Standard Model in Differential Geometry on Discrete Space M4 × Z3
Abstract
Standard model is reconstructed using the generalized differential calculus extended on the discrete space M4 × Z3. Z3 is necessary for the inclusion of strong interaction. Our starting point is the generalized gauge field expressed as A(x, y) = Σia†i(x, y)dai(x, y), (y = 0, +/-), where ai(x, y) is the square matrix valued function defined on M4 × Z3 and d = d + dx is generalized exterior derivative. We can construct the consistent algebra of dx with the introduction of the symmetry breaking function M(y) and the spontaneous breakdown of gauge symmetry is coded in dx. The gauge field Aμ(x, y) and Higgs field Φ(x, y) are written in terms of ai(x, y) and M(y), which might suggest ai(x, y) to be more fundamental object. The unified picture of the gauge field and Higgs field as the generalized connection in noncommutative geometry is realized. Two model constructions are presented, which are distinguished in the particle assignment of Higgs field Φ(x, y). Within neglecting the Sitarz term, we can make the following predictions. The first model deduces the inequality mH <= sqrt{2}mW, whereas the second model leads to the interesting relation mH = 2sqrt{2}mWsinθW. This implies mH = 109.1 GeV if we take sin2θW = 0.233 and mW = 79.9 GeV as the experimental values.
- Publication:
-
Progress of Theoretical Physics
- Pub Date:
- September 1994
- DOI:
- 10.1143/PTP.92.625
- arXiv:
- arXiv:hep-th/9402048
- Bibcode:
- 1994PThPh..92..625O
- Keywords:
-
- High Energy Physics - Theory
- E-Print:
- 27 pages, CHU9402