R-evolution: Improving perturbative QCD

Abstract

Perturbative QCD results in the MSbar 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. The MSR scheme has a very simple relation to MSbar, and can be easily used to reanalyze MSbar results. Results in MSR depend on a cutoff parameter R, in addition to the mu of MSbar. R variations can be used to independently estimate i) the size of power corrections, and ii) higher order perturbative corrections (much like mu in MSbar). 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 ~ 1 GeV, and the size of power corrections is reduced compared to those in MSbar.

Figures (3)

• Figure 1: Perturbative predictions at leading order in $1/m_Q$ for the ratio $r$ of the $B$-$B^\ast$ and $D$-$D^\ast$ mass splittings in the MSR-scheme (solid) versus $\overline{\rm MS}$ (dashed). The $R_0$ dependence of the solid red curve provides an estimate for the power correction, independent of the comparison with the experimental data. Neither $R_1$ nor $\mu$ variation is shown in the figure.
• Figure 2: Perturbative results for the Ellis-Jaffe sum rule in the MSR, RS, and $\overline{\rm MS}$ schemes, at leading order in $1/Q$. For all curves the one parameter, $\hat{a}_0$, is fixed by data at $Q\simeq 5\,{\rm GeV}$.
• Figure 3: Uncertainty estimates in the MSR scheme and $\overline{\rm MS}$ scheme for the Ellis-Jaffe sum rule at leading order in $1/Q$.