Definitions in the Feynman gauge

Hi,

We do not change the polarisation vector of the initial/final state W, and therefore do not need to include ghost for the final state particle.

Cheers,

Olivier

On 19 Jan 2015, at 08:01, Liucheng Wang <email address hidden> wrote:

> New question #260930 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/260930
>
> Hi, the Madgraph group,
>
> I just find that the Feynman gauge is supported by the code Madgraph.
> But the definitions of W+ and g+ in the sm are confusing for me.
> Unitary and Feynman gauge should lead to the same cross-section for a fixed process, such as top quark decay as shown in Chapter 21of Peskin' QFT book.
> The result of t > b w+ in the unitary gauge equals to the combined result of two processes t > b w+ and t > b g+ in the Feynman gauge.
>
> I tried three different processes in Madgraph as follows:
>
> (1) p p > w+ w+ in the default unitary gauge
>
> (2) set gauge Feynman
> Defined multiparticle all = g u c d s u~ c~ d~ s~ a ve vm vt e- mu- ve~ vm~ vt~ e+ mu+ t b t~ b~ z w+ h g0 g+ w- g- ta- ta+
> define v+ = w+ g+
> define v- = w- g-
> p p > v+ v-
>
> (3) set gauge Feynman
> p p > w+ w-
>
> I think (1) and (2) will result in exactly the same cross section. But I am wrong.
> In Madgraph, (1) and (3) lead to the same result while the result of (2) is a bit larger.
> So I am puzzled about the definitions of W+ and g+ in the code.
>
> Maybe this is a stupid question. But could you kindly give me some guidance?
> Thank you for your time and consideration.
>
>
>
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Hi Olivier,

Thank you for your reply.
g0 g+ w- g- are three new particles in the sm if the Feynman gauge is chosen.
Are they all ghost particles?
Before seeing your answer I thought they are three goldstone bosons eaten by Z and W bosons.

Thank you.

Hi,

Those are indeed goldstone which are going to compensate the change for the internal propagator.

Cheers,

Olivier

On 19 Jan 2015, at 17:36, Liucheng Wang <email address hidden> wrote:

> Question #260930 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/260930
>
> Status: Answered => Open
>
> Liucheng Wang is still having a problem:
> Hi Olivier,
>
> Thank you for your reply.
> g0 g+ w- g- are three new particles in the sm if the Feynman gauge is chosen.
> Are they all ghost particles?
> Before seeing your answer I thought they are three goldstone bosons eaten by Z and W bosons.
>
> Thank you.
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Hi Olivier,

Thank you very much.
Your answer solved my question.