Abstract
In the QCD energy-momentum tensor Tμν, 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 Tμν 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 Tμν receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly, \( {T}_{\mu}^{\mu }=\left(\beta /2g\right){F}^{\mu \nu }{F}_{\mu \nu }+m\left(1+{\gamma}_m\right)\overline{\psi}\psi \), 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.
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Tanaka, K. Three-loop formula for quark and gluon contributions to the QCD trace anomaly. J. High Energ. Phys. 2019, 120 (2019). https://doi.org/10.1007/JHEP01(2019)120
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DOI: https://doi.org/10.1007/JHEP01(2019)120