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

TL;DR

This study provides evidence for the $ar ext{kappa}^0$ resonance in semileptonic $D^+$ decays, revealing its dominant contribution and supporting a tetraquark nature, contrasting with traditional quark-antiquark models.

Contribution

It is the first to extract the $ar ext{kappa}^0$ contribution in $D^+$ decays and compare its form factor with theoretical models, supporting a tetraquark interpretation.

Findings

$ar ext{kappa}^0$ dominates the s-wave decay component.

The measured form factor aligns with tetraquark predictions.

Evidence suggests the $ ext{kappa}$ is a compact tetraquark rather than a quark-antiquark state.

Abstract

The $\kappa/K_0^*(700)$ 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 $\kappa$ remains difficult to explore. Through a partial-wave analysis of the semileptonic decay $D^+ \to K^-\pi^+ e^+ \nu_e$, we extract ${\cal B}(D^+ \to \bar\kappa^0 e^+ \nu_e, \bar\kappa^0 \to K^-\pi^+) =(2.2 \pm 0.1) \times 10^{-3}$. Previously considered negligible, this contribution is now shown to dominate the observed s-wave branching fraction. This reveals that clear evidence for the $\kappa$ in weak decays has long existed, but was misidentified as part of the non-resonant background. The extracted $D^+ \to \bar\kappa^0$ 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 $\kappa$ meson.