Regarding discrepancy in LFV result from SPheno

[saiyad]

I have been calculating branching ratio(s) for Lepton Flavor Violating processes like mu to e gamma in the context of a (non-supersymmetric) BSM model. I have calculated the same analytically and also implemented the model in SARAH, and using the SPheno module from SARAH output, I have generated the spectrum file from SPheno. And what I found is that the SPheno result doesn't match with that of my analytical calculation even though both the tool and I are considering the same sets of vertex-type and self-energy-type diagrams, and also the same effective Lagrangian (l-l-gamma dipole interaction). Then I tried to see where the discrepancy is coming from by considering a smaller set of diagrams at a time (instead of considering all the diagrams) by editing the Observables/FlavorKit_LFV_modelname.f90 file. And I found that the discrepancy is coming from only one set of diagrams namely the diagrams in which W boson and doubly charged particles are involved in the loop, and for the other (three) sets of diagrams, the results are in good agreement. I have checked my analytical calculations a few times before writing this here. Any comment or suggestion will be highly appreciated.

[Avelino]

Hi Saiyad, sometimes there are discrepancies for individual loop diagrams that cancel out in the sum. However, I understand that is not your case. You also get a different result in the sum. Is this correct? If so, I can think of two possible reasons:

1) Please check whether the involved loop functions are well-behaved. Sometimes the results turn out to be different just because the loop functions are not adapted to the limit in which they are used numerically. For instance, if two of the particles running in the loop are mass degenerate, there might be some apparently divergent terms in the loop functions that need to be treated properly before using them for a numerical application. So I would suggest you to check whether your (and FlavorKit's) loop functions behave correctly in your numerics.

2) And of course, it could also be that you found a bug in FlavorKit.

[saiyad]

Hi Saiyad, ... If so, I can think of two possible reasons:

1) Please check whether the involved loop functions are well-behaved ... So I would suggest you to check whether your (and FlavorKit's) loop functions behave correctly in your numerics.

Where can I find the loop functions used in FlavorKit? I mean I don't know where these loop functions are written.

[Avelino]

For my understanding: how do you compare your analytical results to those obtained by FlavorKit?

[saiyad]

For my understanding: how do you compare your analytical results to those obtained by FlavorKit?

The LFV process which I am studying is mu to e gamma (Block 701 in SPheno) in the context of a BSM model.

[1] SPheno (FlavorKit) gives branching ratio (BR) for the said LFV process for a given set of parameters (masses and Yukawa couplings) which is provided in LesHouches.in.modelname file in the SPheno directory. I have obtained an analytical expression for BR(mu to e gamma). I am calculating the BR for the same set of given parameters. Finally, I am comparing both the results, and it turns out that these two results are not in agreement.

• While obtaining the analytical expression for the said BR, I have used some approximation like m_e^2 = m_mu^2 = q^2 = 0 (q being the momentum transfer) and also at the end, I have taken some limits like x=m_nu^2 / m_w^2 =0 while calculating the loop functions for obvious reasons. I think these approximations are perfectly fine (these approximations shouldn't affect the result significantly).

[2] Next, I tried to see where the discrepancy is coming from by considering a smaller set of diagrams at a time (instead of considering all the diagrams) by editing the Observables/FlavorKit_LFV_modelname.f90 file.

• example of a smaller set of diagrams: set of diagrams in which a W boson and (or) corresponding "would be Goldstone boson" scalar and neutral leptons are involved on loop. In this set, there are eight diagrams namely four vertex-type (triangular contributions: FVV + FSV + FVS + FSS) and four self-energy-type (wave contributions: FVF + VFF + FSF + SFF)

Then, both the results (analytical and SPheno) are compared for each smaller set of diagrams.

[3] And I found that the discrepancy is coming from only one set of diagrams namely the diagrams in which a W boson and (or) corresponding "would be Goldstone boson" scalar and doubly charged leptons are involved on loop, and for the other (three) sets of diagrams, the results are in good agreement.

[Avelino]

Hi and sorry for the delay in my response. Now I see your approach.

Since you already identified the loops leading to the discrepancy and know how to find their analytical expressions in the Fortran code (as you write, they are in the FlavorKit_LFV_modelname.f90 file), I would compare these to your own analytical expressions. In order to do that you should know that the expressions for the loop functions can be found in src/LoopFunctions.f90. With the information in those two f90 files you can write down the expressions for the troublesome loops and check whether they agree with yours. If not, you can identify the origin of the difference. Have you done that already?