Annihilation diagram contribution to charmonium masses * *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030302), the National Key Research and Development Program of China (2020YFA0406400), and the National Natural Science Foundation of China (NSFC) (11935017, 11775229, 12075253, 12070131001) (CRC 110 by DFG and NNSFC)

Abstract

In this work, we generate gauge configurations with dynamical charm quarks on anisotropic lattices. The mass shift of and charmonia due to the charm quark annihilation effect can be investigated directly in a manner of unitary theory. The distillation method is adopted to treat the charm quark annihilation diagrams at a very precise level. For charmonia, the charm quark annihilation effect barely changes the mass, but lifts the mass by approximately 3–4 MeV. For charmonia, this effect results in positive mass shifts of approximately 1 MeV for and , but decreases the mass by approximately 3 MeV. We did not obtain a reliable result for the mass shift of . In addition, we observed that the spin averaged mass of the spin-triplet charmonia is in good agreement with , as expected by the non-relativistic quark model and measured by experiments.