2020/02/17 by Mattia Dalla Brida, Brida, Mattia Dalla, Leonardo Giusti +3 · 3 citations
Engineering · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Superconducting Materials and Applications
paper · pdf · doi:10.48550/arxiv.2002.06897
openalex publication_date 2020/02/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We present a strategy to define non-perturbatively the energy-momentum tensor\nin Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities\nand has the right trace anomaly. The tensor is defined by regularizing the\ntheory on a lattice, and by fixing its renormalization constants\nnon-perturbatively by suitable Ward identities associated to the Poincare'\ninvariance of the continuum theory. The latter are derived in thermal QCD with\na non-zero imaginary chemical potential formulated in a moving reference frame.\nA renormalization group analysis leads to simple\nrenormalization-group-invariant definitions of the gluonic and fermionic\ncontributions to either the singlet or the non-singlet components of the\ntensor, and therefore of their form factors among physical states. The lattice\ndiscussion focuses on the Wilson discretization of quark fields but the\nstrategy is general. Specific to that case, we also carry out the analysis for\nthe on-shell O(a)-improvement of the energy-momentum tensor. The\nrenormalization and improvement programs profit from the fact that, as shown\nhere, the thermal theory enjoys de-facto automatic O(a)-improvement at finite\ntemperature. The validity of the proposal is scrutinized analytically by a\nstudy to 1-loop order in lattice perturbation theory with shifted and twisted\n(for quarks only) boundary conditions. The latter provides also additional\nuseful insight for a precise non-perturbative calculation of the\nrenormalization constants. The strategy proposed here is accessible to Monte\nCarlo computations, and in this sense it provides a practical way to define\nnon-perturbatively the energy-momentum tensor in QCD.\n