  The product of gauge fields generated by the Yang-Mills gradient flow for
positive flow times does not exhibit the coincidence-point singularity and a
local product is thus independent of the regularization. Such a local product
can furthermore be expanded by renormalized local operators at zero flow time
with finite coefficients that are governed by renormalization group equations.
Using these facts, we derive a formula that relates the small flow-time
behavior of certain gauge-invariant local products and the correctly-normalized
conserved energy-momentum tensor in the Yang-Mills theory. Our formula provides
a possible method to compute the correlation functions of a well-defined
energy-momentum tensor by using lattice regularization and Monte Carlo
simulation.
