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

TL;DR

This paper uses SU(3) flavor symmetry to analyze and predict semileptonic $D$ meson decays into pseudoscalar, vector, and scalar mesons, testing the symmetry's validity and exploring light scalar meson structures.

Contribution

It applies SU(3) flavor symmetry and breaking to relate decay amplitudes and predict unmeasured $D$ decay processes, including scalar meson decays, with implications for meson structure.

Findings

SU(3) symmetry describes $D o P/V$ decays well

Predictions for unmeasured $D o S$ decays are provided

Scalar meson structure scenarios are analyzed

Abstract

Many exclusive $c\to d/s\ell^+\nu_\ell~(\ell=e,\mu,\tau)$ transitions have been well measured, and they can be used to test the theoretical calculations. Motivated by this, we study the $D\to P/V/S\ell^+\nu_\ell$ decays induced by the $c\to d/s\ell^+\nu_\ell$ 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 $D\to P\ell^+\nu_\ell$, $D\to V\ell^+\nu_\ell$ or $D\to S\ell^+\nu_\ell$ decays can be related by using the SU(3) flavor symmetry and by considering the SU(3) flavor breaking. Using the present data of $D\to P/V/S\ell^+\nu_\ell$, we predict the not yet measured or not yet well measured processes in the $D\to P/V/S\ell^+\nu_\ell$ decays. We find that the SU(3) flavor symmetry approach works well in the semileptonic $D \to P/V\ell^+\nu_\ell$ decays. For the $D \to S\ell^+\nu_\ell$ decays, only the decay $D^+_s\to f_0(980)e^+\nu_e$ has been measured, the branching ratios of the $D^+_s\to f_0(980)e^+\nu_e$ and $D\to S(S\to P_1P_2)\ell^+\nu_\ell$ decays are used to constrain the nonperturbative parameters and then predict not yet measured $D \to S\ell^+\nu_\ell$ 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 $D \to S\ell^+\nu_\ell$ decays need to be further tested, and our predictions of the $D \to S\ell^+\nu_\ell$ 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.