Relativity constraints on the two-nucleon contact interaction

Abstract

We construct the most general, relativistically invariant, contact Lagrangian at order Q^2 in the power counting, Q denoting the low momentum scale. A complete, but non-minimal, set of (contact) interaction terms is identified, which upon non-relativistic reduction generate 2 leading independent operator combinations of order Q^0 and 7 sub-leading ones of order Q^2 - a result derived previously in the heavy-baryon formulation of effective field theories (EFT's). We show that Poincare covariance of the theory requires that additional terms with fixed coefficients be included, in order to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass number A>2, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied.

17 pages, 1 eps figure

References in corpus (18)

• Modern Theory of Nuclear Forces
• Chiral Dynamics in Nucleons and Nuclei
• Effective Field Theory for Few-Nucleon Systems
• The Two-Nucleon Potential from Chiral Lagrangians
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Three-Body Interactions Among Nucleons and Pions
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• Pion-nucleon scattering in chiral perturbation theory I: Isospin-symmetric case
• Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism
• Effective Field Theory of Nuclear Forces
• The chiral effective pion-nucleon Lagrangian of order p^4
• Electromagnetic Currents and Magnetic Moments in $\chi$EFT
• Resonance saturation for four-nucleon operators
• Poincare' invariance constraints on NRQCD and potential NRQCD
• Relativity and the low energy nd Ay puzzle
• Variational Monte Carlo Calculations of ${}^3$H and ${}^4$He with a relativistic Hamiltonian - II
• Poincare' invariance and the heavy-quark potential
• Poincare' invariance constraints on non-relativistic effective field theories

Cited by in corpus (28)

• Chiral effective field theory and nuclear forces
• Nuclear effective field theory: status and perspectives
• Subleading contributions to the chiral three-nucleon force II: Short-range terms and relativistic corrections
• Subleading contributions to the three-nucleon contact interaction
• Two-nucleon electromagnetic current in chiral effective field theory: one-pion exchange and short-range contributions
• Electromagnetic structure of A=2 and 3 nuclei in chiral effective field theory
• The two-nucleon electromagnetic charge operator in chiral effective field theory ($\chi$EFT) up to one loop
• Electromagnetic Structure of Few-Nucleon Ground States
• Long-range properties of $1S$ bottomonium states
• Hyperon-nuclear interactions from SU(3) chiral effective field theory
• Thermal neutron captures on $d$ and ${}^3$He
• Leading order relativistic hyperon-nucleon interactions in chiral effective field theory
• Parity- and time-reversal-violating nuclear forces
• Short-range three-nucleon interaction from A=3 data and its hierarchical structure
• Relativistic SU(3) chiral baryon-baryon Lagrangian up to order q^2
• Covariant chiral nucleon-nucleon contact Lagrangian up to order $\mathcal{O}(q^4)$
• A chiral effective field theory study of hadronic parity violation in few-nucleon systems
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• Heavy-particle formalism with Foldy-Wouthuysen representation
• Unitary ambiguity of NN contact interactions and the 3N force
• Time Reversal Violation in Light Nuclei
• Large-$N_c$ Relationships Among Two-Derivative Pionless Effective Field Theory Couplings
• Two-nucleon scattering in a modified Weinberg approach with a symmetry-preserving regularization
• Chiral Electroweak Currents in Nuclei
• Momentum dependent nucleon-nucleon contact interaction from a relativistic Lagrangian
• Large-$N_c$ operator analysis of hyperon-nucleon interactions in SU(3) chiral effective field theory
• Nucleon-nucleon scattering up to next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: low phases and the deuteron
• Four-nucleon contact interactions from holographic QCD