Measurement of Born cross sections of e^+e^-⁰⁰ and search for charmonium (-like) states at s = 3. 51-4. 95 GeV

Using e^+e^- collision data collected by the BESIII detector at BEPCII corresponding to an integrated luminosity of 30 fb^-1, we measure Born cross sections and effective form factors for the process e^+e^-⁰⁰ at forty-five center-of-mass energies between 3. 51 and 4. 95 GeV. The dressed cross section is fitted, assuming a power-law function plus a charmonium (-like) state, i. e. , (3770), (4040), (4160), (4230), (4360), (4415) or (4660). No significant charmonium (-like) state decaying into ⁰⁰ is observed. Upper limits at the 90% confidence level on the product of the branching fraction and the electronic partial width are provided for each decay. In addition, ratios of the Born cross sections and the effective form factors for e^+e^-⁰⁰ and e^+e^-^-^+ are also presented to test isospin symmetry and the vector meson dominance model.