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.

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

References in corpus (10)

• Electron-Ion Collider in China
• The five-loop beta function of Yang-Mills theory with fermions
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Five-loop quark mass and field anomalous dimensions for a general gauge group
• The mass radius of the proton
• Low moments of the four-loop splitting functions in QCD
• Proton Mass Decomposition and Hadron Cosmological Constant
• A Demonstration of Hadron Mass Origin from QCD Trace Anomaly
• Trace anomaly contribution to hydrogen atom mass

Cited by in corpus (4)

• Chiral and trace anomalies in Deeply Virtual Compton Scattering II: QCD factorization and beyond
• Twist-four gravitational form factor at NNLO QCD from trace anomaly constraints
• 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