Probing the elusive $κ/K_0^*(700)$ resonance in semileptonic $D$ decays

Abstract

The $κ/K_0^*(700)$ meson remains the most elusive among the light scalar resonances, with its presence in weak decays obscured by limited precision in branching fraction measurements. As a result, the true nature of the $κ$ remains difficult to explore. Through a partial-wave analysis of the semileptonic decay $D^+ \to K^-π^+ e^+ ν_e$, we extract ${\cal B}(D^+ \to \barκ^0 e^+ ν_e, \barκ^0 \to K^-π^+) =(2.2 \pm 0.1) \times 10^{-3}$. Previously considered negligible, this contribution is now shown to dominate the observed s-wave branching fraction. This reveals that clear evidence for the $κ$ in weak decays has long existed, but was misidentified as part of the non-resonant background. The extracted $D^+ \to \barκ^0$ form factor, $f^+(0) = 0.32 \pm 0.01$, is significantly smaller than the $q\bar q$ prediction of $0.82 \pm 0.05$, and closely aligns with the $q^2\bar q^2$ expectation of $0.36 \pm 0.02$. Notably, this finding supports a compact tetraquark interpretation of the $κ$ meson.