Neutrino Interactions: Z Boson, Electron & Beyond

[Rob Hoff]

When the Z boson is around can a neutrino interact with a particle other than an electron? And how does the neutrino find the electron if the neutrino is neutral and does not interact electromagnetically?

 

[Matterwave]

A neutrino interacts via the weak interactions. An electron neutrino interacts with electrons, a muon neutrino interacts with muons, a tau neutrino interacts with tau (this is how the flavor states are defined). In addition, neutrinos may interact with hadrons as well, since hadrons participate in the weak interaction (e.g. beta decay is a weak interaction). So a neutrino may scatter off of nuclei.

Interestingly enough, a majorana neutrino, although electrically neutral and lacking in dipole moments, may also interact, extremely weakly, with a photon.

 

[Rob Hoff]

What is the structural differences between these types of neutrinos? Also, when a photon is in a magnetic field and bounces between a photon and a neutrino/ electron state, which type of neutrino would that be?

 

[Matterwave]

Structural differences between which types of neutrinos? There are no structural differences between any elementary particles, since they are all structureless. They do have different quantum numbers though, and different interactions.

I have no idea what you are referring two with the photon in a magnetic field "bouncing" between a neutrino/electron state...a photon is a photon, it can not be a neutrino or an electron...

 

[Rob Hoff]

Oh sorry, I screwed that up. It was a photon can turn into a positron and electron when it interacts with a magnetic field. Also, thank you!

 

[Matterwave]

A photon doesn't turn into a positron and electron pair in the presence of a magnetic field...you are perhaps referring to the reverse annihilation reaction:

$\gamma\gamma\rightarrow e^- e^+$

But what's this have to do with a neutrino?

 

[Rob Hoff]

I asked the question with a FALSE knowledge that photons can emit an electron and a neutrino in a magnetic field. Clearly I am having a difficult time understanding my book on QED. Sorry for this rabbit hole of confusion. :)

 

[Matterwave]

Oh ok. There ARE interactions which produce a lepton plus a neutrino. In that case, which lepton is produced gives which neutrino species is produced. In other words, a decay which produces a muon must necessarily produce a muon (anti)neutrino. For example, for tritium beta decay (any beta decay actually, but for notational ease I choose tritium:

$$T\rightarrow ^3\text{He}+e^-+\bar{\nu}_e$$

This is an electron anti-neutrino emitted because the lepton emitted is an electron.

This is actually, in practice, the definition of what flavor the neutrino is.

 

[Orodruin]

A neutrino interacts via the weak interactions. An electron neutrino interacts with electrons, a muon neutrino interacts with muons, a tau neutrino interacts with tau (this is how the flavor states are defined).

All types of neutrinos may interact with electrons through weak interactions via the exchange of a Z boson. The flavor states are relevant only for amplitudes containing the exchange of W bosons. An example of this can be found in the interaction rates of solar neutrinos which are typically detected in one of three ways:

Charged current interactions: Basically $\nu_x + d \to e^- + u$, may only occur for x = e. The measured flux is around a third of that expected from the standard solar model (SSM).

Neutral current interactions: $\nu_x + D \to p + n + \nu_x$, mediated by Z exchange and measured in heavy water by the SNO collaboration. May occur for any neutrino flavor x with the same cross section up to loop corrections. The measured flux is that expected from the SSM.

Elastic scattering: $\nu_x + e^- \to \nu_x + e^-$, as measured by Super-Kamiokande etc. The neutrino may be of any flavor. However, the cross section for $\nu_e$ is higher due to the additional possibility of exchanging a W boson in addition to the basic diagram with Z boson exchange. The measured flux lies between the CC and NC rates (as expected).

 

[Matterwave]

All types of neutrinos may interact with electrons through weak interactions via the exchange of a Z boson. The flavor states are relevant only for amplitudes containing the exchange of W bosons. An example of this can be found in the interaction rates of solar neutrinos which are typically detected in one of three ways:

Charged current interactions: Basically $\nu_x + d \to e^- + u$, may only occur for x = e. The measured flux is around a third of that expected from the standard solar model (SSM).

Neutral current interactions: $\nu_x + D \to p + n + \nu_x$, mediated by Z exchange and measured in heavy water by the SNO collaboration. May occur for any neutrino flavor x with the same cross section up to loop corrections. The measured flux is that expected from the SSM.

Elastic scattering: $\nu_x + e^- \to \nu_x + e^-$, as measured by Super-Kamiokande etc. The neutrino may be of any flavor. However, the cross section for $\nu_e$ is higher due to the additional possibility of exchanging a W boson in addition to the basic diagram with Z boson exchange. The measured flux lies between the CC and NC rates (as expected).

The interactions with inter-flavors are highly suppressed even compared to the already low interaction cross sections present for neutrinos. For example, the MSW effective Hamiltonian in the flavor basis has only basically 1 element at the electron-electron neutrino flavor sector due to the fact that there are only electrons, and no muons or tau in the solar environment.

 

[mfb]

The interactions with inter-flavors are highly suppressed even compared to the already low interaction cross sections present for neutrinos. For example, the MSW effective Hamiltonian in the flavor basis has only basically 1 element at the electron-electron neutrino flavor sector due to the fact that there are only electrons, and no muons or tau in the solar environment.

The Z boson does not care about the flavor - that's why experiments looking for neutral current interactions (and elastic scattering) are sensitive to all three types with a comparable sensitivity.

And how does the neutrino find the electron if the neutrino is neutral and does not interact electromagnetically?

All this has nothing to do with the electromagnetic interaction.

