MadGraph5_aMC@NLO

SM model with polarized propagator

Asked by Philip Chang

Hi Olivier,

I have additional question stating from https://answers.launchpad.net/mg5amcnlo/+question/266533

I want to implement polarized propagators for massive bosons so I can do a full VBS like,

generate p p > j j w+ w+ QCD=0, w+ > l+ vl, w+ > l+ vl

First of all, I don't think it physically make sense, but this is the best I could think of that's "reasonable".

If my memory serves me right from QFT years ago, if I work out the propagators for massive bosons the longitudinal and transverse mode are somewhat intertwined to do something complex (canceling poles? I can't remember) So the following is just taking two terms separately in unitary gauge. Do you have any better suggestions?

propagators.py
----------------------
denominator = "P('mu', id) * P('mu', id) - Mass(id) * Mass(id) + complex(0,1) * Mass(id) * Width(id)"

# transverse

VT = Propagator(name = "VT",
                numerator = "complex(0,1) * (-1 * Metric(l1, l2))",

                denominator = denominator
               )

# longitudinal

VL = Propagator(name = "VL",
                numerator = "complex(0,1) * Metric(l1,'mu')* P('mu', id) * P(l2, id) / Mass(id)**2 ",
                denominator = denominator
               )
----------------------
In particles.py, I modified w+ particle to have propagator = propagators.VT

However, I get index contraction error at the ALOHA. Specifically fails with FFV2PVT_3. What am I missing?

Also in the particles.py I am not sure which particles I should add the custom propagators for. I want to focus on WLWL scattering. I am specifically confused with ghost particles.

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

Dear Philip,

I have check the official reference for that feature: 1308.1668
and the correct syntax is:
# transverse
VT = Propagator(name = "VT",
                numerator = "complex(0,1) * (-1 * Metric(1, 2))",
                denominator = denominator
               )

# longitudinal
VL = Propagator(name = "VL",
                numerator = "complex(0,1) * Metric(1,'mu')* P('mu', id) * P(2, id) / Mass(id)**2 ",
                denominator = denominator
               )

The use of l1 and l2 corresponds to an old version of the format, I realise that FR still indicates that old syntax and ask them to fix it.

Cheers,

Olivier

On 02 Oct 2015, at 08:23, Philip Chang <email address hidden> wrote:

> New question #271989 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/271989
>
> Hi Olivier,
>
> I have additional question stating from https://answers.launchpad.net/mg5amcnlo/+question/266533
>
> I want to implement polarized propagators for massive bosons so I can do a full VBS like,
>
> generate p p > j j w+ w+ QCD=0, w+ > l+ vl, w+ > l+ vl
>
> First of all, I don't think it physically make sense, but this is the best I could think of that's "reasonable".
>
> If my memory serves me right from QFT years ago, if I work out the propagators for massive bosons the longitudinal and transverse mode are somewhat intertwined to do something complex (canceling poles? I can't remember) So the following is just taking two terms separately in unitary gauge. Do you have any better suggestions?
>
> propagators.py
> ----------------------
> denominator = "P('mu', id) * P('mu', id) - Mass(id) * Mass(id) + complex(0,1) * Mass(id) * Width(id)"
>
>
> # transverse
>
> VT = Propagator(name = "VT",
> numerator = "complex(0,1) * (-1 * Metric(l1, l2))",
>
> denominator = denominator
> )
>
> # longitudinal
>
> VL = Propagator(name = "VL",
> numerator = "complex(0,1) * Metric(l1,'mu')* P('mu', id) * P(l2, id) / Mass(id)**2 ",
> denominator = denominator
> )
> ----------------------
> In particles.py, I modified w+ particle to have propagator = propagators.VT
>
> However, I get index contraction error at the ALOHA. Specifically fails with FFV2PVT_3. What am I missing?
>
> Also in the particles.py I am not sure which particles I should add the custom propagators for. I want to focus on WLWL scattering. I am specifically confused with ghost particles.
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Philip Chang (philip-chang-3) said : 		#2

Thanks Olivier for quick answer,

What about in particles.py? which particles should I modify the propagators for? would changing only the W particles suffice? I also see ghost particles and so forth. What should I do about these?

Philip

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said : 		#3

Hi,

> which particles should I modify the
> propagators for? would changing only the W particles suffice?

Yes, but obviously this also depends of the process that you look at.
(i.e. if you look at VBF process, you might want to duplicate the W to have two type of W, one polarised and one unpolarised)

> I also see
> ghost particles and so forth. What should I do about these?

ghost particles are discarded by MG (at LO).
The other type of special particles are goldstone and those are only use in Feynman Gauge.
So if you run in unitary gauge (the default) then you do not care about those.

Cheers,

Olivier

On 02 Oct 2015, at 10:42, Philip Chang <email address hidden> wrote:

> Question #271989 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/271989
>
> Status: Answered => Open
>
> Philip Chang is still having a problem:
> Thanks Olivier for quick answer,
>
> What about in particles.py? which particles should I modify the
> propagators for? would changing only the W particles suffice? I also see
> ghost particles and so forth. What should I do about these?
>
> Philip
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Philip Chang (philip-chang-3) said : 		#4

Thanks Olivier for your response.

It seems like there are lots of places to change including vertices.py . I think I have something "working" but it will take some time to validate it. If I have any more questions I will ask in another thread as the initial questions are answered. I think we can close this issue.

Philip

Revision history for this message
Philip Chang (philip-chang-3) said : 		#5

Thanks Olivier Mattelaer, that solved my question.