Sense and nonsense in the renormalization-scheme-dependence problem

I discuss in detail the issues involved in the renormalization-scheme-dependence problem in perturbative QCD. The problem is not to find a good universal scheme; nor is it a question of how to make coefficients small. The problem is that finite-order results depend on the choice of scheme, even though it is “arbitrary” (in that the exact result is scheme independent). Only the “principle of minimal sensitivity” approach gets to the heart of the problem, and attempts to reconcile this contradiction. I explain the motivation for this approach, defend it against recent criticisms, and explain to what extent it provides a solution to the problem.