Abstract
In this work, we analyze the semi-leptonic decays bar{B}^0/D^0 rightarrow (a_0(980)^{pm }rightarrow pi ^{pm }eta ) l^{mp } nu within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the B meson and the only available two-body LCDA of the D meson are used. To include the finite-width effect of the a_0(980), we use a scalar form factor to describe the final-state interaction between the pi eta mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the D^0 decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the {bar{B}}^0 decay can be tested in future experiments.
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