The proton-deuteron system in pionless EFT revisited

Abstract

We provide a detailed discussion of the low-energy proton-deuteron system in pionless effective field theory, considering both the spin-quartet and doublet S-wave channels. Extending and amending our previous work on the subject, we calculate the 3He-3H binding energy difference both perturbatively (using properly normalized trinucleon wave functions) and non-perturbatively by resumming all O(alpha) Coulomb diagrams in the doublet channel. Our nonperturbative result agrees well with a calculation that involves the full off-shell Coulomb T-matrix. Carefully examining the cutoff-dependence in the doublet channel, we present numerical evidence for a new three-nucleon counterterm being necessary at next-to-leading order if Coulomb effects are included. Indeed, such a term has recently been identified analytically. We furthermore make a case for a simplified Coulomb power counting that is consistent throughout the bound-state and scattering regimes. Finally, using a "partially screened" full off-shell Coulomb T-matrix, we investigate the importance of higher-order Coulomb corrections in low-energy quartet-channel scattering.

arXiv comment56 pages, 23 figures, published version with one nontrivial correction indicated by a footnote on p. 2

References in corpus (50)

• Modern Theory of Nuclear Forces
• Cuba - a library for multidimensional numerical integration
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Effective Field Theory for Short-Range Forces
• Nucleon-Nucleon Effective Field Theory Without Pions
• Effective Theory of the Triton
• More Effective Field Theory for Nonrelativistic Scattering
• Nucleon-Deuteron Scattering from an Effective Field Theory
• Low Energy Expansion in the Three Body System to All Orders and the Triton Channel
• How short is too short? Constraining zero-range interactions in nucleon-nucleon scattering
• Improving the Convergence of NN Effective Field Theory
• Coulomb Effects in Low Energy Proton-Proton Scattering
• Efimov States in Nuclear and Particle Physics
• Achronal averaged null energy condition
• Improved Convergence in the Three-Nucleon System at Very Low Energies
• A renormalisation group approach to two-body scattering in the presence of long-range forces
• Proton-Proton Scattering Lengths from Effective Field Theory
• Range Corrections to Doublet S-Wave Neutron-Deuteron Scattering
• Naive Dimensional Analysis for Three-Body Forces Without Pions
• Causality and the effective range expansion
• Quartet S Wave Neutron Deuteron Scattering in Effective Field Theory
• Higher Partial Waves in an Effective Field Theory Approach to nd Scattering
• Proton-Proton Fusion in Effective Field Theory
• Higher Order Terms of Kerr Parameter for Blandford-Znajek Monopole Solution
• Modeling the horizon-absorbed gravitational flux for equatorial-circular orbits in Kerr spacetime
• Fully Perturbative Calculation of $nd$ Scattering to Next-to-next-to-leading-order
• A phenomenological study of helicity amplitudes of high energy exclusive leptoproduction of the rho meson
• Charge-dependent nucleon-nucleon potential from chiral effective field theory
• Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Poschl-Teller-Ginocchio potential wave functions
• Universal Correlations in Pion-less EFT with the Resonating Group Model: Three and Four Nucleons
• The Three-Boson System at Next-To-Next-To-Leading Order
• Proton-proton fusion in pionless effective theory
• Causality and universality in low-energy quantum scattering
• Low energy proton-proton scattering in effective field theory
• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• Effective field theory of 3He
• Schwarzschild black holes as unipolar inductors: expected electromagnetic power of a merger
• Quartet S-wave p-d scattering in EFT
• Parity-violating neutron spin rotation in hydrogen and deuterium
• Causality constraints for charged particles
• Low-energy p-d scattering and He-3 in pionless EFT
• ${}^3\mathrm{He}$ and $pd$ Scattering to Next-to-Leading Order in Pionless Effective Field Theory
• Charge form factors of two-neutron halo nuclei in halo EFT
• Renormalization-group analysis for low-energy scattering of charged particles
• Measuring a Kaluza-Klein radius smaller than the Planck length
• Constraining the neutron-neutron scattering length with \eftnopi
• Quasi-spherical approximation for rotating black holes
• Precision calculation of the quartet-channel p-d scattering length

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• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• Tritium $\beta$-decay in pionless effective field theory
• Second-order perturbation theory for 3He and pd scattering in pionless EFT
• Do we know how to count powers in pionless and pionful effective field theory?
• $nd$ Scattering and the $A_y$ Puzzle to Next-to-next-to-next-to-leading Order
• Few nucleons scattering in pionless effective field theory
• Three-body systems in pionless effective field theory
• General aspects of effective field theories and few-body applications
• Neutron transfer reactions in halo effective field theory
• Cold Neutron-Deuteron Capture and Wigner-SU(4) Symmetry
• Theoretical evaluation of solar proton-proton fusion reaction rate and its uncertainties
• Few-Nucleon Systems within Finite-Cutoff Pionless EFT
• Two-Body Triton Photodisintegration and Wigner-SU(4) Symmetry
• Halo EFT calculation of charge form factor for two-neutron ${}^6\text{He}$ halo nucleus: two-body resonant P-wave interaction