Implications of the muon anomalous magnetic moment in a Doublet Left-Right Symmetric Model

Abstract

We compute the complete set of one-loop contributions to the muon anomalous magnetic moment, $a_μ=(g-2)_μ/2$, in the Doublet Left-Right Symmetric Model (DLRSM), based on the gauge group $SU(2)_{L}\otimes SU(2)_{R}\otimes U(1)_{B-L}$ with neutrino masses generated via the inverse seesaw (ISS) mechanism. We evaluate all four one-loop topologies VFF, SFF, FVV, and FSS arising from the extended gauge bosons ($W^{\prime}$, $Z^{\prime}$), the new scalar sector ($H_{3}^{0}$, $A_{1}^{0}$, $H_{R}^{\pm}$, $H_{L}^{\pm}$), and the heavy neutrino spectrum generated by the ISS mechanism, using the Casas--Ibarra parametrization to express the neutrino mixing in terms of physical observables. Imposing the experimental bound on $Δa_μ$, we establish that $v_{R}\lesssim1$ TeV is excluded, implying lower bounds $m_{W^{\prime}}\gtrsim325$ GeV, $m_{Z^{\prime}}\gtrsim385$ GeV, and $m_{N}\gtrsim700$ GeV under the manifest left-right symmetry condition $g_{R}=g_{L}$. Relaxing this condition to $g_{R}\neq g_{L}$ strengthens the gauge boson bounds to $m_{W^{\prime}}\gtrsim1625$ GeV and $m_{Z^{\prime}}\gtrsim1650$ GeV.

Figures (5)

• Figure 1: Feynman diagrams for neutral exchange bosons SFF (left) and VFF (right) topologies
• Figure 2: Feynman diagrams for the FSS (left) and FVV (right) topologies
• Figure 3: Dependence of $\Delta a_{\mu}$on the Yukawa coupling $Y_{R}$, with $v_{R}=10$ TeV, $\alpha_{23}=10^{-6}$, $\mu_{X}=1$ MeV. Left: Individual contributions $|\Delta a_{\mu}^{i}|$. Right: Total prediction $\Delta a_{\mu}^{\text{DLRSM}}$ with experimental bands.
• Figure 4: Dependence of $\Delta a_{\mu}$ on the symmetry breaking scale $v_{R}$, with $Y_{R}=0.1$, $\alpha_{23}=10^{-6}$, $\mu_{X}=1$ MeV. Left: Individual contributions $|\Delta a_{\mu}^{i}|$. Right: Total prediction $\Delta a_{\mu}^{\text{DLRSM}}$ compared to experimental bands.
• Figure 5: Results of a multi-parameter random scan projected onto the planes of $(v_{R},Y_{R})$ (left), $(v_{R},\mu_{X})$ (center), and $(v_{R},\alpha_{23})$ (right). Points are color-coded based on their consistency with the experimental measurement of $\Delta a_{\mu}$: green points lie within the $1\sigma$ band, orange points within the $2\sigma$ band, and gray points fall outside the $2\sigma$ allowed region. The clear stratification demonstrates that the viability of the DLRSM solution is primarily determined by the symmetry breaking scale $v_{R}$, favoring a window starting at approximately $1$ TeV, largely independent of the specific values of the other model parameters.