Scalar portal effective Lagrangian Sample Clauses

Scalar portal effective Lagrangian. The general renormalizable SM Lagrangian with a new (CP-even) scalar particle added to the Standard Model (SM) is given by 1 µ 2 † 2 3 4 SM 2 µ 1 2 L = L + ∂ S∂ S + (α S + αS )(H H) + λ S + λ S + λ S , (2.1.1) where S is the new light scalar particle coupled to the Xxxxx doublet H with coupling constants α1, α, and λ2, λ3, λ4 are self-interaction coupling constants of the scalar S. There are two main properties of the Lagrangian (2.1.1) that make it noticeable from the point of view of connection to the hidden sector. Firstly, it contains only renormalizable terms, which means that its phenomenological relevance is not sup- pressed by the energy scale of the new physics. Secondly, as dark matter seems to be not charged under SM interactions, the singlet scalar gives a simple possibility to directly connect dark matter to SM trough this portal. After the spontaneous symmetry breaking, the Xxxxx doublet chooses the follow- ing vacuum,  0    H = v + h , (2.1.2) √2 where v is the vacuum expectation value and h is the Xxxxx boson field. Thus, substituting it into the initial Lagrangian (2.1.1) we get, 1 µ α1 2 α 2 2 2 α1v2S + (αv2 + 2λ2)S2 L = LSM +2 ∂µS∂ h +2vS h)+α1vSh+ +.... (2.1.3) The last term can be written in a form of a mass term as α1v2S + (αv2 + 2λ2)S2 αv2 + 2λ2 = ˜ m2 ˜ S2 + c = − S 2S + c, (2.1.4) S
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