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

Abstract

The $\kappa /K_0^{\ast }(700)$ 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 $\mathcal{B}(D^{+}\to {\bar{\kappa }}^0{e}^{+}{\nu }_e,{\bar{\kappa }}^0\to K^{-}{\pi }^{+})=(2.2\pm 0.1)\times 10^{-3}$. 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.

Comments: 10 pages, 1 table