mu -> e gamma operator in FlavorKit

[WojciechKotlarski]

Hi Florian,

We're looking now into the mu -> e gamma process, which goes through operators you call OA2lSL and OA2lSR. As an example, the left one is defined in FlavourKit as

Code: Select all

{OA2lSL,Op[6] Pair[ec[3],k[1]]}

If I compare it with footnote 9 in your paper 1405.1434 I would expect sth like

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{OA2lSL,Op[-6,ec[3],k[1]]}

I guess I'm missing something basic. Could you comment on that?

cheers,
Wojciech

[FStaub]

Hi,

I don't really understand the operator you have written down: ec[3] and k[1] carry Lorentz indices which need to be contracted. Therefore, the Pair[..]. After doing that, this is just a scalar which can be taken out of Op[..]. So, it seems that we actually agree up to an overall sign? This might come from the FermionOrdering.

Cheers,
Florian

[WojciechKotlarski]

Hi Florian,

Sorry about that (and also about a very late reply). I got confused because I didn't notice that you've used the Gordon identity to express operator with \sigma by the one with a scalar product.

Now, if I look how OA2lSL and OA2lSR are calculated you set all the diagrams which are tagged as wave to 0. Do I miss something, because I think they are not strictly 0. To make it more concrete, I'm now looking into how they are used in the calculation of the muon conversion in the nuclei.

cheers,
Wojciech

[FStaub]

Hi,

You need these additional diagrams only to cancel divergences and prove gauge invariance, but in Feynman gauge they have no finite contributions.

There is a review by Jorge Romao where this is shown.

Cheers
Florian