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New bound on the vectorial axion-down-strange coupling from $K^+ \to π^+ ν\bar ν$ data

Diego Guadagnoli, Axel Iohner, Cristina Lazzeroni, Diego Martinez Santos, Joel C. Swallow, Claudio Toni

Abstract

We reinterpret publicly available $K^+ \to π^+ ν\barν$ data collected by NA62 from 2016 to 2024 to constrain the fundamental vectorial coupling of the QCD axion to down and strange quarks. Using a fully reproducible likelihood analysis and a complete renormalization-group evolution of the axion couplings from the Peccei-Quinn (PQ) scale to the kaon scale, we translate the experimental limit into bounds on both the low-energy flavour-violating coupling and the fundamental UV parameters. In the generic regime where strong contributions dominate the decay amplitude, we obtain $|(F_V)_{sd}(μ_K)| > 1.6 \times 10^{12}\,\text{GeV}$. The coexistence of parametrically suppressed weak contributions implies a second, conceptually distinct constraint: the fact that weak-amplitude dominance arises from highly tuned UV coupling configurations, translates into a conservative general lower limit on the PQ scale, $f_a > 4.9 \times 10^4\,\text{GeV}$. These results provide the strongest accelerator-based constraints on axion-induced $d \leftrightarrow s$ transitions and establish a robust lower bound on $f_a$, complementary to astrophysical limits.

New bound on the vectorial axion-down-strange coupling from $K^+ \to π^+ ν\bar ν$ data

Abstract

We reinterpret publicly available data collected by NA62 from 2016 to 2024 to constrain the fundamental vectorial coupling of the QCD axion to down and strange quarks. Using a fully reproducible likelihood analysis and a complete renormalization-group evolution of the axion couplings from the Peccei-Quinn (PQ) scale to the kaon scale, we translate the experimental limit into bounds on both the low-energy flavour-violating coupling and the fundamental UV parameters. In the generic regime where strong contributions dominate the decay amplitude, we obtain . The coexistence of parametrically suppressed weak contributions implies a second, conceptually distinct constraint: the fact that weak-amplitude dominance arises from highly tuned UV coupling configurations, translates into a conservative general lower limit on the PQ scale, . These results provide the strongest accelerator-based constraints on axion-induced transitions and establish a robust lower bound on , complementary to astrophysical limits.

Paper Structure

This paper contains 9 sections, 24 equations, 8 figures, 2 tables.

Table of Contents

  1. Validations of our reinterpretation procedure
  2. ChPT conventions and $K^+ \to \pi^+ a$ amplitudes
  3. Mass–coupling relation
  4. $f_a$ limit as a function of the UV couplings
  5. Linear form and hierarchy of coefficients
  6. Generic behaviour and geometric interpretation
  7. On specific configurations yielding weak-amplitude dominance
  8. Case (i): single-coupling dominance
  9. Case (ii): cancellations between one parameter and the sum of the rest

Figures (8)

  • Figure 1: (Left) Upper limit on ${\mathcal{B}}(K^+\to\pi^+a)$ from NA62 using the published 2016–2022 dataset NA62:2025upx, and the extended 2016–2024 sample including the new 2023–2024 data LaThuile_2026_update. The gray dashed line shows $\delta{\mathcal{B}}_{\nu \bar{\nu}}$. The range $[100,161]$ MeV is excluded due to $K^+\to\pi^+\pi^0$ background contamination NA62:2020xlgNA62:2024pjp. (Right) Corresponding lower bound on the flavour-violating-coupling rescaled Peccei–Quinn scale (see text for details).
  • Figure 2: Upper limit on ${\mathcal{B}}(K^+\to\pi^+a)$ from the 2017 NA62:2020xlg and 2016-18 NA62:2021zjw datasets. The solid red line is the published result of NA62 collaboration. The gray dashed line shows the corresponding value of $\delta{\mathcal{B}}_{\nu \bar{\nu}}$ for comparison.
  • Figure 3: QCD axion mass $m_a$ as a function of the effective flavor-violating coupling $(k_V)_{sd}$.
  • Figure 4: Distribution of $f_a$ bounds as defined in Eq. (\ref{['eq:faz']}), assuming $c_i \sim \mathrm{Unif}[-5,5]$: (left) scan of all UV couplings; (right) scan with UV flavour-violating couplings set to zero.
  • Figure 5: Empirical determinations of $P(|z| \leq 1)$ from Monte Carlo evaluations of $P(|z| \leq r_0)$, with $r_0$ values in the "intermediate" range $1 \ll r_0 \ll |z|_{\rm peak}$ corresponding to the onset of $r^2$ scaling. See text and Table \ref{['tab:small_ball']} for further details.
  • ...and 3 more figures