In dimensional regularisation and other analytic schemes, on the other hand, renormalisation can be performed exactly and no cutoff $\Lambda$ or residual regulator scale appears in observables at all. Equation is then an exact zero, with no information about $n$ and ${\overline{\Lambda}_\text{EFT}}$. But doubts about proper renormalisation of a calculation which is analytic at each step do not arise, so the test is moot anyway.

An Application: Confirming the Hierarchy of $3N$ Interactions in [EFT($\slashed{\pi}$)]{} {#sec:application}
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Before continuing the discussion of the parameters of the test in Sect. \[sec:notesofnote\], consider the first application (to my knowledge) of this test: the [${}^{2}\mathrm{S}_{\frac{1}{2}}$]{} $Nd$ wave in [EFT($\slashed{\pi}$)]{}. It is well-known that its $3N$ interaction without derivatives does not follow simplistic PC rules (“just count momenta”) which predict $H_0$ at [N${}^{2}$LO]{} or ${\mathcal{O}}(Q^0)$ [@Bedaque:2002mn; @Platter:2009gz]. Instead, it is needed at LO to stabilise the system (Thomas-collapse, Efimov effect); its scaling, $H_0\sim Q^{-2}$, follows from eq.  for $n=3$. If the first momentum-dependent $3N$ interaction $k^2H_2$ follows the simplistic argument and scales as $Q^2$, then new LECs need to be determined from $3N$ data only at [N${}^{4}$LO]{}. Therefore, one could find $2N$ interaction strengths from few-N data with only one new $3N$ datum up 