Systematic Power Counting in Cutoff Effective Field Theories for Nucleon-Nucleon Interactions and the Equivalence With PDS
Thomas D. Cohen, James M. Hansen
Abstract
An analytic expression for the 1S0 phase shifts in nucleon-nucleon scattering is derived in the context of the Schrödinger equation in configuration space with a short distance cutoff and with a consistent power counting scheme including pionic effects. The scheme treats the pion mass and the inverse scattering length over the intrinsic short distance scale as small parameters. Working at next-to-leading order in this scheme, we show that the expression obtained is identical to one obtained using the recently introduced PDS approach which is based on dimensional regularization with a novel subtraction scheme. This strongly supports the conjecture that the schemes are equivalent provided one works to the same order in the power counting.
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