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arXiv · 2110.01755

Annihilation diagram contribution to charmonium masses

Renqiang Zhang·Wei Sun·Feiyu Chen·Ying Chen·Ming Gong·Xiangyu Jiang·Zhaofeng Liu
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Abstract

In this work, we generate gauge configurations with $N_f=2$ dynamical charm quarks on anisotropic lattices. The mass shift of $1S$ and $1P$ charmonia owing 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 $1S$ charmonia, the charm quark annihilation effect almost does not change the $J/\psi$ mass, but lifts the $\eta_c$ mass by approximately 3-4 MeV. For $1P$ charmonia, this effect results in positive mass shifts of approximately 1 MeV for $\chi_{c1}$ and $h_c$, but decreases the $\chi_{c2}$ mass by approximately 3 MeV. We have not obtain a reliable result for the mass shift of $\chi_{c0}$. In addition, it is observed that the spin averaged mass of the spin-triplet $1P$ charmonia is in a good agreement with the $h_c$, as expected by the non-relativistic quark model and measured by experiments.

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Renqiang Zhang, Wei Sun, Feiyu Chen, Ying Chen, Ming Gong, Xiangyu Jiang, Zhaofeng Liu. 2021-10-05. Annihilation diagram contribution to charmonium masses. https://doi.org/10.1088/1674-1137%2Fac3d8c

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