| Summary: | Connes’ non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U{{(1)}_{B-L}}$ gauge symmetry, and a single extra complex scalar field σ , which is a singlet under $SU{{(3)}_{C}}\times SU{{(2)}_{L}}\times U{{(1)}_{Y}}$ , but has $B-L=2$ . This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.
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