 

[Matterwave]

The Z boson does not care about the flavor - that's why experiments looking for neutral current interactions (and elastic scattering) are sensitive to all three types with a comparable sensitivity.

Do you not suppress the total cross sections by getting rid of the charged current interactions?

 

[mfb]

What do you mean with "getting rid"? You might get less events if you are not sensitive to it.
On the other hand, for solar muon and tau neutrinos, the energy is not sufficient for charged current interactions anyway.

 

[Matterwave]

What do you mean with "getting rid"? You might get less events if you are not sensitive to it.
On the other hand, for solar muon and tau neutrinos, the energy is not sufficient for charged current interactions anyway.

I mean am I mistaken when I say that an electron neutrino interacts with electrons, mu neutrinos with muon, and tau neutrinos with tau, at least roughly speaking?

 

[mfb]

That's only true for some (not all!) charged current interactions.

 

[Matterwave]

Hmmm, ok, then I will be more specific in my descriptions from now on. Thanks. :)

 

[James Carter]

It is possible that there are no Neutrino Flavors at all; the different Flavors all have the same speed and therefore the same mass. It may be that the observation of change in Neutrino Flavors due to weak interactions with other Leptons is simply the Neutrino changing the direction of its spin to correspond to that of the other Lepton; meaning that the $\upsilon$_e, $\upsilon$_$\mu$, and $\upsilon$_$\tau$ are all corrisponding Neutrino particles

 

[Orodruin]

Matterwave: The reason NC interactions to not appear in the MSW Hamiltonian is that they are equal (up to loop effects of $\mathcal O(10^{-5})$ times the CC contribution). The NC part of the MSW Hamiltonian is therefore essentially proportional to the unit matrix and only contributes to the neutrino flavor evolution with an overall phase. It is therefore customary to drop this contribution and only work with the CC contribution. This is no longer true when dealing with sterile neutrino flavors where the NC part is proportional to the projection operator onto the active states.

Edit: Relatively recent open accessreview on matter effects in neutrino oscillations: http://dx.doi.org/10.1155/2013/972485
The relevant discussion is on pages 2 and 3.

Carter: Your post goes against the last 52 years of research in neutrino physics (the muon neutrino was discovered in 1962). It is possible you have seen analogies of neutrino oscillations to spin precession (the mathematics is the same), but these are simply analogies. Neutrino oscillations are fundamentally based upon and our currently only confirmation of different neutrinos having different masses.

 

[James Carter]

The sum of the masses of the Neutrinos is .320+/-.081 eV; since the three Neutrinos have different masses that would dictate that, when one of the three Neutrinos comes within a distance of 10^-16 of a meter of either a Muon, Electron, or Tau particle, weak interactions between the two particles would cause the speed of the Neutrino to change and therefore the mass, subsequently, would change.

 

[Orodruin]

You do not give a reference, but from your sum of masses it would seem a cosmological bound.

The HM claim is controversial at best and cosmological bounds tend to depend strongly on assumptions and selected data sets. There are currently no experiments putting solid widely accepted lower bounds on the neutrino masses.

 

[Matterwave]

Matterwave: The reason NC interactions to not appear in the MSW Hamiltonian is that they are equal (up to loop effects of $\mathcal O(10^{-5})$ times the CC contribution). The NC part of the MSW Hamiltonian is therefore essentially proportional to the unit matrix and only contributes to the neutrino flavor evolution with an overall phase. It is therefore customary to drop this contribution and only work with the CC contribution. This is no longer true when dealing with sterile neutrino flavors where the NC part is proportional to the projection operator onto the active states.

Edit: Relatively recent open accessreview on matter effects in neutrino oscillations: http://dx.doi.org/10.1155/2013/972485
The relevant discussion is on pages 2 and 3.

Carter: Your post goes against the last 52 years of research in neutrino physics (the muon neutrino was discovered in 1962). It is possible you have seen analogies of neutrino oscillations to spin precession (the mathematics is the same), but these are simply analogies. Neutrino oscillations are fundamentally based upon and our currently only confirmation of different neutrinos having different masses.

Indeed you are right. But I was told that the cross sections (total, due to both charged and neutral current) for an electron neutrino on an electron is 6-8 times higher than the cross sections for other flavors of neutrinos. This is why I made the statement I made at the beginning.

 

[Orodruin]

Yes, it is about that difference because of the additional diagram with W exchange which interferes constructively with the Z exchange diagram.

This is why elastic scattering experiments are more sensitive to electron neutrinos but still have some sensitivity to mu and tau flavors. The solar fluxes are summarized in figure 14 at http://t2k-experiment.org/neutrinos/beyond-the-standard-model/ (T2K homepage) with the different bands representing results from CC, NC, and ES experiments. The figure is relatively old but the physics behind are still valid.

 

[mfb]

It is possible that there are no Neutrino Flavors at all; the different Flavors all have the same speed and therefore the same mass. It may be that the observation of change in Neutrino Flavors due to weak interactions with other Leptons is simply the Neutrino changing the direction of its spin to correspond to that of the other Lepton; meaning that the $\upsilon$_e, $\upsilon$_$\mu$, and $\upsilon$_$\tau$ are all corrisponding Neutrino particles

The sum of the masses of the Neutrinos is .320+/-.081 eV; since the three Neutrinos have different masses that would dictate that, when one of the three Neutrinos comes within a distance of 10^-16 of a meter of either a Muon, Electron, or Tau particle, weak interactions between the two particles would cause the speed of the Neutrino to change and therefore the mass, subsequently, would change.

Please give references for your claims. Personal theories are not allowed here.