LEFT Running Only Returns QED Part?

[deadlinerJ]

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.

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:

I feel confused with this. Do I miss anything?

Thanks.

[DavidMStraub]

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]

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!