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1)
EFT Concepts:
1) Power counting not in the rest frame
What happens to this discussion and to the power counting rule when we are doing HQET in a frame other than the rest frame, where the leading kinetic energy term is a single gradient term with no m suppression? It sounds like the problem you point out, that
is the first term inducing not trivial dynamics, would go away!
Yes, in HQET you do not count . That counting only arises because | Mathinline |
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| body | \partial_t \sim E \sim p^2 / m \sim \nabla^2 / m |
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for for a Non-Relativistic EFTs of two or more heavy particles. HQET, with a single heavy particle, has a homogeneous scaling for in in frames that are close to the rest frame. You can also look at the power counting of derivatives for HQET in a boosted frame (which is called bHQET). This gives you exactly what you'd expect by applying the boost. See this paper for a description and application of bHQET.