Hadron masses can be decomposed as a sum of quark and glue components that are defined through hadronic matrix elements of QCD operators. The components consist of the quark mass term, the quark energy term, the glue energy term, and the trace anomaly term. We calculate these components for mesons with lattice QCD for the first time. The calculation is carried out with overlap fermion on 2+1 flavor domain-wall fermion gauge configurations. We confirm that ~50% of the light pion mass comes from the quark mass term and ~10% comes from the quark energy; whereas, for the ρ meson, the quark energy contributes roughly half of its mass but the quark mass term contributes little. The combined glue components contribute ~40–50% for both mesons. It is interesting to observe that the quark mass contribution to the mass of the vector meson is almost linear in quark mass over a large quark mass region below the charm quark mass. For heavy mesons, the quark mass term dominates the masses, while the contribution from the glue components is about 200 MeV (a bare value around 2 GeV) for the heavy pseudoscalar and vector mesons. The charmonium hyperfine splitting is found to be dominated by the quark energy term which is consistent with the picture of the quark potential model.

Document Type


Publication Date


Notes/Citation Information

Published in Physical Review D: Particles, Fields, Gravitation, and Cosmology, v. 91, no. 7, article 074516, p. 1-8.

©2015 American Physical Society

The copyright holder has granted permission for posting the article here.

This work is a result of the XQCD Collaboration.

Digital Object Identifier (DOI)


Funding Information

This work is supported in part by the National Science Foundation of China (NSFC) under Grants No. 11075167, No. 11105153, and No. 11335001, and also by the U.S. DOE Award No. DE-FG05-84ER40154. Y. C. and Z. L. also acknowledge the support of NSFC and Deutsche Forschungsgemeinschaft (DFG) through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD.” M. G. and Z. L. are partially supported by the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grants No. 2015013 and No. 2011013).

Fig 1.png (55 kB)
Figure 1

Fig 2.png (26 kB)
Figure 2

Fig 3.png (59 kB)
Figure 3

Fig 4.png (29 kB)
Figure 4

Fig 5.png (38 kB)
Figure 5

Fig 6.png (51 kB)
Figure 6

Fig 7.png (41 kB)
Figure 7

Fig 8.png (44 kB)
Figure 8

Fig 9.png (31 kB)
Figure 9

Fig 10.png (66 kB)
Figure 10

Fig 11.png (45 kB)
Figure 11

Fig 12.png (36 kB)
Figure 12