The renormalization group for correlated scales: one-stage versus two-stage running

Details The renormalization group for correlated scales: one-stage versus two-stage running The renormalization group for correlated scales: one-stage versus two-stage running

2000-06-12

arxiv.org/abs/hep-ph/0006096v2

Phys.Lett. B486 (2000) 400-405

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages, typos fixed, results and conclusions unchanged

Scientific paper

10.1016/S0370-2693(00)00788-7

Nonrelativistic bound states have two low energy scales, a soft scale mu_S of order mv and an ultrasoft scale mu_U of order mv^2. In two-stage running, the soft and ultrasoft scales are lowered from m to mv, and then the ultrasoft scale is lowered from mv to mv^2. In one-stage running, the two scales are lowered in a correlated way using a subtraction velocity. We compare these two methods of summing logarithms and show that only the correlated running in velocity space of the one-stage method correctly reproduces the logarithms in non-relativistic bound states in QED. The argument for one-stage running is general, and should apply to any system with correlated scales.

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