Constraining ALP-Meson overlaps from $Kπ$ form factors

Abstract

We present the first constraints on the overlaps between an Axion-like particle (ALP) and the $π^0$ and $η$ mesons from the analysis of the distortions to the $\langle K|\overline{s}γ^μu | π\rangle$ form factors. We demonstrate that these distortions can be tightly constrained by combining data from $τ^-\to π^0 K^-ν$ and $K^+\to π^0\ell^+ν$ decays, and go on to map the constraints to the ALP-meson overlaps. We establish that, in general, the ALP-meson and meson-ALP overlaps are different due to the presence of ALP-quark derivative couplings in the UV Lagrangian, and need to be treated separately. Using lattice results and BaBar, Belle, and NA48/2 data, we obtain exclusion limits on the overlaps and give projections for Belle II. Our techniques are independent of the branching ratios of the ALP, hence, robust against ALP decay channel assumptions. For masses of the ALP below 1 GeV, the bounds on the effective scale of the ALP physics extend to $\mathcal{O}$(TeV) for restricted regions of the parameter space for the ALP-$π$ and $π$-ALP overlaps. On the other hand, these bounds persist for extended regions of the parameter space for ALP-$η$ and $η$-ALP overlaps.

Figures (2)

• Figure 1: Constraints on form factor modifications $\xi^2\alpha$ and $\xi^2\beta$ is shown in the left plot. The shaded red regions show constraint at $68\%$ and $95\%$ C.L. from $\tau^-\to K^-\pi^0\nu$ differential distribution and total decay width measurement. The blue contours shows the combined constraint after including data from $K^+\to\pi^0\ell^+\nu_\ell (K_{\ell 3})$ differential rate and width measurement. The right plot shows the projection for Belle (green) and Belle-II (magenta) measurement of the same $\tau^-\to K^-\pi^0\nu_\tau$ channel.
• Figure 2: Constraints on the overlaps between the ALP and the $\pi^0$ and $\eta$ mesons. We have the $\pi$-$a$ overlap (top left), the $a$-$\pi$ overlap (top right), the $\eta$-$a$ overlap (bottom left) and the $a$-$\eta$ overlap (bottom right). The green regions indicate the parameter space that we can rule out from BaBar data, the black dashed boundaries indicate the regions we estimate would be ruled out from a Belle analysis, and the blue shaded regions indicate the areas that we project to be accessible by Belle II. In solid black, we have the regions in the mass-overlap plane that are not accessible by perturbative values of the Wilson coefficients. We have grayed out narrow regions around the neutral meson masses ($\pi^0$, $K^0$, $\eta$, $\eta^\prime$), at which the overlaps blow up. We have also indicated by the solid black boundary, existing bounds on $a$-$\pi^0$ mixing from the PiENU and PiBETA experiments Altmannshofer:2019yji.