Critical Examination of the "Field-Theoretical Approach" to the Neutron-Antineutron Oscillations in Nuclei

TL;DR

This paper clarifies misconceptions about infrared divergences in neutron-antineutron oscillations, showing they do not occur with proper analytical treatment, and demonstrates strong suppression of these oscillations in nuclei compared to vacuum.

Contribution

It provides a correct analytical approach to neutron-antineutron oscillations in nuclei, refuting previous claims of infrared divergences and quantifying suppression effects.

Findings

Infrared divergences do not appear with proper amplitude analysis.

Neutron-antineutron oscillations are strongly suppressed in nuclei.

Field theoretical methods have advantages and challenges in nuclear processes.

Abstract

We demonstrate that so called "infrared divergences" which have been discussed in some publications during several years, do not appear within the correct treatment of analytical properties of the transition amplitudes, in particular, of the second order pole structure of the amplitudes describing the $n - \bar n$ transition in nuclei. Explicit calculation with the help of the Feynman diagram technique shows that the neutron-antineutron oscillations are strongly suppressed in the deuteron, as well as in heavier nuclei, in comparison with the oscillations in vacuum. General advantages and some difficulties of the field theoretical methods applied in nuclear theory are reminded for the particular example of the parity violating $np\to d\gamma$ capture amplitude.