Alternative formulation of left-right symmetry with $B-L$ conservation and purely Dirac neutrinos

We propose an alternative formulation of a left-right symmetric model where the difference between baryon number ($B$) and lepton number ($L$) remains an unbroken symmetry. This is unlike the conventional formulation, where $B-L$ is promoted to a local symmetry and is broken explicitly in order to generate Majorana neutrino masses. In our case $B-L$ remains a global symmetry after the left-right symmetry breaking, allowing only Dirac mass terms for neutrinos. In addition to parity restoration at some high scale, this formulation provides a natural framework to explain $B-L$ as an anomaly-free global symmetry of the Standard Model and the nonobservation of ($B-L$)-violating processes. Neutrino masses are purely Dirac type and are generated either through a two-loop radiative mechanism or by implementing a Dirac seesaw mechanism.

Figure 1

Two-loop radiative diagram generating Dirac neutrino masses.

Figure 2

Numerical solutions for $2\times 2$ mixing simultaneously fitting Eqs. (29) and (30) for the case of normal ordering of neutrino masses: (top left) $SU(2{)}_R$ breaking scale $u_R$, (top right) $2\times 2$ PMNS mixing angle, (middle left) the arbitrary rotation matrix angles in ${\mathcal{R}}_l$, (middle right) the arbitrary rotation matrix angles in ${\mathcal{R}}_{\nu }$, and (bottom) the maximal element of the Yukawa matrix $\mathbf{h}$, as a function of the mass difference between two generations of vector-like charged lepton masses $\mathrm{\Delta }{m}_E$ for different benchmark values of $m_B$. See text for the benchmark values of the other relevant parameters.

Figure 3

Numerical solutions for $2\times 2$ mixing simultaneously fitting Eqs. (29) and (30) for the case of inverted ordering of neutrino masses: (top left) $SU(2{)}_R$ breaking scale $u_R$, (top right) $2\times 2$ PMNS mixing angle, (middle left) the arbitrary rotation matrix angles in ${\mathcal{R}}_l$, (middle right) the arbitrary rotation matrix angles in ${\mathcal{R}}_{\nu }$, and (bottom) the maximal element of the Yukawa matrix $\mathbf{h}$, as a function of the mass difference between two generations of vector-like charged lepton masses $\mathrm{\Delta }{m}_E$ for different benchmark values of $m_B$. See text for the benchmark values of the other relevant parameters.