NuOscProbExact: a general-purpose code to compute exact two-flavor and three-flavor neutrino oscillation probabilities

arXiv:1904.12391 · hep-ph, astro-ph.HE, hep-ex · Submitted 2026-08-14 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "NuOscProbExact: a general-purpose code to compute exact two-flavor and three-flavor neutrino oscillation probabilities".

Jocelyn: The paper was written by Mauricio Bustamante from University of Copenhagen.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Paper discussion segment 1: Vera: So, we are looking at "NuOscProbExact: a general-purpose code to compute exact two-flavor and three-flavor neutrino oscillation probabilities" by Mauricio Bustamante from the University of Copenhagen. What I find fascinating here is that he isn't just presenting a new theory, but a tool designed to solve a very specific headache for physicists. When you're trying to figure out how neutrinos change flavors as they travel through the Earth or across the cosmos, the math usually gets incredibly messy.

Jocelyn: It’s that diagonalization process, right?

Vera: Exactly. Usually, to find those probabilities, you have to diagonalize a Hamiltonian matrix, which is mathematically heavy and often results in these massive, unwieldy equations that are hard to use for anything other than a computer simulation. Bustamante uses an alternative method from Ohlsson and Snellman that bypasses that diagonalization entirely by using SU2 and SU3 matrix expansions.

Subrahmanyan: Does that mean the results are more precise than the approximations we usually see in the literature?

Vera: That is precisely the point, Subrahmanyan. Most researchers rely on perturbative expansions—basically educated guesses that work well within certain ranges—but those can lose accuracy when you're exploring "non-standard" physics. This code, NuOscProbExact, aims to provide exact numerical solutions for any time-independent Hamiltonian.

Jocelyn: So instead of saying "this is probably what happens if the density is roughly this," you can actually input the specific, complex environment and get a direct answer?

Vera: Yes, and that opens the door to testing much weirder scenarios. He demonstrates this by showing how oscillations change when you introduce things like non-standard interactions or even Lorentz-invariance violation.

Subrahmanyan: I noticed he mentioned Lorentz violation—that's a pretty big deal for the Standard Model.

Vera: It really is, because it suggests that the fundamental symmetries of nature might not be as absolute as we think. By using NuOscProbExact, scientists can scan through these high-energy, "new physics" parameter spaces much more efficiently to see if any signals match what our detectors are actually seeing.

Jocelyn: It sounds like this is less about finding a new particle and more about giving us a better lens to look for the ones that might be hiding in the noise.

Vera: That's a great way to put it, Jocelyn. By making the math "lightweight" and accessible through Python, he's essentially lowering the barrier for other researchers to test these extreme cosmic theories. Moving forward, we'll look at how he actually applies this to different environments like the Earth's crust or even a vacuum.

Jocelyn: Let's get into the actual mechanics of how those two-flavor and three-flavor calculations differ.

Vera: We will, because the jump from two to three flavors is where the real complexity lies in "NuOscProbExact: a general-purpose code to compute exact two-flavor and three-flavor neutrino oscillation probabilities." Stay with us. Moving on to the next segment.mountains of math coming up.

Jocelyn: Coming up next, we'll look at the specific math behind those flavor transitions. Stay tuned.mountains of math coming up.

Vera: We'll be right back after this short break with more on "NuOscProbExact: a general-purpose code to compute exact two-flavor and three-flavor neutrino oscillation probabilities."mountains of math coming up.