Chiral $3\pi$-exchange potential using the method of unitary transformation

TL;DR

This paper analyzes the chiral three-pion exchange nucleon-nucleon potential using the method of unitary transformation, highlighting scheme dependence and differences from previous approaches, with analytical expressions and numerical discussions.

Contribution

It provides a new derivation of the 3π-exchange potential using unitary transformation, revealing scheme-dependent differences from prior Kaiser results.

Findings

Analytical expressions for the 3π-exchange potential are derived.

Differences from Kaiser’s S-matrix matching results are identified.

Numerical importance of scheme-dependent contributions is discussed.

Abstract

Nuclear potentials are known to exhibit a considerable degree of scheme dependence. For one- and two-pion exchange nucleon-nucleon (NN) potentials, unitary ambiguities start showing up at the level of the leading relativistic corrections to the dominant static contributions. However, for the three-pion exchange potential, scheme-dependent contributions are expected to appear already at the static level. Here, we analyze the leading and subleading chiral $3\pi$-exchange NN potentials using the method of unitary transformation. In line with the expectations, our results for selected classes of contributions differ from those obtained by Kaiser using S-matrix matching. We present analytical expressions for the $3\pi$-exchange potential, which are off-shell consistent with the interactions used by the Bochum group, and discuss the numerical importance of the observed differences.