MadGraph5_aMC@NLO

Changing the electroweak couplings of the top quark

Asked by Baptiste Ravina

Dear Experts,

Using MadGraph v3.2.0, I looked at the electroweak couplings of the top quark, namely in the ttgamma and ttZ vertices, as coded in the sm and loop_sm models. For instance, at LO, I find that the ttZ vertex is
-GC_50 * FFV2 + GC_58 * FFV5
while the ttgamma vertex is
GC_2 * FFV1
Looking up these couplings and Lorentz structures, and doing a bit of algebra, I'm able to recover the expected Lagrangians for the ttZ and ttgamma vertices. However, instead of relying on model parameters for the charge and weak isospin of the top quark (which could be set to a constant somewhere), the values of +2/3 and +1/2 are used implicitly in the definition of these GC couplings.

I have a few questions:

1) Is it by any means safe to make a copy of the sm UFO, create parameters to control the top's Q and T3, and assign new ttZ and ttgamma couplings that depend explicitly on these parameters? (with the intention of then varying these parameters through reweighting) I know that some EFT models come with additional operators that contribute to these vertices, but they also alter other vertices, and here I'm interested purely in the effects of Q and T3 on the tt+V cross section (inclusive and differential).

2) When doing the same investigation at NLO (with loop_sm), I find essentially the same structure than at LO, plus additional terms that are the same as the LO ones but that come with an extra factor called R2MixedFactor. What does this represent? The definition "-(G**2*(1.0+lhv)*(Ncol**2-1.0))/(2.0*Ncol*16.0*cmath.pi**2)" is a bit opaque to me...

3) Still at NLO, I'm slightly surprised to not see any term accounting for the anomalous electric/magnetic dipole moments. For instance, arXiv:1404.1005 mentions (equation 2.5 and following paragraph) that one of these is O(1e-4) at NLO in ttZ. Is it simply neglected here, or hidden somewhere else?

Thanks for your help,
Baptiste.

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Olivier Mattelaer
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Best Olivier Mattelaer (olivier-mattelaer) said : 		#1

>
> 1) Is it by any means safe to make a copy of the sm UFO, create parameters to control the top's Q and T3, and assign new ttZ and ttgamma couplings that depend explicitly on these parameters? (with the intention of then varying these parameters through reweighting) I know that some EFT models come with additional operators that contribute to these vertices, but they also alter other vertices, and here I'm interested purely in the effects of Q and T3 on the tt+V cross section (inclusive and differential).

At LO, I do not see any major difficulites.

> 2) When doing the same investigation at NLO (with loop_sm), I find essentially the same structure than at LO, plus additional terms that are the same as the LO ones but that come with an extra factor called R2MixedFactor. What does this represent? The definition "-(G**2*(1.0+lhv)*(Ncol**2-1.0))/(2.0*Ncol*16.0*cmath.pi**2)" is a bit opaque to me...

This is exactly why NLO should not be done by hand since you do have a lot of computation that are in a way pre-process within the model (like all the R2 term) for a definition of those the best is to look at the cuttools paper (or any loop paper).
Another paper which is likely important for you here is the NLOCT paper.
Additionally you also need the UV-conterterm (as explained within the NLOCT paper).

The strong sugestion here is to use FeynRules/NLOCT to create your NLO model.

> 3) Still at NLO, I'm slightly surprised to not see any term accounting for the anomalous electric/magnetic dipole moments. For instance, arXiv:1404.1005 mentions (equation 2.5 and following paragraph) that one of these is O(1e-4) at NLO in ttZ. Is it simply neglected here, or hidden somewhere else?

Well I do not know the detail here, but the first question is which term do you think is missing with the UFO model for the Standard Model?

