# If a neutrino and his antineutrino has different helicity how can it be a possibility that it is a Majorana particle?

All antineutrinos observed thus far possess right-handed helicity (i.e. only one of the two possible spin states has ever been seen), while neutrinos are left-handed.

Notwithstanding that it is said that because antineutrinos and neutrinos are neutral particles, it is possible that they are the same particle. Particles that have this property are known as Majorana particles.

Majorana neutrinos have the property that the neutrino and antineutrino could be distinguished only by chirality; what experiments observe as a difference between the neutrino and antineutrino could simply be due to one particle with two possible chiralities.

Now helicity and chirality are not the same for mass-particles. So if it is true that there are two kinds of helicity how is it possible that a neutrino could be a Majorana particle?

http://en.wikipedia.org/wiki/Neutrino#Antineutrinos

The answer on such problem is following.

No anti- in the case of Majorana particle

First, if we include the mass term (here it is not important - Majorana or Dirac) of neutrino, then we necessarily come to the statement that the neutrino can be of two helicities.

Second, since Majorana fermion is $$\nu_{M} = \nu + \nu^{c},$$ where $c$ operation is charge conjugation, then fermion and antifermion are the same. Thus we don't distinguish neutrino and antineutrino in the case if neutrino is Majorana fermion.

There is also one additional remark. The charge conjugation of left particle gives right antiparticle, so there is no problem with chirality.

Why Majorana nature of neutrino doesn't contradict the experiment

We thus follow to the statement that neutrino, if it is Majorana one, may be as well left-handed as right-handed. This, however, doesn't contradict the statement that mostly only left-handed (in a sense left-helicity) neutrino interacts (and thus somehow may be detected). This is true because of two facts.

First, if the mass of given particle $\nu$ is small, then this particle is relativistic in most processes which involve it and other particles with masses much larger than $m_{\nu}$. In relativistic limit helicity coincides with chirality; namely, helicity flipping rate is proportional to $\left(\frac{m_{\nu}}{E_{\nu}}\right)^{2}$, with $E_{\nu}$ being the energy of $\nu$. We may therefore conclude, that ultrarelativistic particle has definite helicity which is defined by its chirality.

Second, the Standard model weak sector contains interaction, in which electron interacts only with left-chiral neutrino (while the positron interacts with right chiral). Let's unify these facts. If we have process in which electron and neutrino creates, then due to small neutrino mass and thus its ultrarelativistic motion it will be left-handed (in a sense of helicity) in "99.9%" of interactions.