Dissecting Lepton Number Violating Interactions in the Left-Right Symmetric Model: $0νββ$ decay, Møller scattering, and collider searches

TL;DR

The paper analyzes lepton-number violating interactions in the left-right symmetric model by correlating neutrinoless double beta decay with parity-violating Møller scattering and collider searches for a right-handed doubly-charged scalar. It uses a chiral EFT framework to compute the $0\nu\beta\beta$ decay rate, including contributions from right-handed neutrinos and $W_L-W_R$ mixing, across regimes from heavy to light RH neutrinos. The study shows that MOLLER can surpass ton-scale $0\nu\beta\beta$ sensitivity in the $\delta_R^{++}$-dominated regime with zero mixing, but nonzero left–right mixing alters the balance between low- and high-energy probes; colliders provide crucial complementary constraints, extending reach for the right-handed sector. Overall, the work demonstrates strong complementarity between low-energy precision measurements and high-energy searches, enabling tests of LRSM scenarios and opportunities to distinguish the dominant $0\nu\beta\beta$ mechanism, even when $|(f_R)_{ee}|$ is as small as $\sim 10^{-7}$.

Abstract

In the context of the left-right symmetric model, we study the interplay of neutrinoless double beta ($0νββ$) decay, parity-violating Møller scattering, and high-energy colliders, resulting from the Yukawa interaction of the right-handed doubly-charged scalar to electrons, which could evade the severe constraints from charged lepton flavor violation. The $0νββ$ decay amplitude receives additional contributions from right-handed sterile neutrinos. The half-life, calculated in the effective field theory (EFT) framework, allows for an improved description of the contributions involving non-zero mixing between left- and right-handed $W$ bosons and those arising from exchanging a light right-handed neutrino. We find that the relative sensitivities between the low-energy (or high-precision) and high-energy experiments are affected by the left-right mixing. On the other hand, our results show how the interplay of collider and low-energy searches provides a manner to explore regions that are inaccessible to $0νββ$ decay experiments.

Figures (6)

• Figure 1: Feynman diagrams contributing to ${0\nu\beta\beta}$ decay in the LRSM. The cross vertices $(\bm\times)$ in between $W_L-W_R$ propagators denote the $W_L-W_R$ mixing.
• Figure 2: Doubly-charged scalar contributions to parity-violating Møller scattering. Notice that each vertex violates the lepton number by two units.
• Figure 3: Parameter scan of ${0\nu\beta\beta}$-decay constraints on the right-handed doubly-charged scalar mass $M_{\delta_R^{\pm\pm}}$ and the Yukawa coupling $|(f_R)_{ee}|$ in the LRSM with zero (left column) and non-zero (right column) $W_L-W_R$ mixing. The active neutrino masses are assumed in the normal hierarchy (NH), and the right-handed $W$ boson mass is chosen as $M_{W_R}=7\,\mathrm{TeV}$ (top row) and $M_{W_R}=15\,\mathrm{TeV}$ (bottom row). We take $\xi=0$ and $0.35$ for the left- and right-handed plots, respectively, and use Eq. \ref{['eq:tan_zeta__lambda_sin2beta']} to characterize the results in terms of the physical mixing angle $\zeta$. The right-handed neutrino mass $M_{N_R}$ is also displayed as a secondary vertical axis. The red points (regions above or between the solid red lines) are excluded by the most recent KamLAND-Zen results KamLAND-Zen:2022tow. The solid red lines correspond to the exclusion limits calculated using an analytical estimation (see text for discussion). The dashed magenta lines correspond to the same exclusion limits using the prospect by ton-scale experiments Agostini:2017jim.
• Figure 4: Inverse half-life $(T^{0\nu}_{1/2})^{-1}$ as a function of the Yukawa coupling $|(f_R)_{ee}|$ for zero (left) and non-zero $W_L-W_R$ mixing (right). We fix $\xi=0$ and $\xi=0.35$ for the left and right plots, respectively. We also fix the mass of the doubly-charged scalar at $M_{\delta_R^{\pm\pm}}=2000\,\mathrm{GeV}$. The two curves in the figure show the results for $M_{W_R}=7\,\mathrm{TeV}$ (blue) and $M_{W_R}=15\,\mathrm{TeV}$ (yellow). We also show the corresponding values of the mixing angle $\zeta$. The inverse half-life considering only the light left-handed neutrino contributions is shown in red. The latest KamLAND-Zen exclusion limits are represented by the grey shaded area, with the future ton-scale experiment bounds indicated for comparison.
• Figure 5: Combined sensitivities to the right-handed doubly-charged scalar mass $M_{\delta_R^{\pm\pm}}$ and the Yukawa coupling $|(f_R)_{ee}|$ in the ${0\nu\beta\beta}$-decay, MOLLER, and collider experiments in the LRSM. The normal hierarchy is assumed. We fix the mass of the $W_R$ boson to $M_{W_R}=7\,\mathrm{TeV}$ and present scenarios with zero (left) and non-zero (right) $W_L-W_R$ mixing. The right-handed neutrino mass $M_{N_R}$ is also displayed as a secondary vertical axis. The MOLLER prospect MOLLER:2014iki is shown as a dashed blue line, and ${0\nu\beta\beta}$ decay limits from current and future experiments are shown as solid red and dashed magenta lines, respectively. The figure also displays the direct searches at the LHC (solid gray), pair production prospect at the FCC-hh (dashed gray), and Bhabha scattering limits at LEP (solid orange), the CEPC (dashed green), and the FCC-ee (dashed dark green) prospects.