Reaction Studies of Lepton Number Violation

Abstract

Nuclear isotensor spectroscopy as accessible in nuclear double charge exchange (DCE) reactions is indispensable for quantitative studies of lepton number violation as in double beta decay (DBD). For such studies heavy ion double single charge exchange (DSCE) and direct Majorana double charge exchange (MDCE) reactions are discussed. Isotensor two-body transition densities are investigated for the first time. Pion-potentials, mirroring neutrino potentials, and isotensor short range correlations are explored. Lepton DCE (LDCE) reactions on nuclei at accelerators are introduced as a promising new approach to investigate lepton number violation.

Figures (5)

• Figure 1: Feynman diagrams of the DSCE (left) and the MDCE (right) reaction mechanisms contributing to a DCE reaction $A+A'\to B+ B'$ and the respective four-momenta $k_{A,B}$ and $k_{A',B'}$. NN isovector T-matrices are indicated by filled circles (left), pion-nucleon T-matrices are depicted by grey boxes (right).
• Figure 2: The MDCE pion potentials $U_{00}$ and $U_{22}$ defining the strength of the double-Fermi and the double-Gamow-Teller components, evaluated in the collinear limits for $p_1=p_2=400$ MeV(c. Magnitude and shape are almost independent of the external momenta and the nuclear masses (from Garofalo:2024mth).
• Figure 3: Momentum space isotensor two-body transition density of the double-Fermi spin-scalar component for the DCE transition $^{76}$Se$\to{}^{76}$Ge as function of the momenta $\mathbf{p}_{1,2}$ transferred in the 1$^{st}$ and 2$^{nd}$ SCE step, projected to the total momentum transfer $\mathbf{q}$. Note that the momenta extend over $\pm 400$ MeV/c (from Bellone:2025ada).
• Figure 4: The Feynman diagrams, with LNV-vertices $\Gamma_{BSM}$, for the t-channel capture (center) and the s-channel scattering (right) LDCE processes on a proton pair are compared to the MDBD decay diagram (left). Up- and down-quarks are denoted by red and blue lines, respectively.
• Figure 5: LDCE total cross sections for $e^- + {}^{208}$Pb$\to e^+ + X$ where $X$ is constrained only by the total charge $Z_X=Z-2=80$ and fixed baryon number $A=208$. Cross sections are given in units of the unknown dimensionless LNV parameter $\Gamma_{BSM}$. Cross section in the energy range available at Jefferson Laboratory (green) and at the planned Electron-Ion-Collider EIC (yellow) are marked. The enclosed area indicates uncertainties on relative phases only.