Speaker
Description
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 conservation of energy and momentum. We show 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. We provide a procedure to derive such anomalous trace contributions to all orders in perturbation theory, and present the corresponding explicit decomposition formulas up to three-loop order in the (modified) minimal subtraction scheme in the dimensional regularization. We apply our three-loop formulas of the quark/gluon decomposition of the trace anomaly to calculate the anomaly-induced mass structure of nucleons as well as pions. Another application of our three-loop formulas is a quantitative analysis for the constraints on the twist-four gravitational form factors of a hadron, $\bar{C}_{q,g}$, which receive much attention in connection with the force distribution inside the nucleon and the nucleon's transverse spin sum rule. This talk is based on our work, JHEP 1901 (2019) 120, and some additional results.
