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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.
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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.
Using $e^+e^-$ annihilation data corresponding to an integrated luminosity of 3.19,fb$^{-1}$ collected at a center-of-mass energy of 4.178~GeV with the BESIII detector, we measure the absolute branching fractions $mathcal{B}_{D_s^+ rightarrow eta e^{+} u_e }$ = $(2.323pm0.063_{rm stat}pm0.063_{rm syst})%$ and $mathcal{B}_{D_s^+ rightarrow eta^{prime} e^{+} u_e}$ = $(0.824pm0.073_{rm stat}pm0.027_{rm syst})%$ via a tagged analysis technique, where one $D_s$ is fully reconstructed in a hadronic mode. Combining these measurements with previous BESIII measurements of $mathcal{B}_{D^+toeta^{(prime)} e^{+} u_e}$, the $eta-eta^prime$ mixing angle in the quark flavour basis is determined to be $phi_{rm P} = (40.1pm2.1_{rm stat}pm0.7_{rm syst})^circ$. From the first measurements of the dynamics of $D^+_sto eta^{(prime)}e^+ u_e$ decays, the products of the hadronic form factors $f_+^{eta^{(prime)}}(0)$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ are determined with different form factor parameterizations. For the two-parameter series expansion, the results are $f^{eta}_+(0)|V_{cs}| = 0.4455pm0.0053_{rm stat}pm0.0044_{rm syst}$ and $f^{eta^{prime}}_+(0)|V_{cs}| = 0.477pm0.049_{rm stat}pm0.011_{rm syst}$.
We search for the rare decay $D^+to D^0 e^+ u_{e}$, using a data set with an integrated luminosity of 2.93 $rm fb^{-1}$ collected at $sqrt{s}=3.773$ GeV with the BESIII detector operating at the BEPCII storage rings. No signals are observed. We set the upper limit on the branching fraction for $D^+to D^0 e^+ u_e$ to be $1.0times 10^{-4}$ at the 90% confidence level.
Using $2.93~mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy $sqrt{s}=3.773$ GeV with the BESIII detector operating at the BEPCII collider, we search for the semileptonic $D^{0(+)}$ decays into a $b_1(1235)^{-(0)}$ axial-vector meson for the first time. No significant signal is observed for either charge combination. The upper limits on the product branching fractions are ${mathcal B}_{D^0to b_1(1235)^- e^+ u_e}cdot {mathcal B}_{b_1(1235)^-to omegapi^-}<1.12times 10^{-4}$ and ${mathcal B}_{D^+to b_1(1235)^0 e^+ u_e}cdot {mathcal B}_{b_1(1235)^0to omegapi^0}<1.75times 10^{-4}$ at the 90% confidence level.
A sensitivity of the VEPP-2000 $e^+e^-$ collider in a search for the rare decay $eta rightarrow e^+ e^-$ has been studied. The inverse reaction $e^+ e^- rightarrow eta$ is proposed for this search. We have analyzed a data sample with an integrated luminosity of 108 nb$^{-1}$ collected with the SND detector in the center-of-mass energy range 520-580 MeV and found no background events for the reaction $e^+ e^- rightarrow eta$ in the decay mode $etatopi^0pi^0pi^0$. In the absence of background, a sensitivity to ${cal B}(eta rightarrow e^+ e^-)$ of $10^{-6}$ can be reached during two weeks of VEPP-2000 operation. Such a sensitivity is better than the current upper limit on ${cal B}(eta rightarrow e^+ e^-)$ by a factor of 2.3.
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