Power counting with one-pion exchange

Abstract

Techniques developed for handing inverse-power-law potentials in atomic physics are applied to the tensor one-pion exchange potential to determine the regions in which it can be treated perturbatively. In S-, P- and D-waves the critical values of the relative momentum are less than or of the order of 400 MeV. The RG is then used to determine the power counting for short-range interaction in the presence of this potential. In the P-and D-waves, where there are no low-energy bound or virtual states, these interactions have half-integer RG eigenvalues and are substantially promoted relative to naive expectations. These results are independent of whether the tensor force is attractive or repulsive. In the 3S1 channel the leading term is relevant, but it is demoted by half an order compared to the counting for the effective-range expansion with only a short-range potential. The tensor force can be treated perturbatively in those F-waves and above that do not couple to P- or D-waves. The corresponding power counting is the usual one given by naive dimensional analysis.

18 pages, RevTeX (further details, explanation added)

References in corpus (30)

• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Renormalization of the Three-Body System with Short-Range Interactions
• The Two-Nucleon Potential from Chiral Lagrangians
• Effective Field Theory for Short-Range Forces
• The Three-Boson System with Short-Range Interactions
• Renormalization of One-Pion Exchange and Power Counting
• Nuclear forces from chiral Lagrangians using the method of unitary transformation I: Formalism
• Towards a Perturbative Theory of Nuclear Forces
• Effective Theory of the Triton
• NNLO Corrections to Nucleon-Nucleon Scattering and Perturbative Pions
• Nucleon-Deuteron Scattering from an Effective Field Theory
• A renormalisation-group treatment of two-body scattering
• Low Energy Expansion in the Three Body System to All Orders and the Triton Channel
• Singular Potentials and Limit Cycles
• Coulomb Effects in Low Energy Proton-Proton Scattering
• An Infrared Renormalization Group Limit Cycle in QCD
• A renormalisation group approach to two-body scattering in the presence of long-range forces
• Renormalization of the Deuteron with One Pion Exchange
• Naive Dimensional Analysis for Three-Body Forces Without Pions
• The singular inverse square potential, limit cycles and self-adjoint extensions
• Field Transformations and the Classical Equation of Motion in Chiral Perturbation Theory
• Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions
• Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem
• Removing Pions from Two-Nucleon Effective Field Theory
• Compton Scattering on the Deuteron in Baryon Chiral Perturbation Theory
• Nucleon-nucleon bremsstrahlung: An example of the impossibility of measuring off-shell amplitudes
• Scattering from Singular Potentials in Quantum Mechanics

