A U(1)B−L-extension of the standard model from noncommutative geometry

We derive a U(1)B−L-extension of the standard model from a generalized Connes–Lott model with algebra C⊕C⊕H⊕M3(C). This generalization includes the Lorentzian signature, the presence of a real structure, and the weakening of the order 1 condition. In addition to the SM fields, it contains a ZB−L′ boson and a complex scalar field σ that spontaneously breaks the new symmetry. This model is the smallest one that contains the SM fields and is compatible with both the Connes–Lott theory and the algebraic background framework.