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

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 $D\to S(S\to P_1{P}_2){\ell }^{+}{\nu }_{\ell }$ 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.

Comments: 23 pages, 4 figures