Probability of neutrino switching: more massive, more probable?

[nomadreid]

TL;DR Summary

Hypothetical sterile neutrinos being more massive mean it is more probable for the other flavors to switch to them, and vice-versa? Justified by Energy-time uncertainty, or what?

In Scientific American, July 2020, the article "The Darkest Particle" by Louis and Van de Water, page 46, discussing the hypothetical sterile neutrino, there is the sentence: "Because sterile neutrinos are likely to be more massive than the regular flavors, however, particles could make the switch to this type more quickly and could likewise change back from sterile to one of the three regular flavors over shorter distances." My guess for the justification of this sentence is the Energy-time uncertainty relation, but I am unsure: perhaps I am being overly simplistic? All corrections welcome.

 

[Vanadium 50]

My guess for the justification of this sentence is the Energy-time uncertainty relation, but I am unsure: perhaps I am being overly simplistic?

No, just incorrect. The oscillation rate (not probability) depends on Δm². (And before you ask "Why?" realize that you would be asking "please explain why the outcome of a calculation is what it is without reference to that calculation")

 

[nomadreid]

Ah, thanks, Vanadium 50. That is, I was wrong because I was being simplistic, and of course not only will I not ask "why?" but even will not ask for the formula to which you refer, because it is obvious that I need to do some more reading on neutrino oscillation before I am ready to understand why the mass term is there. But you pointed me in a new direction, for which I am grateful.

I guess I can start with the Wiki explanation
https://en.wikipedia.org/wiki/Neutrino_oscillation#Propagation_and_interference
and follow up with
https://arxiv.org/pdf/1802.05781.pdf

 

[George Jones]

Ah, thanks, Vanadium 50. That is, I was wrong because I was being simplistic, and of course not only will I not ask "why?" but even will not ask for the formula to which you refer, because it is obvious that I need to do some more reading on neutrino oscillation before I am ready to understand why the mass term is there. But you pointed me in a new direction, for which I am grateful.

I guess I can start with the Wiki explanation
https://en.wikipedia.org/wiki/Neutrino_oscillation#Propagation_and_interference
and follow up with
https://arxiv.org/pdf/1802.05781.pdf

Neutrino expert Mark Thomson has made available his excellent lecture slides for an introductory particle physics that he taught in 2011,
https://www.hep.phy.cam.ac.uk/~thomson/MPP/ModernParticlePhysics.html

His "11. Neutrino Oscillations" might be a good place to start.

He gives a simplified, but standard, treatment of neutrino oscillations. From his slides "The full derivation requires a wave-packet treatment and gives the same result"

 

[nomadreid]

Thank you, George Jones. That is very helpful.