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

Aneesh V. Manohar·Joan Soto·Iain W. Stewart
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Abstract

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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Aneesh V. Manohar, Joan Soto, Iain W. Stewart. 2000-06-14. The renormalization group for correlated scales: one-stage versus two-stage running. https://doi.org/10.1016/s0370-2693(00)00788-7

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