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... R.Plaga1
plaga@mppmu.mpg.de, see http://hegra1.mppmu.mpg.de/majorana for additional material on this manuscript
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... phenomenology2
An example where this is obvious is e.g. a Weyl neutrino and a massless electron.
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... field3
I do not discuss the possible case of Dirac neutrino masses in this paper.
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... defined4
I do not explicitely include the condition of fermion number conservation in this definition, as is sometimes done in the literature.
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... 15
This defining constraint for Majorana fields (``Majorana neutrinos are eigenstates of C'') is universally accepted in the literature, also after the discovery of parity violation (e.g. eq.(19) in Pauli's paper[4] written after the discovery of parity violation, or e.g. eq.(10) in Ref.[5]). Even if one prefers Kayser's alternative characterization of Majorana neutrino as a state that is turned into itself with reversed helicity under CPT [3], eq.(2) has to hold. E.g. in a textbook by Mohapatra and Pal [6] the CPT properties of Majorana neutrinos are derived in section 4.4.3 using their eq.(4.16) which is identical to eq.(2). Berestetskii et al.[7] argue that there is no problem with condition (2) even in the presence of weak interactions because it is invariant not only to CPT but also with respect to each of these transformations seperately.
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...kayb,mannheim,fukugita,lee,roman2 6
Only Bilenky and Petcov[12] leave the factor 1/$\sqrt{2}$ out, for reasons that are not clear (they quote Ref.[8] that does use it as standard reference for the definition of a Majorana fermion.)
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... transformation7
The explicit form of U$_1$ can be found in Refs.[13,9]
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... (h=helicity)8
The Pauli I transformation of $\nu_L$ is $U_1 \nu_L U_1^{-1} = U_1 P_L \nu U_1^{-1} \neq P_L (U_1 \nu U_1^{-1}) $
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