I Neutrino flavour eigenstates and expansion of the universe

[mfb]

Looks like a problem of the label, not a problem of the thread. Easy to fix.

One of OP's posts:

What makes no sense to me is to consider the propagation of the quantum superposition of three particles in a classical curved space-time. Unfortunately, I am not aware that we have such a theory. Using QFT formalism in a curved space-time is contradictory (there's no Poincaré invariance). I don't know how it could possibly work.

 

[Carlos L. Janer]

What is (or, better, could be) the renormalization (semi) group flow of the neutrino mass matrix? What particles could be involved? I suppose they're not the only parameters that do (could) flow. What are (could be) the others? Is it conceivable that neutrinos could carry a tiny electrical charge?

I'm asking out of sheer ignorance.

 

[kimbyd]

What is (or, better, could be) the renormalization (semi) group flow of the neutrino mass matrix? What particles could be involved? I suppose they're not the only parameters that do (could) flow. What are (could be) the others?

I'm not sure what you're asking here. Could you please clarify?

Is it conceivable that neutrinos could carry a tiny electrical charge?

I don't think there's any chance of this. Even a very small electric charge would overwhelm the weak force for most interactions, making neutrinos visible in a number of experiments where they are currently invisible. Here's one paper I found that went into these limits back in 1999:
http://wwwth.mpp.mpg.de/members/raffelt/mypapers/199906.pdf

 

[PeterDonis]

Using QFT formalism in a curved space-time is contradictory (there's no Poincaré invariance). I don't know how it could possibly work.

You should be very careful about extrapolating "I don't know" into "it's contradictory". QFT in curved spacetime is perfectly possible. See, for example, Wald's 1993 monograph "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics". The basic idea is to first reformulate QFT in flat spacetime in a way that does not rely on global Poincare invariance, and then extend the reformulated version to curved spacetime. But it's not a simple exercise.

 

[Carlos L. Janer]

I'm not sure what you're asking here. Could you please clarify?

What I have in mind is rather vague.

If there's a unitary matrix relating flavor eigenstates to mass eigenstates, I suppose that this matrix must "flow" as the interaction energy of the flavor neutrinos changes (after all, the SM is a renormalizable gauge theory).

Since there are different known sources of dense neutrino fluxes: solar neutrinos, nuclear reactor and supernova neutrinos. What do the measurements on these sources tell us about these flows? What are the particles involved in this renormalization? W+- and Z vectorial and Higgs bosons? Are they not a bit too heavy?

I cannot make much sense of what I have in mind.

 

[Carlos L. Janer]

You should be very careful about extrapolating "I don't know" into "it's contradictory". QFT in curved spacetime is perfectly possible. See, for example, Wald's 1993 monograph "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics". The basic idea is to first reformulate QFT in flat spacetime in a way that does not rely on global Poincare invariance, and then extend the reformulated version to curved spacetime. But it's not a simple exercise.

I've been told (by some other staff members) that this only works when you study Hawking's radiation and becomes useless when you try apply these ideas to the universe. But you're right, I never tried to work out the involved maths and maybe I should try (at least to find out why it does not work).

 

[PeterDonis]

I've been told (by some other staff members) that this only works when you study Hawking's radiation and becomes useless when you try apply these ideas to the universe.

I don't think it's just limited to Hawking radiation. The key limitation is that the curved spacetime geometry has to be assumed and held fixed, and the QFT is done in that fixed background spacetime. This can be done in any curved geometry; when studying Hawking radiation it's done in the Schwarzschild geometry, but it could be done in the FRW geometry that cosmologists use to describe the universe. But if there is significant stress-energy associated with the quantum fields (as one would expect, for example, in trying to model the universe as a whole), there is no way to dynamically solve, within the QFT, for the spacetime geometry that is determined by that stress-energy. You have to assume a spacetime geometry, do the QFT in that geometry, compute the expectation value of the stress-energy tensor from the QFT, and check to see if it is consistent with the spacetime geometry you assumed. If it isn't, you have to go back and start over again.

(Even this, of course, is not a full theory of quantum gravity, because you're still treating the spacetime geometry as classical.)

 

[Carlos L. Janer]

I suppose that my post #55 does not make any sense at all.

However, the idea that the parameter values involved in elementary particle interactions (mass, "charge" or interaction strength and field normalization constant) depended on the interaction energy scale was deeply engraved in my mind.

Could someone care to explain me what is it that I'm not getting right?

The post was about the renormalization of the unitary matrix that relates neutrino flavor eigenstates to neutrino mass eigenstates and any clarification is welcomed.

 

[Carlos L. Janer]

We cannot rule out neutrino/photon interactions, and at loop-level we have them even in the SM, but they have to be extremely weak. And that is elastic scattering - I still don't see how you would get a decay.

I don't really see why the scattering MUST be elastic. The mass difference between the neutrino mass eigenstates is so tiny, that the incoming and outgoing neutrinos may be different. Instead of an EM elastic scattering (at one loop level) of a neutrino you would have the decay (at one loop level) of a neutrino into a lighter one and the emission of a soft photon. Wouldn't you?

In the RF of the incoming neutrino, the outgoing neutrino and the outgoing photon would propagate in opposite directions. Four momentum would not be conserved exactly but, my guess is (I would actually have to make the calculations) that the difference would be unmeasurable. Moreover, we're talking here about an interaction that is taking place in an expanding universe.

 

[PeterDonis]

the idea that the parameter values involved in elementary particle interactions (mass, "charge" or interaction strength and field normalization constant) depended on the interaction energy scale was deeply engraved in my mind.

the renormalization of the unitary matrix that relates neutrino flavor eigenstates to neutrino mass eigenstates

These questions really belong in a separate thread in the quantum physics forum. Please start one if you would like to pursue them. Also, before starting a new thread, it might help to look through this Wikipedia article and the references it gives:

https://en.wikipedia.org/wiki/Neutrino_oscillation

The original question in this thread has been answered, so it is now closed.