Meson Mass Decomposition

TL;DR

This paper decomposes meson masses into QCD components using lattice QCD, revealing the contributions of quark mass, energy, and glue energy for light and heavy mesons, and confirming theoretical expectations.

Contribution

First lattice QCD calculation of meson mass components based on hadronic matrix elements, providing detailed insights into mass contributions across different meson types.

Findings

Quark mass contributes ~50% to pion mass and less to rho mass.

Glue components contribute ~40-50% to both mesons.

Quark energy dominates charmonium hyperfine splitting.

Abstract

Hadron masses can be decomposed as a sum of components which 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 of 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 $\sim 50\%$ of the light pion mass comes from the quark mass and $\sim 10\%$ comes from the quark energy, whereas, the contributions are found to be the other way around for the $\rho$ mass. The combined glue components contribute $\sim 40 - 50\%$ 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 $400\sim500$ MeV 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 quark potential model.