Covariant chiral nucleon-nucleon contact Lagrangian up to order $\mathcal{O}(q^4)$

Abstract

We adopt a covariant version of the naive dimensional analysis and construct the chiral two-nucleon contact Lagrangian constrained by Lorentz, parity, charge conjugation, hermitian conjugation, and chiral symmetries. We show that at $\mathcal{O}(q^0)$, $\mathcal{O}(q^2)$, $\mathcal{O}(q^4)$, where $q$ denotes a generic small quantity, there are 4, 13, and 23 terms, respectively. We find that by performing $1/m_N$ expansions, the covariant Lagrangian reduces to the conventional non-relativistic one, which includes 2, 7, and 15 terms at each corresponding order.

arXiv comment9 pages

References in corpus (37)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Chiral Dynamics in Nucleons and Nuclei
• The two-nucleon system at next-to-next-to-next-to-leading order
• Precision nucleon-nucleon potential at fifth order in the chiral expansion
• Renormalization of relativistic baryon chiral perturbation theory and power counting
• The chiral effective pion-nucleon Lagrangian of order p^4
• Matching Heavy Particle Approach to Relativistic Theory
• Leading SU(3)-breaking corrections to the baryon magnetic moments in Chiral Perturbation Theory
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Scattering lengths of Nambu-Goldstone bosons off $D$ mesons and dynamically generated heavy-light mesons
• Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Predictive powers of chiral perturbation theory in Compton scattering off protons
• Dominant contributions to the nucleon-nucleon interaction at sixth order of chiral perturbation theory
• Leading order relativistic chiral nucleon-nucleon interaction
• Low-energy interactions of Nambu-Goldstone bosons with $D$ mesons in covariant chiral perturbation theory
• Octet-baryon axial-vector charges and SU(3)-breaking effects in the semileptonic hyperon decays
• $D{D}^{\ast }$ potentials in chiral perturbation theory and possible molecular states
• Scalar strangeness content of the nucleon and baryon sigma terms
• Recent developments in SU(3) covariant baryon chiral perturbation theory
• Leading order relativistic hyperon-nucleon interactions in chiral effective field theory
• Strangeness $S=-2$ baryon-baryon interactions in relativistic chiral effective field theory
• Magnetic moments of the spin-1/2 doubly charmed baryons in covariant baryon chiral perturbation theory
• Relativistic SU(3) chiral baryon-baryon Lagrangian up to order q^2
• Masses and sigma terms of doubly charmed baryons up to $\mathcal{O}(p^4)$ in manifestly Lorentz-invariant baryon chiral perturbation theory
• Masses of doubly charmed baryons in the extended on-mass-shell renormalization scheme
• Pion-nucleon sigma term revisited in covariant baryon chiral perturbation theory
• Strangeness $S=-1$ hyperon-nucleon interactions: chiral effective field theory vs. lattice QCD
• SU(3)-breaking corrections to the hyperon vector coupling $f_1(0)$ in covariant baryon chiral perturbation theory
• Relativity constraints on the two-nucleon contact interaction
• Electromagnetic form factors of spin 1/2 doubly charmed baryons
• Decuplet baryon masses in covariant baryon chiral perturbation theory
• Octet baryon magnetic moments at next-to-next-to-leading order in covariant chiral perturbation theory
• NN scattering in higher derivative formulation of baryon chiral perturbation theory
• Chiral extrapolation and finite-volume dependence of the hyperon vector couplings

Cited by in corpus (18)

• Accurate relativistic chiral nucleon-nucleon interaction up to NNLO
• Strangeness $S=-2$ baryon-baryon interactions in relativistic chiral effective field theory
• Strangeness $S=-2$ baryon-baryon interactions and femtoscopic correlation functions in covariant chiral effective field theory
• Relativistic chiral description of the ${}^1{S}_0$ nucleon-nucleon scattering
• Do we know how to count powers in pionless and pionful effective field theory?
• Two-Pion-Exchange contributions to the nucleon-nucleon interactions in covariant baryon chiral perturbation theory
• Strangeness $S=-3$ and $-4$ baryon-baryon interactions in relativistic chiral effective field theory
• Pion-mass dependence of the nucleon-nucleon interaction
• Saturation of nuclear matter in the relativistic Brueckner Hatree-Fock approach with a leading order covariant chiral nuclear force
• Meson-baryon scattering up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Nonperturbative two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory
• Study of the hidden charm $D{\bar{D}}^{\ast }$ interactions in chiral effective field theory
• Momentum dependent nucleon-nucleon contact interaction from a relativistic Lagrangian
• Reexamination of antinucleon-nucleon interactions in covariant chiral effective field theory
• Neutrinoless double-beta decay in a finite volume from relativistic effective field theory
• Charge dependent nucleon-nucleon potentials in covariant 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