What if an electron hitting a nucleus could come out as a positron, changing the nucleus by two units of charge? That is the basic idea of a Lepton Double Charge Exchange (LDCE) reaction, written A(e−,e+)X, and this paper proposes using such reactions as a way to search for lepton number violation (LNV). Lepton number is a rule of the Standard Model of particle physics that counts leptons (electrons, muons, neutrinos). If that rule is broken, it would be a clear sign of new physics beyond the Standard Model (BSM). The authors argue LDCE reactions at accelerator energies of order 10 GeV or more could provide a clean, controllable laboratory probe of LNV that complements other searches like neutrinoless double beta decay and collider experiments.

The researchers present a theoretical framework that treats the LDCE process as a second‑order weak interaction. They embed LNV effects using the left–right symmetric model (LRSM), a popular BSM idea that treats left‑handed and right‑handed weak currents on similar footing. Practically, the paper uses a phenomenological model to estimate cross sections. Those estimates include contributions from a wide range of nuclear reactions: quasi‑elastic scattering, excitation of nucleon resonances, and deep‑inelastic scattering. The inclusive total LDCE cross section (counting events with the emitted positron) is calculated by integrating over these final states.

The numerical results reported are encouraging for searches. At beam energies near 10 GeV the authors predict inclusive LDCE cross sections of order 100 × |Γ_BSM|^2 femtobarns, where |Γ_BSM| is a factor representing the strength of the unknown BSM interaction. The cross section grows strongly with beam energy and with target mass. The authors also find LDCE reactions are driven mainly by energy‑ and momentum‑dependent left–right mixing terms in the LRSM. Ordinary Majorana mass terms (the kind that make neutrinos their own antiparticles) are negligible for very light neutrinos at these energies, but they could become important if heavy neutral leptons (HNLs) with masses of order 100 GeV exist; in that case mass effects are no longer suppressed and can enhance the signal.