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

Abstract

We reinterpret publicly available $K^+ \to \pi^+ \nu \bar{\nu}$ 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 $|(F_V)_{sd}(\mu_K)| > 1.6 \times 10^{12}\,\text{GeV}$. 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.