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 $\mathcal{B}(D_s^{+}\to {\sigma }_0{e}^{+}{\nu }_e,{\sigma }_0\to {\pi }^{+}{\pi }^{-})=(20.3\pm 1.8\pm 0.5)\times 10^{-4}$ in the $q\bar{q}$ structure, showing significant $9\sigma$ deviations from the experimental upper limit of $3.3\times 10^{-4}$. In contrast, $\mathcal{B}(D_s^{+}\to {\sigma }_0{e}^{+}{\nu }_e,{\sigma }_0\to {\pi }^{+}{\pi }^{-})=(0.58_{-0.57}^{+1.43}\pm 0.01)\times 10^{-4}$ 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.

Comments: 18 pages, 3 figures, 3 tables, matches published version in JHEP