Obervables and relevant NP operators

[Trifis]

Is there a way to check which NP operators contribute to each observable? For example, is there a method to check which operators are relevant to an observable, such as 'BR(B0->K*nunu)'. Also, is the reverse also possible? i.e. to have a list of all observables a NP operator would affect. Finally, is flavio considering only tree-level NP contributions or also loop effects generated by the NP operators?

Looking forward to your reply.

[DavidMStraub]

Hi @Trifis,

there is no function at the moment to do what you want (although it wouldn't be hard to hack one I guess). In practice, if you want to find out which operators contribute without looking at the source code, the best starting point is the WCxf basis file. The operators in in each "sector" in WCxf do not mix with other operators under QCD or QED. Thus you are guaranteed that only operators from a single sector contribute to a given low-energy observable. In the case of B->K*nunu, the relevant sector is sbnunu. You can see there are 18 operators. All of them contribute to this process.

Concerning loop contributions: do you mean insertion of local operators in SM loops? The only case where this used to be implemented was four-quark operator matrix elements in b->sll, but it was recently removed when changing the operator basis and will be added back soon. Which process are you thinking of?

[Trifis]

Thus you are guaranteed that only operators from a single sector contribute to a given low-energy observable.

Thank you very much for the reply. I think the above says it all.

What I had in mind is for example, a leptoquark coupling inducing some contribution to e.g. B-Bbar mixing via a box. It is reassuring to know, that those contributions, have to be put in explicitely by hand as extra terms in the NP WC.

[DavidMStraub]

Oh, I get your point, yes. If you are feeding operators in the weak effective theory, you have to give it the DeltaB=2 operators explicitly.

There is one exception to my statement: the very recent addition of the possibility of directly using SMEFT operators does take into account SMEFT-RG-induced effects in other sectors. But in your explicit case, this would not change the fact that you would have to add it by hand, as it would be a 1-loop effect already in the matching from the LQ model to SMEFT, as done also in this paper: https://arxiv.org/pdf/1712.01295.pdf

[DavidMStraub]

This is a very old issue, but I just added a feature that at least goes into this direction. The next release will contain a function flavio.functions.get_dependent_wcs which will return the WCxf EFT, basis, sector and scale of the Wilson coefficients relevant for any observable. For instance,

import flavio
flavio.functions.get_dependent_wcs('eps_K')
# will return
{(2.0, 'WET-3', 'flavio', ('sdsd',))}

More fine-grained information (i.e. which specific WCs are relevant) will not be possible unfortunately, so I think this issue can be closed.