Demonstration of the hadron mass origin from the QCD trace anomaly

Abstract

Quantum chromodynamics (QCD) claims that the major source of the nucleon invariant mass is not the Higgs mechanism but the trace anomaly in the QCD energy-momentum tensor. Although experimental and theoretical results support such a conclusion, a direct demonstration is still absent. We present the first lattice QCD calculation of the quark and gluon trace anomaly contributions to the hadron masses, using the overlap fermion on the $2+1$-flavor dynamical domain wall quark ensemble at ${m}_{\ensuremath{\pi}}=340\text{ }\text{ }\mathrm{MeV}$ and lattice spacing $a=0.1105\text{ }\text{ }\mathrm{fm}$. The result shows that the gluon trace anomaly contributes to most of the nucleon mass, the contribution in the pion state is smaller than that in others nearly by a factor of $\ensuremath{\sim}10$, and the gluon trace anomaly density in the center of the pion is negative. The gluon trace anomaly coefficient $\ensuremath{\beta}/{g}^{3}=\ensuremath{-}0.056(6)$ we obtained is consistent with its regularization-independent leading-order value $(\ensuremath{-}11+\frac{2{N}_{f}}{3})/(4\ensuremath{\pi}{)}^{2}$ perfectly.