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Semileptonic $D$ Meson Decays $D\to P/V/S\ell^+ν_\ell$ with the SU(3) Flavor Symmetry/Breaking

Many exclusive $c\to d/s\ell^+ν_\ell~(\ell=e,μ,τ)$ transitions have been well measured, and they can be used to test the theoretical calculations. Motivated by this, we study the $D\to P/V/S\ell^+ν_\ell$ decays induced by the $c\to d/s\ell^+ν_\ell$ transitions with the SU(3) flavor symmetry approach, where $P$ denotes the pseudoscalar meson, $V$ denotes the vector meson, and $S$ denotes the scalar meson with a mass below $1$ $GeV$. The different decay amplitudes of the $D\to P\ell^+ν_\ell$, $D\to V\ell^+ν_\ell$ or $D\to S\ell^+ν_\ell$ decays can be related by using the SU(3) flavor symmetry and by considering the SU(3) flavor breaking. Using the present data of $D\to P/V/S\ell^+ν_\ell$, we predict the not yet measured or not yet well measured processes in the $D\to P/V/S\ell^+ν_\ell$ decays. We find that the SU(3) flavor symmetry approach works well in the semileptonic $D \to P/V\ell^+ν_\ell$ decays. For the $D \to S\ell^+ν_\ell$ decays, only the decay $D^+_s\to f_0(980)e^+ν_e$ has been measured, the branching ratios of the $D^+_s\to f_0(980)e^+ν_e$ and $D\to S(S\to P_1P_2)\ell^+ν_\ell$ decays are used to constrain the nonperturbative parameters and then predict not yet measured $D \to S\ell^+ν_\ell$ decays, in addition, the two quark and the four quark scenarios for the light scalar mesons are analyzed. The SU(3) flavor symmetry predictions of the $D \to S\ell^+ν_\ell$ decays need to be further tested, and our predictions of the $D \to S\ell^+ν_\ell$ decays are useful for probing the structure of light scalar mesons. Our results in this work could be used to test the SU(3) flavor symmetry approach in the semileptonic $D$ decays by the future experiments at BESIII, LHCb and BelleII.