Observation of di-structures in $e^{+}{e}^{-}\to J\mathrm{/}\psi \mathrm{X}$ at center-of-mass energies around 3.773 GeV

We report a measurement of the observed cross sections of the inclusive $J\mathrm{/}\psi$ production in $e^{+}{e}^{-}\to J\mathrm{/}\psi \mathrm{X}$ based on 3.21 fb${}^{-1}$ of data accumulated at energies from 3.645 to 3.891 GeV with the BESIII detector operated at the BEPCII collider. The energy-dependent lineshape obtained from the measured cross sections cannot be well described by two Breit-Wigner (BW) amplitudes of the expected decays $\psi(3686)\rightarrow {J}/\psi{\rm X}$and$\psi(3770)\rightarrow {J}/\psi{\rm X}$. Instead it can be better described with three BW amplitudes of the decays $\psi(3686)\rightarrow {J}/\psi{\rm X}$,$R(3760)\rightarrow {J}/\psi{\rm X}$and$R(3790)\rightarrow {J}/\psi{\rm X}$withtwodistinctstructuresreferredtoas$R(3760)$and$R(3790)$. Under this assumption, we extracted their masses, total widths, and the product of the leptonic width and decay branching fractions to be $M_{R(3760)}=3761.7\pm 2.2\pm 1.2$ MeV/$c^2$, $\Gamma^{\rm tot}{R(3760)}= {6.7\pm 11.1 \pm 1.1}$MeV,$\Gamma^{ee}{R(3760)}\mathcal B[R(3760)\rightarrow {J}/\psi {\rm X}]=(4.0\pm 4.3\pm 1.2)$eV,$M_{R(3790)} = {3784.7\pm 5.7 \pm 1.6}$MeV\mathrm{/}$c^2$,$\Gamma^{\rm tot}{R(3790)} = {31.6 \pm 11.9 \pm 3.2}$MeV,$\Gamma^{ee}{R(3790)}\mathcal B[R(3790)\rightarrow {J}/\psi {\rm X}]=(18.1\pm 10.3\pm 4.7)$ eV, where the first uncertainties are statistical and second systematic.