Treat μ and τ flavours separately

[JostMigenda]

Currently, SNEWPY does not distinguish between μ and τ neutrinos, referring to both as NU_X. (Same for μ and τ antineutrinos, referred to as NU_X_BAR.) While this is in line with most computer models, there are a few that treat μ and τ separately and we should consider updating SNEWPY to deal with this.

This would require changes to the Flavor enum in snewpy.neutrino, as well as to all flavor transformations. There will also be performance downsides of having 6 flavours instead of 4—we should see how large that effect is in practice and whether it’s possible to avoid it for models that don’t benefit from the 6-flavour treatment.

[sybenzvi]

Do you have a list of models where this will matter? And how much do we lose by merging mu and tau flavored fluxes into a nu_x flux for models that use 3 flavors instead of nu_e + nu_x + antineutrinos?

[JostMigenda]

Figure 3 of arXiv:1706.04630 indicates a roughly ~10% difference in luminosity between mu and tau antineutrinos if muon production is included in simulations. (Plus overall higher luminosity & mean energy as well as earlier explosions, compared to simulations that ignore this effect.) I don’t know any others off the top of my head (apart from arXiv:2008.13628 fig. 9, which covers just 30 ms around the core bounce), but maybe @evanoconnor can help?

[evanoconnor]

right, so the models will be different. But maybe what @sybenzvi is asking is if we just lump all heavies together into nux, what difference would we see. Currently, I think not much. SNOwGLoBES, for example, doesn't have the charged current muon interactions, so distinguishing mu and tau doesn't do anything (@jpkneller can correct me here, but I think with a six flavour mixing any differences between mu and tau neutrinos show up in the electron flavour at the sin^2(theta{13}) level, or something like that). the neutrino - antineutrino difference is bigger as when rolled in with oscillations (now the differences come in depending on theta{12}) it can impact the electron flavor at earth.

[JostMigenda]

So as an initial (stop-gap) measure, once we have such a model, averaging nu_mu and nu_tau fluxes to get nu_x (and analogous for antineutrinos) is slower but probably more accurate than taking nu_mu and ignoring nu_tau. (Though 1706.04630 seems to indicate that the accuracy difference is more pronounced for antineutrinos, less so for neutrinos.) Not surprising, but still worth noting.

The exact effect would depend on the FlavorTransformation we apply, though. E.g. for ThreeFlavorDecoherence, where we just average the three flavours, there wouldn’t be an issue. If initial differences of ~10% get multiplied by a factor of sin^2(theta_{13}), that would be negligible in most cases, too. So the only thing we’d have to worry about in terms of physical accuracy[*] would be exotic transformations with a larger factor?

Finally, regarding SNOwGLoBES’ lack of CC-nu_mu interactions: Since the nu_mu in 6-species SN simulations would still have similar energy (~0.5 MeV higher, based on arXiv:1706.04630) to those in 3- or 4-species simulations, the issue of the energy threshold for producing detectable muons (~140 MeV in water Cherenkov, slightly lower in LS) would still remain, though. So I don’t think SNOwGLoBES is a limiting factor in this regard.

[*] Plotting fluxes from 6-species simulations accurately would be desirable either way, of course.

[jpkneller]

I thought about this a while and how much a difference between mu and tau matters depends the mixing scenario. Let's take the simplest case of adiabatic propagation where the measured electron neutrino spectrum at Earth in the NMO is 70% of whatever is the mass state 1 spectrum, 30% mass state 2 and only sin^2(theta13) of the original electron neutrino spectrum which is mass state 3. If the spectra of mu and tau are different then we have to know how much of mass state 1 is mu and how much tau, and the same for mass state 2. Those amounts depend on theta23 and also on the CP phase. arXiv:0710.3112.

On Wed, Sep 15, 2021 at 3:19 PM evanoconnor @.***> wrote:

right, so the models will be different. But maybe what @sybenzvi https://github.com/sybenzvi is asking is if we just lump all heavies together into nux, what difference would we see. Currently, I think not much. SNOwGLoBES, for example, doesn't have the charged current muon interactions, so distinguishing mu and tau doesn't do anything @.*** https://github.com/jpkneller can correct me here, but I think with a six flavour mixing any differences between mu and tau neutrinos show up in the electron flavour at the sin^2(theta{13}) level, or something like that). the neutrino - antineutrino difference is bigger as when rolled in with oscillations (now the differences come in depending on theta{12}) it can impact the electron flavor at earth.

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