VBF higgs production at NLO

Asked by Antara Sarkar on 2020-12-23

Hi,

I have few questions related to VBF higgs production at NLO. I am generating this process in the following manner:

define j = j b
generate p p > h j j $$w+ w- z [QCD]

1. With default jet radius = 0.7, anti-kT algo., min jet pT = 20 GeV, maximum rapidity of jets = 5.0, the cross section seems to increase from LO value. However, in https://arxiv.org/pdf/1405.0301.pdf, in table 8 it is mentioned that NLO cross section for VBF decreases to 1.9 pb from LO 1.98 pb. The default jet radius here seems to be a bit large. What implication does it have.. I am asking because usually we set it to 0.5 radius.

2. For NLO event generation with showering, does the Pythia interface in Madgraph automatically merges the parton showers with hard jet emissions? Or should I set ickkw=3? Please correct me if I am wrong in understanding that while in matrix element at NLO, there are born diagrams with 2 partons, virtual diagrams and real emissions with 3 partons. Now the infrared divergence of the virtual diagrams will be cancelled by soft part of real emission partons. So, does parton showering too takes care of this divergence cancellation? If yes, how?

3. So, as a result, I will have three partons in the matrix element at NLO, however I am to study higgs plus 2 jets via VBF at NLO. So, should I do the following then?
generate p p > h j j $$w+ w- z [QCD]
add process p p > h j j j $$w+ w- z [QCD]
and then match?

Your insights will be helpful to understand this matter.

Best regards,
Antara

Question information

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MadGraph5_aMC@NLO Edit question
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Last query:
2020-12-23
Last reply:
2020-12-23

Hi,

> define j = j b

At NLO, this sounds a very bad command to use. Either use a 4 flavor model (and in that case do not include the b in the initial state) or use a 5 flavor model (and then that line is useless since this is automatic). Please check carefully the paper, but this is likely a 4 flavor computation.

> 1. With default jet radius = 0.7, anti-kT algo., min jet pT = 20 GeV, maximum rapidity of jets = 5.0, the cross section seems to increase from LO value. However, in https://arxiv.org/pdf/1405.0301.pdf, in table 8 it is mentioned that NLO cross section for VBF decreases to 1.9 pb from LO 1.98 pb. The default jet radius here seems to be a bit large. What implication does it have.. I am asking because usually we set it to 0.5 radius.

this is not a "standard jet definition", this is applying a cluster algorithm at parton-level (so you have up to 3 particle to merge...) so you should not mixed this with the clustering that you use in your analysis. As for all cuts that you impose at parton-level you need to ensure that you are not sensitive to those at the analysis level (i.e. they should be only optimization cut).

> 2. For NLO event generation with showering, does the Pythia interface in Madgraph automatically merges the parton showers with hard jet emissions? Or should I set ickkw=3? Please correct me if I am wrong in understanding that while in matrix element at NLO, there are born diagrams with 2 partons, virtual diagrams and real emissions with 3 partons. Now the infrared divergence of the virtual diagrams will be cancelled by soft part of real emission partons. So, does parton showering too takes care of this divergence cancellation? If yes, how?

The cancellation occurs between the virtual and the real emissions. The inclusion of the parton-shower is done via the MC@NLO method which requires a specific MC counter-term. The parton-shower does not need to be modified but the MC counter-term are Parton-Shower specific so you need to decide in advance which parton-shower you are going to use. Generated events are un-physical if not showered (or showered by another PS algorithm).

We are also going to release an alternative method MC@NLO-delta which is very similar to MC@NLO but has fewer negative events (both are NLO accurate, have the same main property but will be obviously differ by some subleading term)

> 3. So, as a result, I will have three partons in the matrix element at NLO, however I am to study higgs plus 2 jets via VBF at NLO. So, should I do the following then?
> generate p p > h j j $$w+ w- z [QCD]
> add process p p > h j j j $$w+ w- z [QCD]
> and then match?

If you do this then you need to use a merging method since

> generate p p > h j j $$w+ w- z [QCD]
Will give you events with 2 and 3 jets (2 jets for the born topology and 3 jet for the Real0
and
> add process p p > h j j j $$w+ w- z [QCD]
Will give you events with 3 and 4 jets (3 jets for the born topology and 4 jet for the Real0

In this particular case FxFx merging (ickkw=3) will not be working since it does not support jet in the lower multiplicity sample. UNLOPS might be an option here. But your question seems to indicate that this is not what you are looking for anyway.

Cheers,

Olivier

> On 23 Dec 2020, at 06:05, Antara Sarkar <email address hidden> wrote:
>
> New question #694629 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/694629
>
> Hi,
>
> I have few questions related to VBF higgs production at NLO. I am generating this process in the following manner:
>
> define j = j b
> generate p p > h j j $$w+ w- z [QCD]
>
> 1. With default jet radius = 0.7, anti-kT algo., min jet pT = 20 GeV, maximum rapidity of jets = 5.0, the cross section seems to increase from LO value. However, in https://arxiv.org/pdf/1405.0301.pdf, in table 8 it is mentioned that NLO cross section for VBF decreases to 1.9 pb from LO 1.98 pb. The default jet radius here seems to be a bit large. What implication does it have.. I am asking because usually we set it to 0.5 radius.
>
> 2. For NLO event generation with showering, does the Pythia interface in Madgraph automatically merges the parton showers with hard jet emissions? Or should I set ickkw=3? Please correct me if I am wrong in understanding that while in matrix element at NLO, there are born diagrams with 2 partons, virtual diagrams and real emissions with 3 partons. Now the infrared divergence of the virtual diagrams will be cancelled by soft part of real emission partons. So, does parton showering too takes care of this divergence cancellation? If yes, how?
>
> 3. So, as a result, I will have three partons in the matrix element at NLO, however I am to study higgs plus 2 jets via VBF at NLO. So, should I do the following then?
> generate p p > h j j $$w+ w- z [QCD]
> add process p p > h j j j $$w+ w- z [QCD]
> and then match?
>
> Your insights will be helpful to understand this matter.
>
> Best regards,
> Antara
>
> --
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