Twist-four gravitational form factor at NNLO QCD from trace anomaly constraints

It is known that the trace anomaly in QCD energy-momentum tensor $T^{\mu \nu}$ can be attributed to anomalies for each of gauge-invariant quark part and gluon \nu}$, their explicit three-loop formulas have been derived $\overline{\rm MS}$ scheme dimensional regularization. The matrix elements this quark/gluon decomposition allow us derive constraints on hadron's gravitational form factors, particular, twist-four factor, $\bar{C}_{q,g}$. Using formulas, we calculate forward (zero momentum transfer) value factor $\bar{C}_{q,g}$ at next-to-next-to-leading-order (NNLO) accuracy. We present quantitative results nucleon as well pion, leading a model-independent determination find quite different pattern obtained between pion. In nucleon, information from experiment lattice nonperturbative arising our NNLO formula allows obtain prediction accuracy few percent level.