Decay of the SM Higgs to polarized vector bosons

Asked by Lailin Xu on 2020-11-10

Hi,

Since now MG is able to generate polarized vector bosons, I'm wondering if it's possible to decay the SM Higgs to polarized vector bosons. For example, I want to study ggF H->ZZ->4l, with different polarized Z bosons. Since here the Higgs boson is on-shell, the following syntax would not work:
generate p p > h > z{L} z{L} [noborn=QCD]
because this would give on-shell H with two on-shell Z bosons. Do you have any suggestions on how to generate on-shell H's with one on-shell and one off-shell polarized Z bosons? Or it is not possible yet to generate off-shell polarized bosons?

Thanks,
Lailin

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Last query:
2020-11-10
Last reply:
2020-11-21

This question was reopened

Hi,

> Or it is not possible yet to generate off-shell polarized bosons?

No this is possible. They are theoretical issue with off-shell effect.
(The most important one being that you will break invariance and this will lead to non physical issue)
In MG5aMc, we rely on a cut on the invariant mass to ensure that the mass is very close to be onshell and avoid those gauge invariance issue in this context.

In the OSP method, the gauge invariance does not need a cut, but the result can not be trusted for "too much offshell" effects as well.

Cheers,

Olivier

> On 10 Nov 2020, at 09:41, Lailin Xu <email address hidden> wrote:
>
> New question #693918 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/693918
>
> Hi,
>
> Since now MG is able to generate polarized vector bosons, I'm wondering if it's possible to decay the SM Higgs to polarized vector bosons. For example, I want to study ggF H->ZZ->4l, with different polarized Z bosons. Since here the Higgs boson is on-shell, the following syntax would not work:
> generate p p > h > z{L} z{L} [noborn=QCD]
> because this would give on-shell H with two on-shell Z bosons. Do you have any suggestions on how to generate on-shell H's with one on-shell and one off-shell polarized Z bosons? Or it is not possible yet to generate off-shell polarized bosons?
>
> Thanks,
> Lailin
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Lailin Xu (xlltoade) said : #2

Hi Oliver,

Thanks for your reply! I'm curious because there is recent paper https://arxiv.org/abs/2007.12080 that has performed analytical calculations of H->VV* with different polarizations. I thought that it would be possible to generate polarized H->VV* events if the analytical calculations are possible. Maybe I'm missing something. Do you have any insights?

Thanks,
Lailin

I will refrain myself to comment too much publicly that paper.

If I would be the referee of that paper I would request
 1. some additional validation in order to see that everything is indeed well behaved (it can be that those gauge invariance issue does not pop up in that regime but this is not checked in the paper) and more generally on how "good" the usage of the polarization for the offshell Z is valid.
 2. some statement about the importance of the fourth polarization (mention in the introduction of the paper but not anymore in the subsequent computation)

But I have to be honest here, I have not carefully read this paper.

Technically you can do
generate h > Z{} Z{}, Z > l+ l-
and change bwcutoff parameter to allow the offshell part but as said before this require serious validation.
Do not trust the result (and comparing to the above paper is not good enough)

Cheers,

Olivier

> On 14 Nov 2020, at 17:30, Lailin Xu <email address hidden> wrote:
>
> Question #693918 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/693918
>
> Lailin Xu posted a new comment:
> Hi Oliver,
>
> Thanks for your reply! I'm curious because there is recent paper
> https://arxiv.org/abs/2007.12080 that has performed analytical
> calculations of H->VV* with different polarizations. I thought that it
> would be possible to generate polarized H->VV* events if the analytical
> calculations are possible. Maybe I'm missing something. Do you have any
> insights?
>
> Thanks,
> Lailin
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Lailin Xu (xlltoade) said : #4

Hi Olivier,

Many thanks for your clarification!

I was trying to run the following:
generate g g > h > z z QCD=2 QED=2 NP=0 [noborn=QCD]

then with madspin:
set spinmode None
decay z > l+ l-

Even though I set bwcutoff with a large number, the two Z bosons are always on-shell, as they are in the final state. Do you have any other suggestions?

Thanks,
Lailin

That's true that for loop-induced processes we do not have any solution for this.
since loop-induced processes are not compatible with decay-chain syntax
and that we need to use that syntax (obviously) if one wants to specify the polarization.

The solution in this particular case is to use the heft model/approach where the ggh vertex is approximate by a tree-level diagram. Such approximation is off-course bad if you have hard jet since in that case this is not a good approximation.

Cheers,

Olivier

Lailin Xu (xlltoade) said : #6

Hi Olivier,

Many thanks for your clarification! I still have one more question.
My understanding is that, to run MadSpin with loop-induced processes, one has to use "spinmode=None", which means no spin correlations are included. This might not be good for the purpose of polarization study. If I run "generate g g > h > z{0} z{0} QCD=2 QED=2 NP=0 [noborn=QCD]", then decay the Z's with madspin and spinmode=None, do the final state leptons still contain the full polarization information of the parent Z bosons?

In your paper https://arxiv.org/pdf/1912.01725.pdf, you have a specific note on this:

"While possible, we discourage using polarization features with special modes of MadSpin. For the
spinmode=none case (no spin correlation and no off-shell effects), the polarization of particles will be defined
in the rest-frame of the primary decay particle"

Does this mean that, each of the two Z bosons has its own reference frame, even though I set "me_frame=[3,4]"? So basically with "spinmode=None", one Z boson has me_frame=[3], and the other one has me_frame=[4]. Do I understand this correctly? Do you have any suggestions to avoid this inconsistency?

Thanks,
Lailin

Hi,

> Do I understand this correctly?

Yes.
The decay of the Z will be done assuming me_frame=[3] or me_frame=[4], but the production will be done with me_frame=[3,4]. The point is that the spinmode=none is a stupid mode (designed for the Higgs) where we simply glue together events coming from different generation.

> Do you have any
> suggestions to avoid this inconsistency?

Using heft approximation for the Higgs.

Cheers,

Olivier

> On 21 Nov 2020, at 07:35, Lailin Xu <email address hidden> wrote:
>
> Question #693918 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/693918
>
> Lailin Xu posted a new comment:
> Hi Olivier,
>
> Many thanks for your clarification! I still have one more question.
> My understanding is that, to run MadSpin with loop-induced processes, one has to use "spinmode=None", which means no spin correlations are included. This might not be good for the purpose of polarization study. If I run "generate g g > h > z{0} z{0} QCD=2 QED=2 NP=0 [noborn=QCD]", then decay the Z's with madspin and spinmode=None, do the final state leptons still contain the full polarization information of the parent Z bosons?
>
> In your paper https://arxiv.org/pdf/1912.01725.pdf, you have a specific
> note on this:
>
> "While possible, we discourage using polarization features with special modes of MadSpin. For the
> spinmode=none case (no spin correlation and no off-shell effects), the polarization of particles will be defined
> in the rest-frame of the primary decay particle"
>
> Does this mean that, each of the two Z bosons has its own reference
> frame, even though I set "me_frame=[3,4]"? So basically with
> "spinmode=None", one Z boson has me_frame=[3], and the other one has
> me_frame=[4]. Do I understand this correctly? Do you have any
> suggestions to avoid this inconsistency?
>
> Thanks,
> Lailin
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

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