  In the QCD energy-momentum tensor $T^{\mu\nu}$, the terms that contribute to
physical matrix elements are expressed as the sum of the gauge-invariant quark
part and gluon part. Each part undergoes the renormalization due to the
interactions among quarks and gluons, although the total tensor $T^{\mu\nu}$ is
not renormalized thanks to the conservation of energy and momentum. Recently it
has been shown that, through the renormalization, each of the quark and gluon
parts of $T^{\mu\nu}$ receives a definite amount of anomalous trace
contribution, such that their sum reproduces the well-known QCD trace anomaly,
$T^\mu_\mu= (\beta/2g)F^{\mu\nu}F_{\mu\nu}+ m (1+\gamma_m)\bar{\psi}\psi$, and
the corresponding formulas have been derived up to two-loop order. We extend
this result to the three-loop order, working out all the relevant three-loop
renormalization structure for the quark and gluon energy-momentum tensors in
the (modified) minimal subtraction scheme in the dimensional regularization. We
apply our three-loop formula of the quark/gluon decomposition of the trace
anomaly to calculate the anomaly-induced mass structure of nucleons as well as
pions.
