https://doi.org/10.1140/epjc/s2003-01204-7
Original Paper
Non-commutative standard model: model building
1
High Energy Physics Division, Department of Physics, University of Helsinki, Helsinki, Finland
2
High Energy Physics Division, Department of Physics, Helsinki Institute of Physics, P.O. Box 64, 00014, Helsinki, Finland
3
Department of Theoretical Physics, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia
4
Department of Theoretical Physics, The Abdus Salam ICTP, Strada Costiera 11, Trieste, Italy
5
Department of Theoretical Physics, Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5531, Tehran, Iran
A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U* (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just $0, \pm 1$. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the $U_{*}(3)\times U_{*}(2)\times U_{*}(1)$ gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions.
© Springer-Verlag, 2003
