Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting

Abstract

Low-energy theorems (LETs) for effective-range parameters in nucleon-nucleon scattering encode properties of the long-range part of the nuclear force. We compute LETs for S-wave neutron-proton scattering using chiral effective field theory with a modified version of Weinberg power counting. Corrections to the leading order amplitude are included in distorted-wave perturbation theory and we incorporate contributions up to the third order in the power counting. We find that LETs in the ${}^1{S}_0$ and ${}^3{S}_1$ partial waves agree well with empirical effective-range parameters. At the same time, phase shifts up to laboratory scattering energies of about 100 MeV can be reproduced. We show that it is important to consider the pion mass splitting in the one-pion exchange potential in the ${}^1{S}_0$ partial wave while the effect is negligible in the ${}^3{S}_1$ partial wave. We conclude that pion exchanges, as treated in this power counting, accurately describe the long-range part of the $S$-wave nuclear interaction.

arXiv comment25 pages, 4 figures

References in corpus (41)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• The two-nucleon system at next-to-next-to-next-to-leading order
• Three-Nucleon Forces from Chiral Effective Field Theory
• The Two-Nucleon Potential from Chiral Lagrangians
• Nuclear effective field theory: status and perspectives
• Charge, neutron, and weak size of the atomic nucleus
• Renormalization of One-Pion Exchange and Power Counting
• An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Ab initio predictions link the neutron skin of ${}^{208}$Pb to nuclear forces
• NNLO Corrections to Nucleon-Nucleon Scattering and Perturbative Pions
• Singular Potentials and Limit Cycles
• Improving the convergence of the chiral expansion for nuclear forces I: Peripheral phases
• Regularization, renormalization and "peratization" in effective field theory for two nucleons
• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• A recipe for EFT uncertainty quantification in nuclear physics
• Reconciling threshold and subthreshold expansions for pion-nucleon scattering
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Ground-State Properties of ${}^4$He and ${}^{16}$O Extrapolated from Lattice QCD with Pionless EFT
• Dominant contributions to the nucleon-nucleon interaction at sixth order of chiral perturbation theory
• Short-range nuclear forces in singlet channels
• Renormalization of Singular Potentials and Power Counting
• Bayesian Methods for Parameter Estimation in Effective Field Theories
• Weinberg's approach to nucleon-nucleon scattering revisited
• Low Energy Theorems For Nucleon-Nucleon Scattering
• Renormalizing Chiral Nuclear Forces: A Case Study of 3P0
• Ab initio computation of charge densities for Sn and Xe isotopes
• How (not) to renormalize integral equations with singular potentials in effective field theory
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Testing Low Energy Theorems in Nucleon-Nucleon Scattering
• Power counting in chiral effective field theory and nuclear binding
• Low-energy theorems for nucleon-nucleon scattering at unphysical pion masses
• Improved convergence of chiral effective field theory for 1S0 of NN scattering
• Low-energy theorems for nucleon-nucleon scattering at $M_{\pi }=450$ MeV
• Deconstructing 1S0 nucleon-nucleon scattering
• Effective range corrections from effective field theory with di-baryon fields and perturbative pions
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Perturbative chiral nucleon-nucleon potential for the ${}^3{P}_0$ partial wave

Cited by in corpus (2)

• A further study on the renormalization group aspect of perturbative corrections
• Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO