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We propose an alternative formulation of a Left-Right Symmetric Model (LRSM)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 orderto generate Majorana neutrino masses. In our case $B-L$ remains a globalsymmetry after the left-right symmetry breaking, allowing only Dirac mass termsfor neutrinos. In addition to parity restoration at some high scale, thisformulation provides a natural framework to explain $B-L$ as an anomaly-freeglobal symmetry of the Standard Model and the non-observation of$(B-L)$-violating processes. Neutrino masses are purely Dirac type and aregenerated either through a two loop radiative mechanism or by implementing aDirac seesaw mechanism.

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