CERN develops a project for explore what's beyond matter and what's beyond the spacetime, and its results are reasonable possible for the existence of things beyond matter and what's beyond the spacetime

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CERN develops a project for explore what's beyond matter and what's beyond the spacetime, and its results are reasonable possible for the existence of things beyond matter and what's beyond the spacetime. For example, if there's only 5 dimensions, how to explore them? Or some phenomena like parallel universes, or other dimensions or parallel worlds?
CERN is a good place to discuss about these kind of things, I guess.

In the paper I want to discuss, they used a neutrino telescope in the sea. It means if you are in the water, you can detect particles. Neutrinos can travel everywhere. So, if there is something in the sea, you can detect its presence. There is still a problem in this experiment: neutrinos have two types, neutrino mass and left/right-handed.
They used the Super-Kamiokande, which is able to distinguish the type of neutrino mass (Left/Right-handed). This is great.
But, if we want to discuss something about the "other side of matter" and "other side of spacetime", we must separate two type of neutrino mass, right/left-handed and particle/anti-particle.
I suggest that we must separate particle and anti-particle of neutrino. Otherwise, we can't understand what's behind this "other side of matter". We can't find any other dimensions, right? Because if neutrino is not particle, there must be dimension about "other side of matter" and "other side of spacetime".
It's possible to discover neutrino with anti-particle. It's possible to construct a detector to distinguish anti-particle and particle. To detect anti-particle, we should go to anti-particle world.

We are on the border of two worlds, or two states of existence. We must use the state of "particle" to see "other side of matter". We need to go to particle state, or use some device which is able to interact with "other side of matter", not "this side of matter".
In short, the neutrino is neither particle nor anti-particle.
However, if we consider the neutrino to be a particle, then the problem is solved. We can distinguish "left-handed" particle from "left-handed" anti-particle.

In this case, we need to separate one particle and one anti-particle, so that we can observe left-handedness and right-handedness.
We need to construct a particle detector, which can distinguish a left-handed particle from a left-handed anti-particle. We can use anti-matter detector to detect left-handed particle.
If we use anti-particle detector, it's impossible to find the particle left-handedness. Therefore, if neutrino is particle, we should separate one neutrino from anti-neutrino and detect it with particle detector.
In other words, it's possible to find a way to separate one neutrino from anti-neutrino, and the neutrino left-handedness and anti-neutrino right-handedness. However, we should understand "neutrino" first.

So, I am just trying to ask for the meaning of it is. If it's an anti-particle of electron, the electron left-handedness and right-handedness can't be observed. In other words, neutrino can't be anti-particle of electron.

A:

Neutrino has both right-handed and left-handed components: a right-handed neutrino and a left-handed neutrino. As you know, particles with both right-handed and left-handed components can be treated as two-component objects, in analogy with spin states, but in 3+1 dimensions (3 spatial dimensions + one time dimension) instead of 2. A state vector $psi$ can be written
begin{align}
psi &= psi_L + psi_R, \
psi_R &= i sigma_2 psi_L, \
psi_L &= i sigma_2 psi_R.
end{align}
The spin of the state vector is $S = 1/2$, but you can also add an operator $L_z$ to get the total angular momentum $J_z = S + L_z$ with $J_z = 1/2$ and $J_z = -1/2$ states. The neutrino left-handed component $psi_L$ has the right helicity and the right spin and has $J_z = +1/2$, while the right-handed component $psi_R$ has the left helicity and the left spin and has $J_z = -1/2$.
There is no right-handed neutrino because there is no left-handed anti-neutrino, and vice versa. However, you can have neutrinos with both left-handed and right-handed components. This is sometimes called a Majorana neutrino.
Because the leptons (including neutrinos) are Dirac particles (meaning that they have the left-handed and right-handed components), it's a different story for the quarks.
Right-handedness is not a physical property. So if you see a neutrino that is right-handed, it is simply an unfortunate accident of the way the experiments have been designed.