Cheers,

Olivier

> On 15 Jun 2022, at 20:35, Baptiste Ravina <email address hidden> wrote:
>
> New question #702194 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/702194
>
> Dear Experts,
>
> Using MadGraph v3.2.0, I looked at the electroweak couplings of the top quark, namely in the ttgamma and ttZ vertices, as coded in the sm and loop_sm models. For instance, at LO, I find that the ttZ vertex is
> -GC_50 * FFV2 + GC_58 * FFV5
> while the ttgamma vertex is
> GC_2 * FFV1
> Looking up these couplings and Lorentz structures, and doing a bit of algebra, I'm able to recover the expected Lagrangians for the ttZ and ttgamma vertices. However, instead of relying on model parameters for the charge and weak isospin of the top quark (which could be set to a constant somewhere), the values of +2/3 and +1/2 are used implicitly in the definition of these GC couplings.
>
> I have a few questions:
>
> 1) Is it by any means safe to make a copy of the sm UFO, create parameters to control the top's Q and T3, and assign new ttZ and ttgamma couplings that depend explicitly on these parameters? (with the intention of then varying these parameters through reweighting) I know that some EFT models come with additional operators that contribute to these vertices, but they also alter other vertices, and here I'm interested purely in the effects of Q and T3 on the tt+V cross section (inclusive and differential).
>
> 2) When doing the same investigation at NLO (with loop_sm), I find essentially the same structure than at LO, plus additional terms that are the same as the LO ones but that come with an extra factor called R2MixedFactor. What does this represent? The definition "-(G**2*(1.0+lhv)*(Ncol**2-1.0))/(2.0*Ncol*16.0*cmath.pi**2)" is a bit opaque to me...
>
> 3) Still at NLO, I'm slightly surprised to not see any term accounting for the anomalous electric/magnetic dipole moments. For instance, arXiv:1404.1005 mentions (equation 2.5 and following paragraph) that one of these is O(1e-4) at NLO in ttZ. Is it simply neglected here, or hidden somewhere else?
>
> Thanks for your help,
> Baptiste.
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Baptiste Ravina (bravina) said : 		#2

Hi Olivier - thanks for the prompt reply!

>> 3) Still at NLO, I'm slightly surprised to not see any term accounting for the anomalous electric/magnetic dipole moments. For instance, arXiv:1404.1005 mentions (equation 2.5 and following paragraph) that one of these is O(1e-4) at NLO in ttZ. Is it simply neglected here, or hidden somewhere else?

> Well I do not know the detail here, but the first question is which term do you think is missing with the UFO model for the Standard Model?

Looking at this paper https://arxiv.org/pdf/1404.1005.pdf page 6 equation 2.5, I believe the term that is missing from both the sm and loop_sm UFO models is the second one, that goes as \sigma_{\mu\nu}q_\nu over M(Z). See also page 6 of https://arxiv.org/pdf/hep-ph/9812298.pdf.
The claim there is that one of these additional coefficients is generated at one-loop but is still 3 orders of magnitude smaller than the standard vector and axial couplings, and the other one only appears beyond two loops.

Cheers,
Baptiste

Revision history for this message
Baptiste Ravina (bravina) said : 		#3

Thanks Olivier Mattelaer, that solved my question.

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said : 		#4

> Looking at this paper https://arxiv.org/pdf/1404.1005.pdf page 6 equation 2.5, I believe the term that is missing from both the sm and loop_sm UFO models is the second one, that goes as \sigma_{\mu\nu}q_\nu over M(Z). See also page 6 of https://arxiv.org/pdf/hep-ph/9812298.pdf.
> The claim there is that one of these additional coefficients is generated at one-loop but is still 3 orders of magnitude smaller than the standard vector and axial couplings, and the other one only appears beyond two loops.

If it is generated at one loop this should not be part of the model.
Obviously first for the sm model (since this is a LO model)
But also for the loop_sm model which is able to compute the loop exactly
But does not include the loop itself in the model (only the R2 part and the UV conter-term in top of the tree-level coupling).

Now those can also be included with effective operator but then this is typically done in an anothre model which can be seen as an extension of the sm (like the heft model add the ggh interaction to the sm to speed-up (and approximatie) the Higgs production at LHC)

Cheers,

Olivier

> On 15 Jun 2022, at 22:45, Baptiste Ravina <email address hidden> wrote:
>
> Question #702194 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/702194
>
> Baptiste Ravina posted a new comment:
> Hi Olivier - thanks for the prompt reply!
>
>>> 3) Still at NLO, I'm slightly surprised to not see any term
> accounting for the anomalous electric/magnetic dipole moments. For
> instance, arXiv:1404.1005 mentions (equation 2.5 and following
> paragraph) that one of these is O(1e-4) at NLO in ttZ. Is it simply
> neglected here, or hidden somewhere else?
>
>> Well I do not know the detail here, but the first question is which
> term do you think is missing with the UFO model for the Standard Model?
>
> Looking at this paper https://arxiv.org/pdf/1404.1005.pdf page 6 equation 2.5, I believe the term that is missing from both the sm and loop_sm UFO models is the second one, that goes as \sigma_{\mu\nu}q_\nu over M(Z). See also page 6 of https://arxiv.org/pdf/hep-ph/9812298.pdf.
> The claim there is that one of these additional coefficients is generated at one-loop but is still 3 orders of magnitude smaller than the standard vector and axial couplings, and the other one only appears beyond two loops.
>
> Cheers,
> Baptiste
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.