to test the KOTO anomaly with FASER
• Pair production of dark particles in meson decays
• Search for the $K_L\to {\pi }^0\nu \bar{\nu }$ Decay at the J-PARC KOTO Experiment
• Evading the Grossman-Nir bound with $\Delta I=3/2$ new physics
• Three Exceptions to the Grossman-Nir Bound
• Imprint of a new light particle at KOTO?
• Cosmological implications of the KOTO excess
• New Physics Searches at Kaon and Hyperon Factories