# Two-pion exchange three-nucleon potential: O(q^4) chiral expansion

## TL;DR

This paper extends the two-pion exchange three-nucleon potential to chiral order q^4, providing numerical corrections and new structures, with small impact on three-body observables, advancing theoretical nuclear physics models.

## Contribution

It introduces the q^4 chiral expansion of the TPE-3NP, including new structures and corrections based on the mplitude at O(q^3), enhancing the theoretical framework.

## Key findings

- Numerical corrections are typically smaller than 10%.
- New structures arise from loop functions or non-local gradients.
- Impact on three-body observables is small, consistent with perturbative corrections.

## Abstract

We present the expansion of the two-pion exchange three-nucleon potential (TPE-3NP) to chiral order q^4, which corresponds to a subset of all possibilities at this order and is based on the \piN amplitude at O(q^3). Results encompass both numerical corrections to strength coefficients of previous O(q^3) terms and new structures in the profile functions. The former are typically smaller than 10% whereas the latter arise from either loop functions or non-local gradients acting on the wave function. The influence of the new TPE-3NP over static and scattering three-body observables has been assessed and found to be small, as expected from perturbative corrections.