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.

• The paper computes one-loop contributions to aμ in the DLRSM, including vector and scalar loops along with heavy neutrino effects.
• It employs the Casas‑Ibarra parametrization to reconcile neutrino oscillation data while constraining the symmetry breaking scale to vR > 1 TeV.
• The dominant W' boson loop establishes strict lower limits for new gauge boson masses, impacting the overall model viability.

Implications of the Muon Anomalous Magnetic Moment in a Doublet Left-Right Symmetric Model

Theoretical Framework

The paper develops a comprehensive analysis of the muon anomalous magnetic moment ($a_\mu = (g-2)_\mu/2$) within the Doublet Left-Right Symmetric Model (DLRSM), based on the gauge structure $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$, and incorporating an inverse seesaw (ISS) mechanism for neutrino mass generation. The DLRSM employs a bidoublet $\Phi$ and two doublets $\chi_{L}$ and $\chi_{R}$ in the scalar sector, allowing for parity restoration at high energies and facilitating right-handed neutrino masses at the TeV scale, which is phenomenologically accessible.

Leptons and quarks are realized as left- and right-handed doublets, and the electric charge is assigned via a generalized Gell-Mann–Nishijima formula. The implementation of the ISS introduces three additional gauge-singlet fermions $S_i$, with Yukawa couplings and mass matrices structured to naturally accommodate small active neutrino masses even when the right-handed neutrino scale is at the TeV regime. The authors utilize the Casas-Ibarra parametrization for the Yukawa sector, ensuring compatibility with neutrino oscillation data.

The gauge boson spectrum includes $W'$, $Z'$, with explicit masses derived from the model’s symmetry breaking vev $v_R$. The scalar spectrum contains multiple heavy neutral and charged states, with detailed mass formulae elucidated in the $k_1 \ll v_R$ regime appropriate for the model's phenomenology.

One-Loop Calculation of $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$0

The analysis computes the full set of one-loop topologies contributing to $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$1 in the DLRSM: VFF (vector-fermion-fermion), SFF (scalar-fermion-fermion), FVV (fermion-vector-vector), and FSS (fermion-scalar-scalar). All relevant new states—heavy gauge bosons ($SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$2), neutral and charged scalars ($SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$3, $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$4, $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$5, $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$6), and TeV-scale heavy neutrinos—are systematically included. The paper provides analytic expressions for all contributions, observing that the primary dependence of each term is through various combinations of vevs, gauge and Yukawa couplings, and the scalar potential parameter $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$7.

For the dominant $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$8 and $SU(2)_L\otimes SU(2)_R\otimes U(1)_{B-L}$9 gauge boson loops, contributions manifest as $\Phi$0 with positive (for $\Phi$1) and negative (for $\Phi$2) signs, respectively. Scalar contributions, particularly from $\Phi$3 and $\Phi$4, typically scale as $\Phi$5 and exhibit opposite signs due to different chiral structures. Charged scalar and heavy neutrino loops can yield mixed-sign contributions and are sensitive to specific parameter choices.

A crucial outcome is that in the $\Phi$6 limit, mass splittings within the heavy scalar sector become negligible, leading to partial cancellations among certain diagrams. Additionally, the leading terms involving the new scalar states are suppressed by powers of $\Phi$7 and, in some cases, by lepton masses.

Constraints from Muon $\Phi$8 and Parameter Space

The current status of the muon $\Phi$9 anomaly has evolved, with refined experimental values and lattice-QCD-based SM predictions resulting in $\chi_{L}$0, showing consistency between measurement and SM expectation (2603.28041). This null result obviates the need for a large positive new physics contribution, but instead stringently bounds new contributions to be small in magnitude.

Numerical analyses are performed, scanning the parameter space spanned by $\chi_{L}$1, $\chi_{L}$2, $\chi_{L}$3 (the small Majorana mass controlling the ISS), and $\chi_{L}$4. The fit consistently absorbs neutrino oscillation best-fit data via the Casas-Ibarra scheme. The dominant constraint arises from the $\chi_{L}$5 contribution, which overwhelmingly sets the lower limit for the symmetry breaking scale. States with $\chi_{L}$6 TeV overpredict $\chi_{L}$7, while viable points for consistent $\chi_{L}$8 appear only for $\chi_{L}$9 TeV, essentially decoupling other model parameters such as $\chi_{R}$0 and $\chi_{R}$1.

Mass bounds for the new gauge bosons and heavy neutrinos are derived: in the manifest left-right symmetric limit ($\chi_{R}$2), $\chi_{R}$3 GeV, $\chi_{R}$4 GeV, and $\chi_{R}$5 GeV. Relaxing the manifest symmetry condition ($\chi_{R}$6) enhances these lower limits significantly, with $\chi_{R}$7 GeV and $\chi_{R}$8 GeV as $\chi_{R}$9 approaches the perturbativity bound.

These findings are robust against variations in the ISS parameters and scalar sector quartics, reconfirming the dominance of the gauge sector in controlling the magnitude of new physics corrections to $S_i$0.

Implications and Outlook

This study demonstrates that precision measurements of $S_i$1 tightly constrain the symmetry breaking scale and the new particle spectrum in the DLRSM. Importantly, the result is not sensitive to the fine details of the ISS mechanism or scalar sector besides the quartic coupling $S_i$2 for the degenerate spectra considered. Thus, direct searches for $S_i$3, $S_i$4, and heavy neutrinos at hadronic colliders gain even more pertinence, with the muon $S_i$5 data effectively ruling out low-scale scenarios.

From a theoretical perspective, the DLRSM, in conjunction with the ISS, provides a UV-complete, phenomenologically viable framework for TeV-scale seesaw mechanisms, albeit now forced to higher scales by the null $S_i$6 result. The formalism and analytic approach in the paper are extendable to other gauge-extended models (e.g., 331 models), and the comprehensive calculation of all one-loop topologies sets a standard for further assessment of flavor and precision electroweak observables.

Future progress in experimental precision or possible deviations in $S_i$7 could significantly alter these constraints, while further collider results on direct production of $S_i$8, $S_i$9, or heavy neutrinos will provide complementary and, potentially, more stringent tests of the DLRSM scenario.

Conclusion

The DLRSM with inverse seesaw, when confronted with the current experimental and theoretical status of the muon anomalous magnetic moment, is forced into a parameter regime with $W'$0 TeV, and correspondingly heavy new gauge bosons and neutrinos. The gauge sector, particularly the $W'$1 boson loop, dominates the new physics contribution to $W'$2, with the scalar and heavy-neutrino sectors yielding numerically subdominant corrections. These results furnish important guidance for model building and motivate collider searches targeting the TeV-scale left-right symmetry sector (2603.28041).