The Born series for $S$-wave quartet $nd$ scattering at small cutoff values

TL;DR

This paper investigates the use of the Born series expansion in pionless effective field theory to accurately compute neutron-deuteron scattering parameters at small cutoff values, demonstrating effective approximations with few terms.

Contribution

It introduces a renormalized three-body contact interaction and applies the inverted Born series to improve convergence at moderate cutoff values.

Findings

The inverted Born series reproduces scattering length and phase shift well with few terms.

Good agreement achieved at cutoff values around 100 MeV.

Method enhances perturbative calculations in three-body scattering.

Abstract

Perturbative expansions, the Born series, of the scattering length and the amplitude of $S$-wave neutron-deuteron scattering for spin quartet channel below deuteron breakup threshold are studied in pionless effective field theory at small cutoff values. A three-body contact interaction is introduced when the integral equation is solved using the small cutoffs. After renormalizing the three-body interaction by using the scattering length, we expand the integral equation as the ordinary and inverted Born series. We find that the scattering length and the phase shift are considerably well reproduced with a few terms of the inverted Born series at relatively large cutoff values, $\Lambda\simeq 100$ MeV.