Pionless EFT calculations find unexpectedly small O(alpha) Coulomb corrections to three-nucleon magnetic moments and GT matrix elements, yielding a fitted prediction for the proton-proton fusion reduced matrix element of 2.776(331).
The proton-deuteron system in pionless EFT revisited
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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.
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Non-perturbative Coulomb corrections in LO pionless EFT give a 0.85(3) MeV He-3/H-3 binding split, 0.043(2) fm charge-radius shift, 0.036(2) fm magnetic-radius shift, and -0.0041(1) μ_N moment shift.
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Coulomb Corrections to Three-Nucleon Moments
Pionless EFT calculations find unexpectedly small O(alpha) Coulomb corrections to three-nucleon magnetic moments and GT matrix elements, yielding a fitted prediction for the proton-proton fusion reduced matrix element of 2.776(331).
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Coulomb Effects and Wigner-SU(4) Symmetry in He-3 Charge and Magnetic Properties
Non-perturbative Coulomb corrections in LO pionless EFT give a 0.85(3) MeV He-3/H-3 binding split, 0.043(2) fm charge-radius shift, 0.036(2) fm magnetic-radius shift, and -0.0041(1) μ_N moment shift.