The momentum-space topological invariants, which characterize the ground state of the Standard Model, are continuous functions of two parameters, generated by the hypercharge and by the weak charge. These invariants provide the absence of the mass of the elementary fermionic particles in the symmetric phase above the electroweak transition (the mass protection). All the invariants become zero in the broken symmetry phase, as a result all the elementary fermions become massive. Relation of the momentum-space invariants to chiral anomaly is also discussed.
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Univ Tokyo, Dept Appl Phys, Bunkyo Ku, Tokyo 1138656, JapanUniv Tokyo, Dept Appl Phys, Bunkyo Ku, Tokyo 1138656, Japan
Ishizuka, Hiroaki
Hayata, Tomoya
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Chuo Univ, Dept Phys, Bunkyo Ku, 1-13-27 Kasuga, Tokyo 1128551, JapanUniv Tokyo, Dept Appl Phys, Bunkyo Ku, Tokyo 1138656, Japan
Hayata, Tomoya
Ueda, Masahito
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Univ Tokyo, Dept Phys, Bunkyo Ku, Tokyo 1130033, Japan
RIKEN, Ctr Emergent Matter Sci CEMS, Wako, Saitama 3510198, JapanUniv Tokyo, Dept Appl Phys, Bunkyo Ku, Tokyo 1138656, Japan