Lepton Double Charge Exchange Reactions as Probes for Lepton Number Violation

Abstract

Lepton number violating (LNV) $A(e^-,e^+)X$ double charge exchange (LDCE) reactions on nuclei at accelerator facilities with multi-GeV beams are proposed as a probe for physics beyond the Standard Model (BSM). A second order formalism is presented including LNV dynamics by the left-right symmetric model (LRSM). For practical studies a phenomenological model is used to estimate LDCE cross sections numerically. Sizable cross sections are predicted for multi-GeV beam energies. LDCE reactions proceed preferentially by the energy-momentum dependent left-right mixing terms. While Majorana mass terms are negligible for light neutrinos, they may become sizable for heavy neutral leptons at higher beam energies. In the ~10 GeV region inclusive total LDCE cross sections of about $100\times|Γ_{BSM}|^2$~fb in units of the BSM vertices are predicted, increasing strongly with energy and target mass. LDCE experiments seem to be feasible with existing equipment under full laboratory control and free of the constraints imposed on decay or capture experiments of nuclear and hadronic systems.

Figures (6)

• Figure 1: Pictorial illustration of the Black Box theorem Schechter:1982dbd and its application to three physical processes, namely $0\nu\beta\beta$, $l^\pm l^\pm jj$ and LDCE, compliant with it.
• Figure 2: Nuclear $0\nu\beta\beta$ (left) and the quasi-elastic $(e^-,e^+ )$ LDCE reaction (right), both inducing a $\Delta Z=-2$ nuclear transition through t-channel exchange of massive Majorana neutrinos $\nu_i=\nu^C_i$, are compared on the quark level. The LNV vertices (filled blue ellipsoids) are denoted by $\Gamma_{BSM}$. The SM-CC vertices are indicated by filled boxes. Time is running from left to right.
• Figure 3: Feynman graph emphasizing the s-channel nature of a LDCE reaction $A\to B$ with a change of hadronic charge by $\Delta Z=-2$, illustrated for QE modes. The reaction proceeds either by virtual emission of $W^+$ bosons from the nucleus or by radiating $W^-$ bosons off weak lepton CC processes. The time order of the protons may be exchanged and short-range correlations will play a role. In practice, gauge boson propagation is replaced by contact interactions of strength $G_F\cos(\theta_C)/\sqrt{2}$ - see text.
• Figure 4: Charged current matrix elements (top) and total cross sections per nucleon and energy (bottom) for the $^{208}$Pb$(e^-,\nu_e)$X CC reaction. The QE, RE, and DI contributions as predicted by our phenomenological approach are also displayed. Statistical and systematical uncertainties of at least 20% should be added.
• Figure 5: Schematic $(e^-,e^+)$ cross-sections on a $^{16}$O and a $^{208}$Pb target as a functions of the incident beam energy, representative for the two L/R mixing components (see text). JLab (yellow) and EIC (light yellow) energy regions are marked. An uncertainty of at least 20% is expected already from the input CC matrix elements plus hardly to specify systematic contributions.