The QCD Trace Anomaly in Pion Gravitational Form Factors with Sudakov Resummation

Abstract

We discuss the pion gravitational form factors at intermediate and large spacelike momentum transfer in a perturbative-QCD factorization framework. The short-distance kernel is supplemented by the one-loop non-Abelian $TJJ$ correlator, where the energy--momentum tensor couples to two off-shell gluons. Its trace sector contains the QCD conformal anomaly and admits a scalar, dilaton-like pole interpretation. A transverse-momentum-dependent pion wave function, combined with Sudakov resummation and a Gaussian intrinsic-transverse-momentum profile, suppresses endpoints and large transverse separations. The projection on the pion form factors exhibits a characteristic hierarchy: the isolated anomaly cancels in the momentum form factor 4A_π$, remains important in the mechanical form factor $D_π$, and dominates the $TJJ$ correction to the trace form factor. The result identifies a beta-function-controlled short-distance contribution to pion mechanical structure and clarifies the relation between the perturbative anomaly pole and a correlated scalar partonic channel.