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I was reading this article on neutrino physics, and there's one point in the Seesaw mechanism I didn't understand:

If neutrinos have mass, the mass eigenstates need to have an admixture of left-handed and right-handed chirality.

This implies the light eigenstates having a tiny right-handed component, and the heavy ones having a tiny left-handed component too.

Wouldn't that mean they could couple to the currents of the weak force, due to that small component, even if very poorly?

Or can the flavor eigenstates have a pure chirality despite the mass eigenstates necessarily having a mix?

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    $\begingroup$ The article explains this well. If there are Majorana mass terms, which is not necessary, the seesaw mechanism dictates the light neutrinos have a teeny-tiny sterile component, and the freak heavy ones an infinitesimal active component. Sterile is the definition of decoupled from the weak force, and active means coupled to it… $\endgroup$
    – Cosmas Zachos
    Commented Nov 26 at 18:07
  • $\begingroup$ @CosmasZachos But doesn't this also happen when the Majorana mass terms are set to zero? I mean, even in a purely Dirac case, how could massive neutrinos be in a pure chiral state, as for a sterile neutrino have no left-handed, active component? $\endgroup$
    – user2934303
    Commented Nov 27 at 3:58
  • $\begingroup$ What is this pure chiral state stuff? In a pure Dirac case left fermions are active under weak interactions, and right ones are sterile. Leptons, charged or not, and quarks. What don’t you understand? $\endgroup$
    – Cosmas Zachos
    Commented Nov 27 at 5:56
  • $\begingroup$ @CosmasZachos My point is that Dirac fermions don't have a single chirality, they have both, even if at some limit they almost conserve chirality and it almost coincides with helicity. Hence, I understand calling the components active and sterile, but my question is: How could a massive neutrino be only left-handed or only right-handed? Shouldn't them always have a component of each, hence making any "sterile" neutrino not perfectly sterile? Even if it had only Dirac mass? $\endgroup$
    – user2934303
    Commented Nov 27 at 15:02
  • $\begingroup$ You might as well ask this about electrons or quarks! The mass term propagation connects sterile to active species, of course… a massive fermion is not only left or right handed. Can you rewrite your question? $\endgroup$
    – Cosmas Zachos
    Commented Nov 27 at 16:50

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