Update flavor_transformation.py

[jpkneller]

I think there's a mistake in the formulae for P11 and P12 in the QuantumDecoherence class. They don't match what is found in equation II.4 of the dos Santos et al paper.

[JostMigenda]

@santosmv If you have a moment, can you check this and confirm whether the issue is here or in the paper?

Once that’s confirmed, the test failures are quite straightforward to fix; I can take care of this while I review & merge.

[JostMigenda]

@jpkneller After a closer look at the paper, I noticed the line just under eqn. (II.6):

leading to \gamma_3 = \Gamma_3 + \Gamma_8 / 3 and \gamma_8 = \Gamma_8

It looks like that’s where this additional term is coming from? (The notation with upper/lower case gammas easily leads to confusion; so even if the current code is correct, it might be useful to add a comment for clarity?)

[santosmv]

Apologies for the notation. You're correct that the uppercase \Gamma_3 and \Gamma_8 originate from equations (II.5) and (II.6), respectively, and come from the decomposition of lowercase gammas into coefficients of V_p operators. This notation has two primary purposes: firstly, to derive parameters that remain independent of each other (in terms of V_p coefficients), and secondly, to simplify the comparison with results of another paper that introduced this notation (available at https://arxiv.org/abs/1909.09504).

[JostMigenda]

No worries; I think the notation makes perfect sense in the paper. It’s just that code isn’t typeset as nicely, so legibility is necessarily impaired a bit.

It looks like this is resolved, so I’ll close it now.