Avoiding Blindness in Baryon Number Violating Processes: Free-Beam and Intranuclear Paths to Neutron-Antineutron Transitions

Experimental searches for neutron--antineutron ($n \rightarrow \bar n$) transitions can be considered via two approaches: conversion in free-neutron beams and intranuclear transformation leading to matter instability in large-mass detectors. Plans for next-generation searches make it timely to highlight the complementarity, necessity, and limitations of each method. Converting the bound neutron limit into one for free neutrons traditionally utilizes nucleus-specific estimates of the in-medium suppression of $n \rightarrow \bar n$, obtained within mean-field theory under a single-operator assumption. This paper highlights how this suppression can be scenario-dependent, which can lead to deviations from the standard approach that can span several orders of magnitude. A further goal of the paper is to point out the need for a broader phenomenology program for $n\rightarrow \bar{n}$ that is akin to those developed for electric dipole moments and other systems for which short-distance new physics must be studied in-medium.