One-Loop Renormalization of the Improved Energy-Momentum Tensor in Lattice QCD

Abstract

We present a one-loop renormalization analysis of the improved gluonic energy-momentum tensor in pure SU(3) lattice gauge theory, employing a tadpole-improved tree-level Symanzik gauge action and a three-loop-improved clover discretization of the field-strength tensor. The calculation is conducted in Landau gauge by matching the amputated two-gluon matrix element of the lattice energy-momentum tensor to the continuum MSbar scheme. The one-loop correction is separated into sail, operator-tadpole, and external-leg contributions, each expressed in terms of a minimal set of scalar Brillouin-zone integrals. This approach yields explicit expressions for the finite lattice coefficient B_lat(u0) and the multiplicative renormalization factor Z_T(u0) associated with the traceless spin-2 component of the energy-momentum tensor. A key result is the clear distinction between the spin-2 sector, governed by Z_T, and the scalar trace sector, which encodes the Yang-Mills trace anomaly. We demonstrate that the improved lattice construction maintains the correct continuum anomaly structure, with the trace determined by the scalar operator F_{rho sigma}F_{rho sigma} and the Yang-Mills beta function, rather than by the spin-2 renormalization factor. The resulting renormalized energy-momentum tensor alters the normalization and short-distance behavior of Euclidean energy-density correlators through both traceless and scalar-channel contributions. Comparison with existing lattice thermodynamic data indicates that the improved operator accurately reproduces the expected temperature dependence of the trace anomaly and provides a systematically improvable framework for studying the equation of state, gluon condensate, and transport coefficients in lattice QCD.