Renormalization of $NN$ scattering: contact potential

Abstract

The renormalization of the $T$-matrix for $NN$ scattering with a contact potential is reexamined in a nonperturbative regime through rigorous nonperturbative solutions. Based on the underlying theory point of view, it is shown that the UV divergences in the nonperturbative solutions of the $T$-matrix should be subtracted through 'endogenous' counter terms, which in turn leads to a nontrivial prescription dependence. Moreover, employing the effective range expansion, the important procedure for imposing physical boundary conditions to remove the nontrivial prescription dependence is discussed and highlighted, especially before making physical claims. As byproducts, some relations between the effective range expansion parameters are derived. We also discussed the power counting of the couplings for the nucleon-nucleon interactions and other subtle points present within EFT framework beyond perturbative treatment.

18 pages(2 figures, 1 table), published in Phys. Rev. C, typos removed (including the ones in Appendix A, not corrected in Erratum)

References in corpus (6)

• Effective Field Theory for Few-Nucleon Systems
• Towards a Perturbative Theory of Nuclear Forces
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Renormalizing the Lippmann-Schwinger equation for the one pion exchange potential
• Renormalization of the 1S0 One-Pion-Exchange NN Interaction in Presence of Derivative Contact Interactions
• Dynamical symmetry breaking of $\lambda {\varphi }^4$ in two loop effective potential

Cited by in corpus (19)

• Modern Theory of Nuclear Forces
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Scattering Models for Ultracold Atoms
• $D{D}^{\ast }$ potentials in chiral perturbation theory and possible molecular states
• Perturbative $NN$ scattering in chiral effective field theory
• Taking dibaryon fields seriously
• The nucleon-nucleon potential beyond the static approximation
• Effective field theory of interactions on the lattice
• A nonperturbative parametrization and scenario for EFT renormalization
• A Padé-aided analysis of nonperturbative $NN$ scattering in ${}^1{S}_0$ channel
• $NN$ scattering in ${}^3{S}_1{-}^3{D}_1$ channels of EFT ($/\pi$)
• A note on nonperturbative renormalization of effective field theory
• Effective theory with dibaryons and perturbative pions
• Padé expansion and the renormalization of nucleon-nucleon scattering
• Effective range expansion in various scenarios of EFT($\notpi$)
• Closed-form Brückner $G$-matrix and nuclear matter in EFT($/\pi$)
• A simple strategy for renormalization: QED at one-loop level
• 'Running' under tight constraints in pionless effective field theory