Radiative Instability: How Far the Vacuum Density Runs Between the Electroweak and Planck Scales

A vacuum density tuned to its observed value at one renormalisation scale does not stay tuned at others, because quantum corrections shift it by terms proportional to the fourth powers of particle masses. This paper evaluates a stated one-loop estimate for five Standard Model species between 246 GeV and scales up to 1e19 GeV. The accumulated shift to the Planck scale is -1.21 x 10^9 GeV^4, some 4.79 x 10^55 times the observed density of 2.52 x 10^-47 GeV^4, dominated by the top quark's contribution. Rescaling the coefficient by a factor of sixteen changes nothing qualitatively. The smallness of the vacuum density is therefore radiatively unstable in a precisely computable sense. The paper is a computation from stated assumptions, not a measurement.