Cited by in corpus (138)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Nuclear effective field theory: status and perspectives
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Consequences of Heavy Quark Symmetries for Hadronic Molecules
• Local three-nucleon interaction from chiral effective field theory
• Three-Nucleon Low-Energy Constants from the Consistency of Interactions and Currents in Chiral Effective Field Theory
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Signatures of three-nucleon interactions in few-nucleon systems
• Light-nuclei spectra from chiral dynamics
• Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Central Phases and the Deuteron
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
• Regularization, renormalization and "peratization" in effective field theory for two nucleons
• A renormalized approach to neutrinoless double-beta decay
• The Effective Chiral Lagrangian From Dimension-Six Parity and Time-Reversal Violation
• Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering
• Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Renormalization of NN Interaction with Chiral Two Pion Exchange Potential. Non-Central Phases
• Perturbative Renormalizability of Chiral Two Pion Exchange in Nucleon-Nucleon Scattering: P- and D-waves
• Short-range nuclear forces in singlet channels
• Renormalization of chiral two-pion exchange NN interactions. Momentum vs. coordinate space
• Renormalization of Singular Potentials and Power Counting
• Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory
• Ground state energy of dilute neutron matter at next-to-leading order in lattice chiral effective field theory
• Towards grounding nuclear physics in QCD
• Power Counting of Contact-Range Currents in Effective Field Theory
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
• Renormalizing Chiral Nuclear Forces: A Case Study of 3P0
• P- and T-Violating Lagrangians in Chiral Effective Field Theory and Nuclear Electric Dipole Moments
• Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• The Effective Chiral Lagrangian From the Theta Term
• On the renormalization of the one-pion exchange potential and the consistency of Weinberg's power counting
• Deconstructing triplet nucleon-nucleon scattering
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• How (not) to renormalize integral equations with singular potentials in effective field theory
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• The Time-Reversal- and Parity-Violating Nuclear Potential in Chiral Effective Theory
• Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higher NN partial waves
• Leading order relativistic hyperon-nucleon interactions in chiral effective field theory
• New Ideas in Constraining Nuclear Forces
• First-principle calculations of Dark Matter scattering off light nuclei
• Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
• The Theory of Parity Violation in Few-Nucleon Systems
• ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions in chiral effective field theory
• Heavy Baryon-Antibaryon Molecules in Effective Field Theory
• Chiral effective theory predictions for deuteron form factor ratios at low Q^2
• Power Counting in Peripheral Partial Waves: The Singlet Channels
• Short-range three-nucleon interaction from A=3 data and its hierarchical structure
• The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory
• Parity- and time-reversal-violating nuclear forces
• Power counting in chiral effective field theory and nuclear binding
• Perturbative $NN$ scattering in chiral effective field theory
• Strangeness $S=-1$ hyperon-nucleon scattering in covariant chiral effective field theory
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Exotic Doubly Charmed Ds0*(2317)D and Ds1*(2460)D* Molecules
• Improved convergence of chiral effective field theory for 1S0 of NN scattering
• On the convergence of nuclear effective field theory with perturbative pions
• Geometry and entanglement in the scattering matrix
• Chiral effective field theory on the lattice at next-to-leading order
• Two-nucleon scattering: merging chiral effective field theory with dispersion relations
• Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter
• Effective Field Theory and Finite Density Systems
• How to renormalize integral equations with singular potentials in effective field theory
• The multiple-scattering series in pion-deuteron scattering and the nucleon-nucleon potential: perspectives from effective field theory
• Interpretations of the new LHCb $P_c(4337{)}^{+}$ pentaquark state
• Can chiral EFT give us satisfaction?
• Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory
• The magnetic form factor of the deuteron in chiral effective field theory
• Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation
• Nuclear Reactions from Lattice QCD
• Nuclear forces from chiral EFT: The unfinished business
• Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory
• Pion-mass dependence of three-nucleon observables
• Taking dibaryon fields seriously
• Nucleon-nucleon interactions from dispersion relations: Elastic partial waves
• Deconstructing 1S0 nucleon-nucleon scattering
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• The renormalisation group and nuclear forces
• Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order
• The nucleon-nucleon potential beyond the static approximation
• Chiral potential renormalized in harmonic-oscillator space
• Do we know how to count powers in pionless and pionful effective field theory?
• The exact discontinuity of a partial wave along the left-hand cut and the exact $N/D$ method in non-relativistic scattering
• Relativistic chiral description of the ${}^1{S}_0$ nucleon-nucleon scattering
• Pions are neither perturbative nor nonperturbative: Wilsonian renormalization group analysis of nuclear effective field theory including pions
• Similarity Renormalization Group Evolution of Chiral Effective Nucleon-Nucleon Potentials in the Subtracted Kernel Method Approach
• Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves
• Nuclear Effective Field Theories: Reverberations of the early days
• Renormalization of chiral two-pion exchange NN interactions with Delta-excitations: Central Phases and the Deuteron
• A Consistency Test of EFT Power Countings from Residual Cutoff Dependence
• Temperature-dependent errors in nuclear lattice simulations
• Nucleon-Nucleon scattering from the dispersive N/D method: next-to-leading order study
• What Can Possibly Go Wrong?
• Nucleon Polarizabilities from Deuteron Compton Scattering within a Green's-Function Hybrid Approach
• Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange
• Power counting for nuclear forces in chiral effective field theory
• Heavy hadron molecules in effective field theory: the emergence of exotic nuclear landscapes
• Renormalization of chiral two pion exchange NN interactions with delta excitations: correlations in the partial wave expansion
• Power counting and renormalization group invariance in the subtracted kernel method for the two-nucleon system
• More about the Wilsonian analysis on the pionless NEFT
• Renormalizability of leading order covariant chiral nucleon-nucleon interaction
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Toroidal Quadrupole Form Factor of the Deuteron
• Comment on "How (not) to renormalize integral equations with singular potentials in effective field theory"
• Effective field theory for shallow P-wave states
• Perturbative chiral nucleon-nucleon potential for the ${}^3{P}_0$ partial wave
• Contact operators in renormalization of attractive singular potentials
• Renormalization of nuclear chiral effective field theory with non-perturbative leading order interactions
• Hadronic states with both open charm and bottom in effective field theory
• Large-cutoff behavior of local chiral effective field theory interactions
• Two-pion exchange as a leading-order contribution in chiral effective field theory
• Improved description of light nuclei through chiral effective field theory at leading order
• Renormalization of a Finite Range Inverse Cube Potential
• Perturbative Calculations of Deuteron Form Factors
• Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N${}^3$LO
• Femtoscopy correlation functions and hadron-hadron scattering amplitudes in presence of Coulomb potential
• On the Wilsonian renormalization group equation for nuclear current operators
• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
• Renormalization of pionless effective field theory in the A-body sector
• Non-perturbative methods for NN singular interactions
• Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases
• The longitudinal response function of the deuteron in chiral effective field theory
• Renormalization of proton-proton fusion in chiral effective field theory
• A nonperturbative parametrization and scenario for EFT renormalization
• Perturbative renormalization of chiral nuclear forces at subleading order in 3S1-3D1 channel
• Regulator constraints for the perturbative renormalizability of attractive triplets
• Reexamining the perturbative renormalizability of the coupled triplets
• Renormalization of One-Pion Exchange in Chiral Effective Field Theory for Antinucleon-Nucleon Scattering
• Unitarization Technics in Hadron Physics with Historical Remarks
• Renormalization of NN Chiral EFT, my personal mixed feelings
• Perturbative $\chi$EFT calculations of the deuteron and triton up to N${}^2$LO
• Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory
• Renormalizing the Schrodinger Equation for NN scattering
• Auxiliary counterterms and their role in effective field theory
• Renormalization of One-Pion Exchange in Higher Partial Waves in Chiral Effective Field Theory for Antinucleon-Nucleon System