# alpha_qed seems to be calculated with zero widths in loop_qcd_qed_sm_Gmu

My problem is the following:
For the process pp -> e+ ν_e μ ν_μ which is at O(α^4) I found the following LO cross section for MG5:

total cross section (MG5) = 5.08170e-01 +- 7.1e-05 pb

Here I used the complex mass scheme and imported the model "loop_qcd_qed_sm_Gmu".
I did the same with Whizard+OpenLoops for the same parameters and cuts and I got:

total cross section (Whizard+OL) = 5.09334e-01 +- 1.54e-04 pb

Since the deviation is about 7σ, I (of course) checked again all the parameters/cuts but did not find anything which differs. However I then looked more specifically on the α which is calculated for both cases. In the "alllogs_<0/1/2/3>.html" file MG5 produced the value (same process folder, same run):

mdl_aEW = (7.55543540019748636E-003,0.0000000000000000)

While for WHIZARD, the α, which is calculated from OpenLoops and is used for the matrix elements, is:

alpha_qed_gmu = 7.5590620203331640E-003

When I calculate the ratio of these different values and take it to the power of 4 I get ≈1.0019, which would explain the 0.2% difference in the cross sections at LO for the process.
So this inconsistency in the alpha_qed drives me to the question which alpha is actually correct from the theory point of view. So I calculated it by hand from formula (5.59) from arXiv: 1804.10017.
Taking into account all the masses and widths as demanded I get
α=0.007559062020333 (A: all widths included)
And I also calculated how α would look without any widths (and I set them to 0):
α=0.007555435400197 (B: No widths included)
So I conclude from this, since the mdl_aEW output from MG5 is the same as value B, that somehow the widths get lost in the MG5 run. Again, indeed I set them different from 0 in the param_card. All the schemes/models are set correctly, i.e. the complex mass scheme and the model "loop_qcd_qed_sm_Gmu" are present in the proc_card_mg5.dat (and I repeated these steps as well with the same param/run_card but I see exactly the same alpha). So my questions are

1. Is the formula (5.59) indeed used in the model in MG for calculating alpha and does it take into account all the non-zero widths? Does the output mdl_aEW just correspond to a different scheme but actually is not used explicitly in the calculation of the cross sections?

2. I see in my old process folders in MG for which I used the same input values in the param_card (and also applied the complex mass scheme and took the model "loop_qcd_qed_sm_Gmu"), that the mdl_aEW value was a different one! It corresponds to value A, so takes into account all the widths. I also saw from http://madgraph.physics.illinois.edu/Downloads/models/ that the last change for "loop_qcd_qed_sm_Gmu" happend at march the 8th. My old process folders (for which there is the right alpha value A) were all initialized before. So maybe the model changed in the mean time? Do you know what happend for this model in that change?

3. Our institutes' cluster was upgraded to Ubuntu 20 in the meantime too so the installation of MadGraph I am using now is different than it was in my first attempt. I really tried a lot of times to reinstall MG5 and set up everything as in my first attempt. I also did this with different gfortran compilers (v7 on the cluster and v5 on my local computer). It's very unlikely but can it be that some files are not correctly compiled due to a wrong compiler version or anything like this?

I would be very glad if you can give any hints. Thanks already for considering!

Cheers,
Pia

## Question information

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Huasheng Shao Edit question
Solved by:
Hua-Sheng Shao
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 Revision history for this message marco zaro (marco-zaro) said on 2021-04-30: #1

Dear Pia,
thanks for reporting.
Indeed, it seems that the Gmu model downloaded automatically by MG5_aMC does not implement the relations dictated by eq Is the 5.59 in the 1804 paper.
Could you try to replace the model with the one you find here?
http://pcteserver.mi.infn.it/~mzaro/files/
(which was the model as shipped with the code, before the model database was set up)

For what I can see in parameters.py, alpha_EW should be derived correctly.

Best wishes,

Marco

 Revision history for this message Hua-Sheng Shao (erdissshaw) said on 2021-04-30: #2

Dear Pia,

thanks for pointing it out. Indeed, due to several versions (some are online and some are shipped by MG5), we have screwed up the model on the web (i.e. you downloaded via MG5 prompt). We will update the model in the next hour.

Let us know if you have any other question.

Best regards,

Hua-Sheng

 Revision history for this message Pia Bredt (bredtpia) said on 2021-04-30: #3

Thanks for solving this problem so quickly!

Now from both (either using http://pcteserver.mi.infn.it/~mzaro/files/ or importing the model via MG5 prompt) I get the correct alpha (taking into account non-zero widths):

mdl_aEW = (7.55906202033315971E-003,9.05919709075708747E-020)

Thanks again!

Best,
Pia

 Revision history for this message Pia Bredt (bredtpia) said on 2021-04-30: #4

Thanks Hua-Sheng Shao, that solved my question.