# Double counting, how to avoid

Asked by Xiaojun Yao on 2017-10-31

I tried to generate the event: p p > g g, g > b b~, g > g

Madgraph gives me four diagrams with initial gluons. For the first two, the b-bbar comes only from one of the two outgoing gluons while for the last two, they are the same except the b-bbar coming from either outgoing gluon. See the diagrams:

There is a inconsistency in the b-bbar vertex. I can generate another event p p > g g, g > g, g > b b~
but then there will be double counting. Can you tell me how to get the correct non-double counting but all diagrams?

Many thanks,
Xiaojun

## Question information

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Olivier Mattelaer
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2017-10-31
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2017-10-31
2017-10-31
 Olivier Mattelaer (olivier-mattelaer) said on 2017-10-31: #1

Hi,

This syntax does not make sense for gluon!
This syntax is for on shell particles (up to N times the width), since the width of the gluon is 0, all the result from such syntax with a gluon should be consider as not physical.

Cheers,

Olivier

> On Oct 31, 2017, at 15:14, Xiaojun Yao <email address hidden> wrote:
>
> New question #660175 on MadGraph5_aMC@NLO:
>
>
> I tried to generate the event: p p > g g, g > b b~, g > g
>
> Madgraph gives me four diagrams with initial gluons. For the first two, the b-bbar comes only from one of the two outgoing gluons while for the last two, they are the same except the b-bbar coming from either outgoing gluon. See the diagrams:
>
>
> There is a inconsistency in the b-bbar vertex. I can generate another event p p > g g, g > g, g > b b~
> but then there will be double counting. Can you tell me how to get the correct non-double counting but all diagrams?
>
> Many thanks,
> Xiaojun
>
> --

 Xiaojun Yao (colo4k) said on 2017-10-31: #2

So what is the correct syntax if I want the process of p p > g g (both offshell) and one gluon splits to onshell b-bbar?

 Olivier Mattelaer (olivier-mattelaer) said on 2017-10-31: #3

Hi,

Well before speaking of syntax, let's speak of physics. I doubt that such computation makes ANY sense.
To check that, I have done the computation with madgraph and check the lorentz invariance and the gauge invariance of such computation and as i was expected the result is such that such computation does not make sense.

The syntax used to produce those result is one syntax that I do not advise to use (precisely for the reason that it can lead to unphysical result like this is the case here). So I will not indicated it in this thread.

Cheers,

Olivier

PS: The output of the command that I run to convince myself that indeed what you ask is not physical:

Note That all width have been set to zero for those checks

Lorentz invariance results:
Process Min element Max element Relative diff. Result
g g > b b~ g 2.4640685884e-03 2.9913270485e-03 1.7626239177e-01 Failed
JAMP 0 2.6587817855e-04 4.7535150497e-04 4.4067037600e-01 Failed
JAMP 1 1.9652602857e-02 2.2478186246e-02 1.2570335334e-01 Failed
JAMP 2 1.4916576672e-02 1.9710627570e-02 2.4322162657e-01 Failed
JAMP 3 1.9652602857e-02 2.2478186246e-02 1.2570335334e-01 Failed
JAMP 4 1.4916576672e-02 1.9710627570e-02 2.4322162657e-01 Failed
JAMP 5 2.6587817855e-04 4.7535150497e-04 4.4067037600e-01 Failed
Summary: 0/1 passed, 1/1 failed
Failed processes: g g > b b~ g
Gauge results:
Process matrix BRS ratio Result
g g > b b~ g 5.1279675740e-04 1.2487046324e-04 2.4350868339e-01 Failed
JAMP 0 1.4373155404e-03 6.1902538651e-04 4.3068162078e-01 Failed
JAMP 1 4.8280692268e-03 1.0685267518e-03 2.2131554077e-01 Failed
JAMP 2 1.0277246714e-03 8.8383338870e-05 8.5999043648e-02 Failed
JAMP 3 4.8280692268e-03 1.0685267518e-03 2.2131554077e-01 Failed
JAMP 4 1.0277246714e-03 8.8383338870e-05 8.5999043648e-02 Failed
JAMP 5 1.4373155404e-03 6.1902538651e-04 4.3068162078e-01 Failed
Summary: 0/1 passed, 1/1 failed
Failed processes: g g > b b~ g
Gauge results (switching between Unitary/Feynman):
Process Unitary Feynman Relative diff. Result
g g > b b~ g 2.7753182848e-03 2.7753182848e-03 0.0000000000e+00 Passed
Summary: 1/1 passed, 0/1 failed
Process permutation results:
Process Min element Max element Relative diff. Result
g g > b b~ g 2.8778596723e-03 2.8778596723e-03 1.5069562744e-16 Passed

Well I do not think that such computation makes sense. How do you preserve gauge invariance in that case?

 Xiaojun Yao (colo4k) said on 2017-10-31: #4

Thank you for the warning. But I still want to know the syntax not just for this problem and also for future applications to other problems.

Let me explain why I want it in this problem. I want to generate b bbar pair at NLO in alpha_s so that the pair has non-zero pT. I used the syntax p p > g b b~. But this is not enough for me. Because I want to focus on the b b~ that are moving collinearly (their momenta are close). The process p p > g b b~ gives a lot of pairs in the unwanted phase space. So I need the b bbar to come from the process describe above. I agree gauge invariance is important but since my following calculations are done in non-relativistic EFT and gauge invariance is lost in any way. Can you tell me the syntax you are using?

 Olivier Mattelaer (olivier-mattelaer) said on 2017-10-31: #5

Hi,

Note that also lorentz invariance are violated.
What you try to do does not make any sense to me but ok.
Actually my syntax was equivalent to yours as long as you are using standalone output.
Both will return the same non sense.

Cheers,

olivier

> On Oct 31, 2017, at 18:14, Xiaojun Yao <email address hidden> wrote:
>
> Question #660175 on MadGraph5_aMC@NLO changed:
>
>
> Xiaojun Yao is still having a problem:
> Thank you for the warning. But I still want to know the syntax not just
> for this problem and also for future applications to other problems.
>
> Let me explain why I want it in this problem. I want to generate b bbar
> pair at NLO in alpha_s so that the pair has non-zero pT. I used the
> syntax p p > g b b~. But this is not enough for me. Because I want to
> focus on the b b~ that are moving collinearly (their momenta are close).
> The process p p > g b b~ gives a lot of pairs in the unwanted phase
> space. So I need the b bbar to come from the process describe above. I
> agree gauge invariance is important but since my following calculations
> are done in non-relativistic EFT and gauge invariance is lost in any
> way. Can you tell me the syntax you are using?
>
> --

 Xiaojun Yao (colo4k) said on 2017-10-31: #6

Let me ask this question. What is the syntax to generate p p > g (QQ~)[n], i.e., generate a QQbar pair with certain quantum numbers, which is used in NRQCD factorization.

 Olivier Mattelaer (olivier-mattelaer) said on 2017-10-31: #7

Hi,

We do not support such syntax in the official version of the code.
You should refer to either Madonia or HelacOnia code.

I guess that code is not supported anymore.
HelacOnia is more recent and should still be supported.

Cheers,

Olivier

> On Oct 31, 2017, at 19:44, Xiaojun Yao <email address hidden> wrote:
>
> Question #660175 on MadGraph5_aMC@NLO changed:
>
>
> Xiaojun Yao is still having a problem:
> Let me ask this question. What is the syntax to generate p p > g
> (QQ~)[n], i.e., generate a QQbar pair with certain quantum numbers,
> which is used in NRQCD factorization.
>
> --