R evolution: Improving perturbative QCD

Perturbative QCD results in the (MS) over bar scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the MSR scheme'' which achieves this in a Lorentz and gauge invariant way and has a very simple relation to (MS) over bar. Results in MSR depend on a cutoff parameter R, in addition to the mu of (MS) over bar. R variations can be used to independently estimate (i.) the size of power corrections, and (ii.) higher-order perturbative corrections (much like mu in (MS) over bar). We give two examples at three-loop order, the ratio of mass splittings in the B*-B and D*-D systems, and the Ellis-Jaffe sum rule as a function of momentum transfer Q in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for Q similar to 1 GeV, and power corrections are reduced compared to (MS) over bar.