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In [2], Weinberg also suggested the global U (1) symmetry is the WIMP number by adding in the model one single Dirac field ψ with W = + 1 while the S field has W = + 2 so that its VEV leaves an unbroken Z 2 symmetry ψ → - ψ. The physical spectrum will contain two Majorana fields w ±. The one with lighter mass w - could then be the dark matter candidate which has an interaction - f θ 2 w - ̄ w - H with the Higgs boson through mixing. If 2 m w - < m H, it will contribute to the invisible Higgs decay width as Γ H → w - ̄ w - = (1 / 16 π) (f g âŸ̈⟩ âŸ̈ r ⟩ / (m H 2 - m σ 2)) 2(m H 2 - 4 m w - 2) 3 / 2. The exponent 3/2 reflects the P-wave feature of the decay amplitude. We do not include this in our analysis since more free parameters are necessary to bring in.
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In [2], Weinberg also suggested the global U (1) symmetry is the WIMP number by adding in the model one single Dirac field ψ with W = + 1 while the S field has W = + 2 so that its VEV leaves an unbroken Z 2 symmetry ψ →-ψ. The physical spectrum will contain two Majorana fields w ±. The one with lighter mass w-could then be the dark matter candidate which has an interaction-f θ 2 w-̄ w-H with the Higgs boson through mixing. If 2 m w-< m H, it will contribute to the invisible Higgs decay width as Γ H → w-̄ w-= (1 / 16 π) (f g âŸ̈⟩ âŸ̈ r ⟩ / (m H 2-m σ 2)) 2(m H 2-4 m w-2) 3 / 2. The exponent 3/2 reflects the P-wave feature of the decay amplitude. We do not include this in our analysis since more free parameters are necessary to bring in.
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