A:

Left handed and right handed neutrinos are Dirac particles, meaning that they do not have any associated antiparticles, like in the Standard Model. In the Standard Model, left and right-handed components of a fermion are related by a simple "Hermitian conjugation" (which flips sign to a fermion with negative-energy, and multiplies the fermion's charge by -1). This is a consequence of the fact that the interaction between the fermion and the gauge boson $A^mu$ are linear in the fields of the theory, and is what ensures that electric charge is conserved. However, neutrinos do not interact with gauge bosons at all, and the weak interaction of neutrinos with charged leptons is mediated by the weak interaction, whose charge is (as we see in the Standard Model) $-2/3$, thus we do not have a similar operation that takes our Hermitian-conjugate charged leptons to a Hermitian-conjugate right-handed neutrino (which you could call a right-handed antineutrino), and we do not flip the weak charge. Thus, neutrinos are left-handed, in the sense that the standard model charge assigned to the weak interaction of the fermion, does not change sign when flipping our fermion to a Dirac fermion with negative-energy.

So how does the theory of Dirac fermions differ from Majorana fermions? For Majorana fermions, which have a fermion spinor representation where the weak charge is 1, the fermion and the antiparticle have the same charge. This means the two objects cannot be distinguished. This is the case even for right-handed neutrinos, which also carry a fermion spinor representation of a weak charge of -1. And if you want to build a left-handed Majorana neutrino, you don't need to have the "opposite" antineutrino of your Majorana neutrino.

You may have noticed that in the Standard Model, all the elementary particles that we know of are either left- or right-handed. This is related to the fact that we are dealing with Majorana fermions. The weak interaction of charged leptons is mediated by the $W^pm$, and the weak interaction of the up-type quarks is mediated by the $W^pm$ and $Z^0$. However, this distinction doesn't necessarily hold for other types of interactions. For example, there is an interaction of the muon with a neutrino that is mediated by a contact interaction, in which no intermediate boson is exchanged. This interaction will therefore have the same weak charge for all three lepton flavours.

This, and other possible differences, have been studied for quite some time now, and I will mention a few important results. It turns out that the interaction of muons with neutrinos depends on whether you have Dirac or Majorana neutrinos, as shown by the following figure, which shows a comparison of the interactions of $mu^pm$ with neutrinos.

So we see that the interaction of a charged muon with a Dirac neutrino is mediated by a left-handed, electroweak $W^pm$ and the interaction of a Majorana neutrino with a charged muon is mediated by a right-handed, electroweak $W^pm$. The interaction of a Dirac neutrino with a charged electron is mediated by a left-handed $W^pm$ and the interaction of a Majorana neutrino with a charged electron is mediated by a right-handed $W^pm$.

This may also be seen in the language of interactions, which, just as in the case of the weak interactions, can be split into left- and right-handed components. The left-handed interaction looks like

$$mathcal{L}_{nu,text{ left}} = g_nuoverline{nu_L}gamma_mu nu_L W^mu+ cdots, tag{6}$$

where the ellipses denote the interactions of a neutrino with the right-handed $W^pm$ that do not contribute to $betabeta$ decay. The right-handed interaction looks like

$$mathcal{L}_{nu,text{ right}} = g_nu overline{nu_R}gamma_mu nu_R W^mu+ cdots, tag{7}$$

and, therefore, the difference between a Dirac neutrino and a Majorana neutrino is that a Majorana neutrino has only a left-handed component.

The left-handed currents are a result of the fact that the weak $W$ is a member of a triplet under SU(2)$_L$. Therefore, all members of the weak isospin doublet share the same transformation properties under the $L$-charges and the $mathcal{L}$-charges. This results in that there is no difference between $mathcal{L}$ and $L$ in the case of leptons. Since, in turn, there is no difference between $mathcal{L}$ and $L$ in the case of leptons, we conclude that there is no difference between $mathcal{L}$ and $L$ in the case of neutrinos, that is, $mathcal{L}$ and $L$ have the same meaning in the case of neutrinos, even though the theory is not relativistic. This is why we call left-handed currents in Eq. (1) and right-handed currents in Eq. (2) left- and right-handed, even though they are not the currents in the relativistic Lagrangian. If we had used the conventional notation where left- and right-handed neutrinos were denoted by $nu_L$ and $nu_R$, then we would have denoted by $L$ the $L$-charge of the right-handed neutrino and by $mathcal{L}$ the $L$-charge of the left-handed neutrino.