The s-wave pi d scattering length from pi d atom using effective field theory

TL;DR

This paper derives the s-wave pi d scattering length from the energy-level shift of pionic deuterium using effective field theory, considering the deuteron as a vector particle and applying a zero-range interaction model.

Contribution

It introduces a novel effective field theory approach to relate the energy shift in pionic deuterium to the s-wave scattering length, incorporating the deuteron's vector nature.

Findings

Derived a Deser-type formula linking energy shift and scattering length.

Modeled deuteron as a vector field in the effective field theory.

Applied zero-range approximation for strong interaction.

Abstract

The pi- d atom strong energy-level shift in the 1s state is derived by using the effective field theory. Taking into account the large value of radius of pionic deuterium and short radius of strong interaction between pion and deuteron we have considered deuteron as particle described by vector field. Pion is described by scalar field. To obtain non-relativistic Hamiltonian for pi d system Foldy-Wouthuysen transformation has been derived for the vector field. The strong interaction between pion and deuteron has been taken at the zero-range approach. We have found the Deser type formula for relation between the strong energy-level shift and the s-wave pi d scattering length.