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Using 6.32 fb$^{-1}$ of electron-positron collision data recorded by the BESIII detector at center-of-mass energies between 4.178 and 4.226~GeV, we present the first search for the decay $D_s^+to a_0(980)^0 e^+ u_e,,a_0(980)^0rightarrow pi^0eta$, which could proceed via $a_0(980)$-$f_0(980)$ mixing. No significant signal is observed. An upper limit of $1.2 times 10^{-4}$ at the $90%$ confidence level is set on the product of the branching fractions of $D_{s}^{+}to a_0(980)^0 e^+ u_e$ and $a_0(980)^0rightarrow pi^0eta$ decays.
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Using an $e^+e^-$ collision data sample of 2.93 fb$^{-1}$ collected at a center-of-mass energy of 3.773 GeV by the BESIII detector at BEPCII, we report the observation of $D^0 to a_0(980)^- e^+ u_e$ and evidence for $D^+ to a_0(980)^0 e^+ u_e~$ with significances of $6.4sigma$ and $2.9sigma$, respectively. The absolute branching fractions are determined to be $mathcal{B}(D^0 to a_0(980)^- e^+ u_e)timesmathcal{B}(a_0(980)^- to eta pi^-) = (1.33_{-0.29}^{+0.33}({rm stat})pm0.09({rm syst}))times10^{-4}~$ and $mathcal{B}(D^+ to a_0(980)^0 e^+ u_e)timesmathcal{B}(a_0(980)^0 to eta pi^0) = (1.66_{-0.66}^{+0.81}({rm stat})pm0.11({rm syst}))times10^{-4}~$. An upper limit of $mathcal{B}(D^+ to a_0(980)^0 e^+ u_e)timesmathcal{B}(a_0(980)^0 to eta pi^0)<3.0times10^{-4}~$ is also determined at the $90%~$ confidence level.
A search for the rare radiative leptonic decay $D_s^+togamma e^+ u_e$ is performed for the first time using electron-positron collision data corresponding to an integrated luminosity of 3.19 fb$^{-1}$, collected with the BESIII detector at a center-of-mass energy of 4.178 GeV. No evidence for the $D_s^+togamma e^+ u_e$ decay is seen and an upper limit of $mathcal B(D_s^+togamma e^+ u_e)<1.3times 10^{-4}$ is set on the partial branching fraction at a 90% confidence level for radiative photon energies $E_{gamma}^*>0.01$~GeV.
Using 2.93~fb$^{-1}$ of data taken at 3.773 GeV with the BESIII detector operated at the BEPCII collider, we study the semileptonic decays $D^+ to bar K^0e^+ u_e$ and $D^+ to pi^0 e^+ u_e$. We measure the absolute decay branching fractions $mathcal B(D^+ to bar K^0e^+ u_e)=(8.60pm0.06pm 0.15)times10^{-2}$ and $mathcal B(D^+ to pi^0e^+ u_e)=(3.63pm0.08pm0.05)times10^{-3}$, where the first uncertainties are statistical and the second systematic. We also measure the differential decay rates and study the form factors of these two decays. With the values of $|V_{cs}|$ and $|V_{cd}|$ from Particle Data Group fits assuming CKM unitarity, we obtain the values of the form factors at $q^2=0$, $f^K_+(0) = 0.725pm0.004pm 0.012$ and $f^{pi}_+(0) = 0.622pm0.012pm 0.003$. Taking input from recent lattice QCD calculations of these form factors, we determine values of the CKM matrix elements $|V_{cs}|=0.944 pm 0.005 pm 0.015 pm 0.024$ and $|V_{cd}|=0.210 pm 0.004 pm 0.001 pm 0.009$, where the third uncertainties are theoretical.
In this work, we have investigated the process $D_s^+to K^+ K^- pi^+$, taking into account the contributions from the $S$-wave pseudoscalar-pseudoscalar interaction within the chiral unitary approach, and also the intermediate $phi$ resonance. By analyzing the BESIII and {it BABAR} measurements, we conclude that the $f_0(980)$ state, dynamically generated from the $S$-wave pseudoscalar-pseudoscalar interaction, gives the dominant contribution close to the $K^+K^-$ threshold in the $K^+K^-$ invariant mass distribution of the decay $D_s^+to K^+ K^- pi^+$ in $S$-wave. On the other hand, our results imply that the lineshape adopted by BESIII and {it BABAR} for the resonances $a_0(980)$ and $f_0(980)$ is not advisable in the fit to the data close to the $K^+K^-$ threshold.
From the amplitude analysis of the $D^+_s to pi^+ pi^0 eta$ decay, the BESIII Collaboration firstly observed the $D^+_s to a_0(980)^+pi^0$ and $D^+_s to a_0(980)^0pi^+$ decay modes, which are expected to occur through the pure $W$-annihilation processes. The measured branching fraction $mathcal{B}[D_{s}^{+}to a_{0}(980)^{+(0)}pi^{0(+)},a_{0}(980)^{+(0)}to pi^{+(0)}eta]$ is, however, found to be larger than those of known $W$-annihilation decays by one order of magnitude. This apparent contradiction can be reconciled if the two decays are induced by internal $W$-conversion or external $W$-emission mechanisms instead of $W$-annihilation mechanism. In this work, we propose that the $D^+_s$ decay proceeds via both the external and internal $W$-emission instead of $W$-annihilation mechanisms. In such a scenario, we perform a study of the $D^+_s to pi^+pi^0eta$ decay by taking into account the contributions from the tree diagram $D^+_s to rho^+ eta to pi^+ pi^0 eta$ and the intermediate $rho^+ eta$ and $K^*bar{K}/Kbar{K}^*$ triangle diagrams. The intermediate $a_0(980)$ state can be dynamically generated from the final state interactions of coupled $K bar{K}$ and $pi eta$ channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of $a_0(980)$ as a molecular state.
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