P -wave coupled channel effects in electron-positron annihilation

P-wave coupled channel effects arising from the D¯D, D¯D∗+c.c., and D∗¯D∗ thresholds in e+e− annihilations are systematically studied. We provide an exploratory study by solving the Lippmann-Schwinger equation with short-ranged contact potentials obtained in the heavy quark limit. These contact potentials can be extracted from the P-wave interactions in the e+e− annihilations, and then be employed to investigate possible isosinglet P-wave hadronic molecules. In particular, such an investigation may provide information about exotic candidates with quantum numbers JPC=1−+. In the mass region of the D¯D, D¯D∗+c.c., and D∗¯D∗ thresholds, there are two quark model bare states, i.e. the ψ(3770) and ψ(4040), which are assigned as (13D1) and (31S1) states, respectively. By an overall fit of the cross sections of e+e−→D¯D, D¯D∗+c.c., D∗¯D∗, we determine the physical coupling constants to each channel and extract the pole positions of the ψ(3770) and ψ(4040). The deviation of the ratios from that in the heavy quark spin symmetry (HQSS) limit reflects the HQSS breaking effect due to the mass splitting between the D and the D∗. Besides the two poles, we also find a pole a few MeV above the D¯D∗+c.c. threshold which can be related to the so-called G(3900) observed earlier by BABAR and Belle. This scenario can be further scrutinized by measuring the angular distribution in the D∗¯D∗ channel with high luminosity experiments