Anomalous "mapping" between pionfull and pionless EFT's
The pion contributions to the coupling C0 of pionless EFT are studied via both non-relativistic and relativistic forms of chiral effective field theory for nuclear forces. A definite item in the 2N-reducible component of the box diagram is shown to be dominant over the 2N-irreducible (potential) ones due to the pinching of low-lying nucleon poles, and this anomalous mapping between pionless and pionfull EFT's occurs right within the non-relativistic regime. A natural strategy for renormalization of the pionfull theory emerges as a byproduct through the interactive analysis of the box diagram. Such mapping perspective may shed some light on the efficient organization of the pionfull effective field theory for nuclear forces.