Next-to-leading order effective field theory $\Lambda N\to NN$ potential in coordinate space

TL;DR

This paper derives a detailed coordinate space potential for the $\Lambda N o NN$ weak transition within effective field theory up to next-to-leading order, aiding understanding of hypernuclear decay mechanisms.

Contribution

It provides explicit expressions and analytical coefficients for the potential, including two-pion-exchange diagrams and baryon mass differences, advancing theoretical modeling of hypernuclear weak decay.

Findings

Explicit coordinate space potential expressions provided.

Inclusion of baryon mass differences discussed.

Analytical coefficients for spin and isospin operators derived.

Abstract

The potential in coordinate space for the $\Lambda N\to NN$ weak transition, which drives the weak decay of most hypernuclei, is derived within the effective field theory formalism up to next-to-leading order. This coordinate space potential allows us to discuss how the different contributions to the potential add up at the different scales. Explicit expressions are given for each two-pion-exchange diagram contributing to the interaction. The potential is also reorganized into spin and isospin operators, and the coefficient for each operator is given in analytical form and represented in coordinate space. The relevance of explicitly including the mass differences among the baryons appearing in the two-pion-exchange diagrams is also discussed in detail.