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In this work, we study an extension of the Standard Model (SM) based on thegauge symmetry $SU(3)_C\times SU(2)_L\times U(1)_{Y'}\times U(1)_R$ where onlythe right-handed fermions have nonzero $U(1)_R$ charge and the $U(1)_Y$ weakhypercharge of the SM is identified as a combination of the $U(1)_{Y'}$ and$U(1)_R$ charges. The gauge charge assignment of the fields is constrained bythe conditions of the anomaly cancellation and the gauge invariance of theYukawa couplings. The light neutrino masses are generated via the type-I seesawmechanism where the Majorana masses of the right-handed neutrinos are relatedto the $U(1)_{Y'}\times U(1)_R$ symmetry breaking scale. Then, we discuss theconstraints on the free parameters of the model from the various currentexperiments, such as precision measurement of the total $Z$ width, $\rho$parameter, atomic parity violation of Cesium, LEP and LHC bounds. In addition,we investigate the potential of probing for the signal of the new neutral gaugeboson based on the forward-backward asymmetry for the process$e^+e^-\rightarrow\mu^+\mu^-$ which is the most sensitive mode at ILC.

A flipped $U(1)_R$ extension of the Standard Model