We derive a $U(1)_{ B-L}$-extension of the Standard Model from a generalized Connes-Lott model with algebra ${ \mathbb C}\oplus{ \mathbb C}\oplus { \mathbb H}\oplus M_3({ \mathbb C})$. This generalization includes the Lorentzian signature, the presence of a real structure, and a weakening of the order $1$ condition. In addition to the SM fields, the model contains a $Z_{ B-L}'$ boson and a complex scalar field $\sigma$ which spontaneously breaks the new symmetry. This model is the smallest one which contains the SM fields and is compatible with both the Connes-Lott theory and the algebraic background framework.
Categories: hep-th