Lattice-QCD validation of hadron mass and trace-anomaly decomposition sum rules
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914263654727680 |
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| author | Bollweg, Dennis Ding, Heng-Tong Gao, Xiang Luo, Ran Mukherjee, Swagato |
| author_facet | Bollweg, Dennis Ding, Heng-Tong Gao, Xiang Luo, Ran Mukherjee, Swagato |
| contents | We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $η_c$ and $J/ψ$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lattice-QCD validation of hadron mass and trace-anomaly decomposition sum rules Bollweg, Dennis Ding, Heng-Tong Gao, Xiang Luo, Ran Mukherjee, Swagato High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory We present the first lattice-QCD validation of multiple sum rules associated with quark-gluon decomposition of hadron mass by computing all components from first principles. We achieve this through nonperturbative renormalization of the QCD energy-momentum tensor, including its trace, in a gradient-flow scheme, followed by continuum extrapolations, two-loop matching to the $\overline{\mathrm{MS}}$ scheme, and zero-flow-time extrapolations. These ingredients enable a direct and simultaneous verification, in a common renormalization scheme and scale, of multiple energy-density-based and trace-based mass decomposition sum rules proposed in the literature. We demonstrate the framework for the $η_c$ and $J/ψ$ charmonia using three fine lattice spacings with a physical strange-quark and near-physical up- and down-quark masses. We present the first lattice-QCD results for the gravitational form factor $\bar{C}$. We find sizable gluonic contributions to charmonia masses at the hadronic scale, $\sim 15\%$ in the Lorcé and Metz-Pasquini-Rodini decompositions. The trace-anomaly contribution in the Ji sum rule is $\sim 6\%$, while the gluonic component of the trace anomaly in the Hatta-Rajan-Tanaka sum rule is $\sim 35\%$. The method is general and can be straightforwardly adopted for lattice-QCD calculations of mass and spin decompositions as well as gravitational form factors of other hadrons and nuclei. |
| title | Lattice-QCD validation of hadron mass and trace-anomaly decomposition sum rules |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2601.13070 |