Tritium $\beta$-decay and Proton-Proton Fusion in Pionless Effective Field Theory

TL;DR

This paper calculates the Gamow-Teller and Fermi matrix elements for tritium beta decay using pionless effective field theory at next-to-leading order, fixing key constants and exploring symmetry implications.

Contribution

It provides the first NLO calculations of these matrix elements in pionless EFT and determines the axial current low energy constant from experimental data.

Findings

NLO predictions for matrix elements are provided.

The axial current low energy constant is determined as L_{1,A}=6.01±2.08 fm^3.

Implications of Wigner-SU(4) symmetry on the Gamow-Teller matrix are discussed.

Abstract

The Gamow-Teller and Fermi matrix elements, ${\left<\mathbf{GT}\right>}$ and ${\left<\mathbf{F}\right>}$, respectively, for tritium $\beta$-decay are calculated to next-to-leading order (NLO) in pionless effective field theory in the absence of Coulomb and isospin violation giving the leading order predictions ${\left<\mathbf{GT}\right>}_{0}=0.9807$ and ${\left<\mathbf{F}\right>}_{0}=1$. Using an experimentally determined value for the tritium-$\beta$ decay GT matrix element, the two-body axial current low energy constant is fixed at NLO yielding $L_{1,A}=6.01\pm2.08$ fm$^{3}$ at the renormalization scale of the physical pion mass, which agrees with predictions based on naive dimensional analysis. Finally, the consequences of Wigner-SU(4) spin-isospin symmetry are considered for the Gamow-Teller matrix element.