A note on quark and gluon energy-momentum tensors

Abstract

We discuss the constraints on quark and gluon energy-momentum tensors in QCD that follow from the requirement of Renormalisation-Group invariance of the traces of these operators. Our study covers the most general form of the latter traces, while the energy-momentum tensors themselves are only subjected to very mild constraints. We derive Renormalisation-Group equations for the two finite independent functions of the strong coupling constant and renormalisation scale of minimal subtraction which completely define the energy-momentum tensors. We demonstrate that previously proposed definitions of the renormalized quark and gluon energy-momentum tensors are special cases of our results assuming no explicit dependence on the renormalisation scale. Finally, we present $\overline{\mathrm{MS}}$-renormalised quark and gluon energy-momentum tensors at four-loop order.

arXiv commentAdditional comments on the physics implications of the results and the scheme proposed added, matched to the version accepted for publication in JHEP

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• Pion-production cross sections in neutrino reactions for studying generalized parton distributions of the nucleon
• On-shell Matrix Elements of the EMT Trace in Gauge Theories and Heavy Quark Masses