A low-energy perspective on the minimal left-right symmetric model

Abstract: We perform a global analysis of the low-energy phenomenology of the minimal left-right symmetric model (mLRSM) with parity symmetry. We match the mLRSM to the Standard Model Effective Field Theory Lagrangian at the left-right-symmetry breaking scale and perform a comprehensive fit to low-energy data including mesonic, neutron, and nuclear $\beta$-decay processes, $\Delta F=1$ and $\Delta F=2$ CP-even and -odd processes in the bottom and strange sectors, and electric dipole moments (EDMs) of nucleons, nuclei, and atoms. We fit the Cabibbo-Kobayashi-Maskawa and mLRSM parameters simultaneously and determine a lower bound on the mass of the right-handed $W_R$ boson. In models where a Peccei-Quinn mechanism provides a solution to the strong CP problem, we obtain $M_{W_R} \gtrsim 5.5$ TeV at $95\%$ C.L. which can be significantly improved with next-generation EDM experiments. In the $P$-symmetric mLRSM without a Peccei-Quinn mechanism we obtain a more stringent constraint $M_{W_R} \gtrsim 17$ TeV at $95\%$ C.L., which is difficult to improve with low-energy measurements alone. In all cases, the additional scalar fields of the mLRSM are required to be a few times heavier than the right-handed gauge bosons. We consider a recent discrepancy in tests of first-row unitarity of the CKM matrix. We find that, while TeV-scale $W_R$ bosons can alleviate some of the tension found in the $V_{ud,us}$ determinations, a solution to the discrepancy is disfavored when taking into account other low-energy observables within the mLRSM.