By Bloom S. L.

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This means that the inner parity of a Majorana particle is imaginary, η P = ±i if λC = ±1. 34) † because γ5 ψ¯ M = (γ5 ψ M )† γ0 = ψ M γ5 γ0 = −ψ¯ M γ5 . 27) one concludes that an eigenstate to C cannot be at the same time an eigenstate to chirality. A Majorana neutrino, therefore, has no fixed chirality. However, because ψ and ψ c obey the Dirac equation, ψ M will also do so. For a discussion of T transformation and C, C P and C PT properties, see [Kay89, Kim93]. 4 Dirac and Majorana mass terms Consider the case of free fields without interactions and start with the Dirac mass.

Had Assuming again lepton-universality, which is justified by the equality of the measured leptonic decay width, the number of neutrino flavours can be determined as Nν = inv l l ν = SM 12π Rl 0 m 2Z σhad − Rl − 3 l ν . 41) SM This form is chosen because in this way radiative corrections are already included in the Standard Model (SM) prediction. 42) can be deduced [PDG02], in excellent agreement with the theoretical expectation of three. Chapter 2 Properties of neutrinos In quantum field theory spin- 12 particles are described by four-component wavefunctions ψ(x) (spinors) which obey the Dirac equation.

45): Ä 2 = m 1 φ¯1 φ1 + m 2 φ¯2 φ2 . 58) From this general discussion one can take some interesting special aspects: (1) m L = m R = 0 (θ = 45◦ ), resulting in m 1,2 = m D and Majorana eigenstates, two degenerated states emerge: 1,2 1 1 φ1 = √ (ψ L − ψ Rc − ψ Lc + ψ R ) = √ (ψ − ψ c ) 2 2 1 1 c c φ2 = √ (ψ L + ψ R + ψ L + ψ R ) = √ (ψ + ψ c ). 2 2 = ∓1. 43). 43) result. Properties of neutrinos 28 These can be used to construct a Dirac field ψ: 1 √ (φ1 + φ2 ) = ψ L + ψ R = ψ. 58) is (because φ¯1 φ2 + φ¯2 φ1 = 0) ¯ Ä = 12 m D (φ¯1 + φ¯2)(φ1 + φ2) = m D ψψ.

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