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wilson-eft / wilson

A Python package for the running and matching of Wilson coefficients above and below the electroweak scale
https://wilson-eft.github.io
MIT License
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LEFT Running Only Returns QED Part? #107

Open deadlinerJ opened 1 year ago

deadlinerJ commented 1 year ago

Hi,

I am using the LEFT running from Mz to b quark mass. The code is done in "flavio" basis. To simplify the issue I encountered, a simplified code is shown below.

Screen Shot 2022-11-01 at 5 04 12 PM

Only CSR_bctaunutau and CS_bstautau are turned on. The change of the 2 should be comparable. My question is why the change of CS_bstautau is so small and it seems only QED part is considered.

Here is my check of the Mathematica code attached to: https://arxiv.org/pdf/1704.06639.pdf

For CS_bstautau, it returns:

Screen Shot 2022-11-01 at 5 17 07 PM

I feel confused with this. Do I miss anything?

Thanks.

DavidMStraub commented 1 year ago

If you look at the basis, you'll notice that the scalar operator in the charged current case is defined without a mass factor, while the neutral current one has a mass factor included. Consequently, the QCD part of the b->s operator is a conserved current and you're seeing only QED running. For the b->c operator, the Wilson coefficient renormalizes under QCD like the mass.

deadlinerJ commented 1 year ago

Exactly. The neutral scalar operator in 1704 doesn't have such a mass factor but the one in flavio basis does. Thank you very much!