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If a neutrino has mass it must travel at less than the speed of light. So how can it possess helicity, which can change depending on relative velocity?

Qmechanic
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    Have a look at this http://physics.stackexchange.com/q/1111/ – anna v Mar 01 '16 at 10:38
  • Good question. If there is a nonvanishing mass, there is the rest frame and therein the helicity does vanish! I think an answer could be related to the fact that the neutrino mass is not defined in quantum sense (its operator does not commute with the Hamiltonian). – Valter Moretti Mar 01 '16 at 12:55
  • @annav The link you provide does not actually explain, except to say spin and helicity are related –  Mar 01 '16 at 13:00
  • look up chirality https://en.wikipedia.org/wiki/Chirality_%28physics%29 – anna v Mar 01 '16 at 15:02
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    @anna v Yes, but I cannot see the answer to the question there. How can helicity be defined (independent form the reference frame) if the particle has mass? – Valter Moretti Mar 01 '16 at 15:21
  • From the link "For massless particles—such as the photon, the gluon, and the (hypothetical) graviton—chirality is the same as helicity; a given massless particle appears to spin in the same direction along its axis of motion regardless of point of view of the observer." – anna v Mar 01 '16 at 17:11
  • "For massive particles—such as electrons, quarks, and neutrinos—chirality and helicity must be distinguished. In the case of these particles, it is possible for an observer to change to a reference frame that overtakes the spinning particle, in which case the particle will then appear to move backwards, and its helicity (which may be thought of as 'apparent chirality') will be reversed." – anna v Mar 01 '16 at 17:12
  • I think this is an excellent answer to this puzzling question. Actually neutrinos haven’t a definite helicity, so that when the boost reverse the momentum of the particle the dominant spin component is also the flipped one. https://physics.stackexchange.com/questions/371983/spin-up-with-indefinite-helicity/372019#372019 – Tetis Sep 07 '18 at 22:03

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Helicity is well-defined for both massive and massless particles, as far as we keep the velocity $v>0$. See, M. Jacob and G. C. Wick, Annals of Physics 281, (2000), 774-799

Wen Chern
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  • The helicity can be defined as $\vec{S}\cdot \vec{P}/P^0$ in both cases. For massive particles it depends on the reference frame and can be reversed. For massless particles it cannot be reversed and is a intrinsic property of the particle. The question is what is the meaning of statements like "the helicity of a neutrino is such" (see,e.g. here https://en.wikipedia.org/wiki/Neutrino#Mass at the item Chirality) when it is not an intrinsic property. The spin should be the relevant intrinsic property. Otherwise we could speak about helicity of electrons as an intrinsic property of them. – Valter Moretti Mar 01 '16 at 15:29
  • The weak interaction of electrons does depend on the helicity. See, for instance, the results of the $G^0$ experiment. The reason that we don't talk about it much is that the weak interactions are dominated by electromagnetic ones in most settings, but neutrinos only interact weakly so their leading interaction shows the oddities of the weak force. – dmckee --- ex-moderator kitten Mar 01 '16 at 15:31
  • @dmckee I do not understand anyway. Are you saying that the electron has a definite helicity? – Valter Moretti Mar 01 '16 at 15:34
  • @ Valter Moretti , Helicity is conserved even for massive particles, as far as we keep $v>0$. Just take look at the literature just mentioned. – Wen Chern Mar 01 '16 at 15:34
  • I'm saying you can construct an experiment that can tell the difference between and electron beam with helicity + from one with helicity - by taking advantage of the helicity dependence of the weak interaction. That is, that an electron can have a definite helicity in a particular interaction. – dmckee --- ex-moderator kitten Mar 01 '16 at 15:36
  • @ dmckee I understand. So also a fixed type of neutrinos can be prepared with different helicity values? – Valter Moretti Mar 01 '16 at 15:37
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    That depend on the nature of neutrinos. It's obviously true if neutrinos are Majorana (because we experiment with both matter and anti-matter neutrinos which would be the two states of a single particle) and not technologically feasible if neutrinos are Dirac (because then we need to boost to very high relative velocities to get a helicity reversal). – dmckee --- ex-moderator kitten Mar 01 '16 at 15:44
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    @Wen Chern Thanks. The point is that, if I understand well what you are saying, I can always fix a reference frame where $v<0$ reversing the helicity. On the other hand, if the particle is massless, I cannot. In this sense the helicity is intrinsic for massless particles. – Valter Moretti Mar 01 '16 at 15:44
  • @dmckee Thanks! So, if the neutrinos are massive and Majorana, their helicity is an intrinsic property. If, conversely they are Dirac, barring the lack of electric charge they are just like small and quick electrons and thus, in principle their helicity can be reversed changing our reference frame. Am I correct? And is it still unknown the nature Majorana / Dirac of neutrinos? – Valter Moretti Mar 01 '16 at 15:48