The Pion Gravitational Form Factors and the Trace Anomaly in QCD Factorization

We study the pion gravitational form factor in QCD factorization, focusing on the trace-anomaly component generated by the non-Abelian \(TJJ\) vertex. The calculation combines a Sudakov-resummation-improved pion hard kernel with the anomaly form factor suggested by momentum-space conformal field theory and by the perturbative dilaton sum rule. Comparison with lattice QCD data shows a refined projection hierarchy: the isolated anomaly cancels in the form factor \(A_\pi(Q^2)\), while the full \(TJJ\) insertion lowers the leading-order curve at small momentum transfer squared \(Q^2\); the anomaly is important in \(D_\pi(Q^2)\), and it gives the dominant \(TJJ\) contribution to the trace form factor.