The proton-deuteron system in pionless EFT revisited

TL;DR

This paper revisits the low-energy proton-deuteron system using pionless effective field theory, calculating binding energy differences, examining Coulomb effects, and identifying the need for a new three-nucleon counterterm at next-to-leading order.

Contribution

It extends previous work by including Coulomb effects nonperturbatively and proposes a simplified Coulomb power counting scheme for bound and scattering states.

Findings

Nonperturbative Coulomb calculations agree with off-shell T-matrix results.

Evidence for a new three-nucleon counterterm at NLO with Coulomb effects.

Higher-order Coulomb corrections are significant in low-energy scattering.

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.