hence Eqs. \[one way of normalizing\] and \[0000 components\] are valid for low energies $E<M_P$. For spacelike $q^2$ this corresponds to an increase in the strength of gravity, while for timelike values it is a decrease. Of course this sign ambiguity is a signal of the crossing problem. It is present no matter which components of the propagator are considered. If converted to Euclidean space by the Wick rotation $q^2 \to (iq_4)^2 -\mathbf{q}^2 =-q_E^2$, the effective strength increases.

At one loop order, it would be hard to convincingly favor one of the two definitions Eqs. \[one way of normalizing\] or \[0000 components\]. However, they do at least have a common sign.

However, we know ahead of time that this definition is not going to enter into any physical one-loop processes in pure gravity. Since on-shell processes are one loop finite, any reference to the higher order operators $R^2$ or $R_{\mu\nu}R^{\mu\nu}$ must drop out of physical observables at one loop. The coefficients $\mu_1$ and $\mu_2$ are in this category and will not appear in on-shell processes. On-shell reactions may have logarithms such as $\ln s/t$, but not $\ln s/\mu_{1,2}^2$.

Pure gravity: Graviton scattering
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The simplest physical process in pure gravity 