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2024

Quantifying the breakdown scale of pionless effective field theory

Ekström, Andreas, Platter, Lucas

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We use Bayesian statistics to infer the breakdown scale of pionless effective field theory in its standard power counting and with renormalization of observables carried out using the power-divergence subtraction scheme and cutoff regularization.

We condition our inference on predictions of the total neutron-proton scattering cross section up next-to-next-to leading order.
We quantify a median breakdown scale of approximately 1.4$m_\pi$.
The 68% degree of belief interval is $[0.96,1.69]m_\pi$.

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During the preparation of this manuscript, we became aware of Ref. [ 25 ] , which investigates the breakdown scale of a theory constructed solely from contact interactions in the context of nucleon-nucleon scattering. That work follows a non-standard ordering scheme for subleading interactions, which differs from the approach typically used in pionless EFT. Consequently, its results are not directly comparable to our findings

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See the supplemental material for more information on regularization and renormalization with a hard momentum space cutoff

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