Testing the light scalar meson as a non-$q\bar q$ state in semileptonic $D$ decays

Abstract

While the light scalar mesons ($S_0$) are considered to be either ordinary $q\bar q$ or exotic tetraquark states, we investigate the semileptonic decays $D\to S_0 e^+\nu_e$, by taking into account the resonant effects of $S_0\to M_1 M_2$, where $S_0=a_0(980)$, $f_0(980)$, and $f_0(500)/\sigma_0$, and $M_{1(2)}$ represents a pseudoscalar meson. For the first time, the $D\to S_0$ form factors in the two quark structures are both presented. Subsequently, we calculate ${\cal B}(D_s^+\to \sigma_0 e^+\nu_e,\sigma_0\to\pi^+\pi^-)=(20.3\pm 1.8\pm 0.5)\times 10^{-4}$ in the $q\bar q$ structure, showing significant $9\sigma$ deviations from the experimental upper limit of $3.3\times 10^{-4}$. In contrast, ${\cal B}(D_s^+\to \sigma_0 e^+\nu_e,\sigma_0\to\pi^+\pi^-)=(0.58^{+1.43}_{-0.57}\pm 0.01)\times 10^{-4}$ in the $q^2\bar q^2$ structure is within the allowed experimental range. Clearly, the light scalar meson is tested as a non-$q\bar q$ state. We hence demonstrate a highly sensitive new approach for exploring the true nature of scalar mesons, which can be extended to non-leptonic $D$ decays as well as $B$ meson decays.