2026/06/23 by Mushtaq Loan, Nasser Demir
#hep-lat
We present the one-loop renormalization of the improved gluonic energy-momentum tensor (EMT) by employing a three-loop-improved clover discretization of the field-strength tensor in pure SU(3) lattice gauge theory. The renormalization factor is extracted by matching the amputated two-gluon matrix element of the lattice energy-momentum tensor to the continuum MSbar scheme. The one-loop contribution is separated into sail, operator-tadpole, and external-leg corrections, each expressed in terms of a minimal set of scalar Brillouin-zone integrals to obtain the explicit expression for the finite lattice coefficient Blat(u0) and the multiplicative renormalization factor ZT(u0) associated with the traceless spin-2 component of the energy-momentum tensor. A key result, obtained in this framework, is the clear distinction between two sectors: the spin-2 sector, governed by ZT, and the scalar trace sector, which encompasses the Yang-Mills trace anomaly. The trace is determined by the scalar operator FρσFρσ and the Yang-Mills beta function, rather than by the spin-2 renormalization factor. The renormalized EMT modifies the normalization and short-distance behaviour of energy-density correlators through both traceless and scalar-channel contributions. Comparison with existing lattice thermodynamic data demonstrates that the improved operator accurately reproduces the expected temperature dependence of the trace anomaly and offers a systematically improvable framework for investigating the equation of state, gluon condensate, and transport coefficients in lattice QCD.