Normalisation B to Kll - FlavorKit

[ldarme]

Dear Florian,

I know you did some changes for this particular decay a year ago, but I am wondering if the normalisation of the contribution for the C7 coefficients does not miss an (4pi alpha) factor. The reason is the following:
- FlavorKit uses CC7 for both B->Kll (based on 1308.1501, correcting the normalisation with a factor N1) and B->X_s gamma (based on 0612166, correcting the normalisation with a factor N2). The two factor correction for the normalisation are different with N1 = 4 pi alpha N2. However, both 1308.1501 and 0612166 uses exactly the same effective Hamiltonian and should therefore have the same normalisation for their C7, one of the decay should thus be badly normalised in FlavorKit
- Assuming that the effective Lagrangian used by FlavorKit is still the same as Eq. (A.11) of the original FlavorKit paper, you get that the badly normalised one is the B->Kll one.
- Interestingly the normalisation for the C9/C10 coefficients for B->Kll are okay.

My conclusion so far is that in the B->Kll branching rate calculation, the C7, C7' term should be further multiplied by (4pi alpha) while the rest should not be modified.

That said, I may have missed something, especially since you made some modifications on this particular decay since the FlavorKit paper.

Thanks a lot in advance,
Cheers,
Luc

Ps. I tried the Madgraph output flag (78) with the latest SARAH 4.10.2 (downloaded today), it still throws segfaults with useless backtrace (tested with MSSM, B-L-SM and SM+octet). Is the latest version online really the corrected one (cf your changelog from version 4.10.1)?

[Avelino]

Salut Luc,

thanks a lot for pointing this out. I believe you are absolutely right.

We actually had to fix the normalization of the Wilson coefficients used in B -> K l+ l- [perhaps because we missed the e^2 / (16 pi^2) factor included in equation (1) of 1308.1501, but I can't remember the reason]. You can notice this by looking at page 52 of the FlavorKit manual, where you can see the original definition of 'norm' for this observable, different from the current one. So I guess we fixed the normalization for the C9 and C10 contributions but we spoiled the normalization for the C7 contribution.

Bottom line: I just re-checked and I agree with you, the C9 and C10 contributions are normalized correctly but the C7 contribution should be multiplied by e^2 = 4 pi alpha.

[FStaub]

Hi Luc,

I will change the coefficient in the next update which is most likely on Monday. This will also include changes in the MG compatible output of SPheno, (which are hopefully really compatible with the new version).

Cheers,
Florian

[ldarme]

Dear both,

Great! Thanks a lot for your quick answers and for the awesome code.

Cheers,
Luc

[FStaub]

Hi Luc,

are you aware of https://flav-io.github.io/ ? This might be quite helpful for you when you want to study B anomalies. We just confirmed in a private discussion with David that the normalisation of the SPheno ouptut is correctly included in the interface.

Cheers,
Florian