Search for C = + charmonium and XYZ states in e ⁺ e ^- rarr;gamma; + H at BESIII

Within the framework of nonrelativistic quantum chromodynamics, we study the production of C = + charmonium states H in e ⁺ e ^- rarr; gamma; + H at BESIII with H = eta;_c(nS) (n = 1, 2, 3, and 4), chi; _cJ (nP) (n = 1, 2, and 3), and ¹ D ₂(nD) (n = 1 and 2). The radiative and relativistic corrections are calculated to next-to-leading order for S and P wave states. We then argue that the search for C = + XYZ states such as X(3872), X(3940), X(4160), and X(4350) in e ⁺ e ^- rarr; gamma; + H at BESIII may help clarify the nature of these states. BESIII can search for XY Z states through two body process e ⁺ e ^- rarr; gamma;H, where H decay to J/psi;pi;⁺pi;^-, J/psi;phgr;, or D D. This result may be useful in identifying the nature of C = + XYZ states. For completeness, the production of C = + charmonium in e ⁺ e ^- rarr; gamma; + H at B factories is also discussed.