Implication of $K\to \pi \nu \bar{\nu }$ for generic neutrino interactions in effective field theories

Abstract

In this work we investigate the implication of $K\to \pi \nu \bar{\nu }$ from the recent KOTO and NA62 measurements for generic neutrino interactions and the new physics scale in effective field theories. The interactions between quarks and left-handed Standard Model (SM) neutrinos are first described by the low energy effective field theory (LEFT) below the electroweak scale. We match them to the chiral perturbation theory ($\chi$PT) at the chiral symmetry breaking scale to calculate the branching fractions of Kaon semi-invisible decays and match them up to the SM effective field theory (SMEFT) to constrain new physics above the electroweak scale. In the framework of effective field theories, we prove that the Grossman-Nir bound is valid for both dim-6 and dim-7 LEFT operators, and the dim-6 vector and scalar operators dominantly contribute to Kaon semi-invisible decays based on LEFT and chiral power counting rules. They are induced by multiple dim-6 lepton-number-conserving operators and one dim-7 lepton-number-violating operator in the SMEFT, respectively. In the lepton-number-conserving $s\to d$ transition, the $K\to \pi \nu \bar{\nu }$ decays provide the most sensitive probe for the operators with $\tau \tau$ component and point to a corresponding new physics scale of ${\Lambda }_{\mathrm{NP}}\in [47\text{TeV},72\text{TeV}]$ associated with a single effective coefficient. The lepton-number-violating operator can also explain the observed $K\to \pi \nu \bar{\nu }$ discrepancy with the SM prediction within a narrow range ${\Lambda }_{\mathrm{NP}}\in [19.4\text{TeV},21.5\text{TeV}]$, which is consistent with constraints from Kaon invisible decays.

arXiv comment26 pages, 3 figures, version published in PRD

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• General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays
• When Energy Goes Missing: New Physics in $b\to s\nu \nu$ with Sterile Neutrinos
• Light gauge boson interpretation for $(g-2{)}_{\mu }$ and the $K_L\to {\pi }^0+\text{(invisible)}$ anomaly at the J-PARC KOTO experiment
• Looking forward to test the KOTO anomaly with FASER
• Exploring SMEFT Induced Non-Standard Interactions from COHERENT to Neutrino Oscillations
• Pair production of dark particles in meson decays
• Three Exceptions to the Grossman-Nir Bound
• Imprint of a new light particle at KOTO?
• Nonperturbative effects in neutrino magnetic moments
• New Physics Searches at Kaon and Hyperon Factories
• Kaon physics overview
• A Tale of Invisibility: Constraints on New Physics in $b\to s\nu \nu$