Tritium $\beta$-decay in chiral effective field theory

Abstract

We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $\beta$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($\chi$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either $\chi$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.

19 pages,6 figures, corrections to Text as suggested by Referee added; Erratum: 4 pages, 3 figures, corrections to Eq.(20), Tables I, II, III, Figures 4, 5, conclusions unchanged

References in corpus (5)

• Chiral effective field theory and nuclear forces
• 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
• A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
• Muon capture on deuteron and 3He

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