fK form factor correlation with fpi

[MJKirk]

It's not clear to me where the flavio value of the correlation between f_K and f_pi comes from. Reading the comments in https://github.com/flav-io/flavio/blob/3b8032913b79d01a48190ca7ab3366ff67b70173/flavio/data/parameters_correlated.yml#L26-L41 it suggests it comes from FLAG, but I can't see that value in the review. Alternatively if it comes from reverse engineering it to reproduce the ratio f_K/f_pi as suggested by @DavidMStraub's earlier commit (https://github.com/flav-io/flavio/commit/0f75d69eed5746b8d939a0140755f40a1b20dbbd), then it seems to me that both the error on f_K and the correlation between f_K and f_pi are not known, and there is a whole range of values for both that would reproduce the FLAG error on the ratio. E.g f_K = 0.1554(8) and a correlation of 0.975 would also reproduce the ratio correctly.

[DavidMStraub]

Which is the value you can't see in the review? From table 1:

[MJKirk]

The correlation coefficient between fK and fpi. I'm saying it seems like you took fK/fpi and fpi from FLAG, and then reverse engineered both fK and the correlation between fK and fpi. But I don't see how there is enough information for that. Unless the correlation is already known

[DavidMStraub]

I see your point. The central value for fK obviously comes from the ratio, but the correlation can only be extracted if the uncertainty on fK is known, and there is no reference given for that. No idea where it came from. But I suspect there was a perfectly well thought through & legitimate reasoning behind it :thinking:

What's clear is that the 0.3 MeV error (2+1+1) is not applicable as it uses the experimental value of fpi to set the lattice scale.

[MJKirk]

Okay, glad I have not missed something. It appears from some quick calculations that if you just take both the uncertainty and the correlation as free parameters, then that particular value for the fK uncertainty minimises the correlation you need to reproduce fK/fpi. So maybe 2019 David thought that was a good reason?

[DavidMStraub]

Fortunately 2019 David didn't throw away his data.

I found the notebook: https://gist.github.com/DavidMStraub/813bd0c4296837936a188a29c8d8b981

Apparently, what he assumed is that fpi and the ratio fpi/fK are fully uncorrelated. Is that justified? No idea.

Btw all of this was part of a detailed numerical comparison of K and beta decay predictions with Martin G-A & Adam F for an awesome paper that unfortunately was never finished.

[MJKirk]

:clap: and a :medal_sports: to 2019 David. Naively, since FLAG does not mention any correlation between fpi and fK/fpi I would think it is reasonable to assume there isn't one, and therefore your method is fine. Maybe something to ask next time I see some lattice person...

Does any of this work live on in https://arxiv.org/abs/2010.13797? I guess/hope you don't check the arXiv much these days. The whole beta vs K decays and Vus/Vud stuff is something I have been working on, and specifically why I was looking at this - to be able to change these parameters.

[MJKirk]

Anyway, thanks for digging this out! Actually, another general history question - is there some reason you didn't choose to just use fpi and fK/fpi straight as the inputs to flavio, and then do fK/fpi * fpi everywhere as needed?

[DavidMStraub]

Does any of this work live on in https://arxiv.org/abs/2010.13797

No, not really, but v2.0 added most of the observables we considered.

is there some reason you didn't choose to just use fpi and fK/fpi straight as the inputs to flavio, and then do fK/fpi * fpi everywhere as needed?

I guess it just seemed more natural to treat all decay constants equally as parameters; similarly for the B bag parameters. But it would work just as well with fK/fpi and fpi.

[MJKirk]

Fair enough. Thanks again for the information!