Difference between /z, $z and $$z in generator level

That tutorial was for version 1.1.0.

So clearly this is outdated and that version was not able to compute loop, so do not infer any conclusion about loop from that tutorial.
Actually the meaning of the syntax change since that version/tutorial (as written in the update Notes)

The meaning of the syntax "$" was changed in 1.3.18 (04/10/11)
and the new syntax "$$" (taking back the meaning of the previous $ syntax) has been added in 1.4.3 (08/03/12)

So make sense that those explanation are wrong in such tutorial.

So the meaning of the "$$" is actually forbids the s-channel.
The meaning of the "$" denoted the exclusion of ONSHELL s-channels while
                      keeping all diagrams (i.e., complemetary to the decay
                      chain formalism). This reduces the problems with
                      gauge invariance compared to previously.
                      "Onshell" is as usual defined by the "bwcutoff" flag
                      in the run_card.dat.

So this is implemented as a phase-space cut and not as a diagram removal method.

Cheers,

Olivier

PS: Here is a list of lecture/tutorial which are much more up-to-date

Okay I understand. But please tell me one thing:
generate mu+ mu- > mu+ mu- h

This command generates two diagrams.

generate mu+ mu- > mu+ mu- h $$z

removes the "diagram 1" and only generates "diagram 2".

How can I get only the "diagram 1"?

I mean how can I only get the "s-channel" diagram?

Also, I am not able to see the list of the lectures/tutorials that you mentioned.

Hi,

Like $$ is a bad syntax since it is common that such syntax breaks gauge invariance.
But yes we have a similar opposite syntax which is
generate mu+ mu- > z > mu+ mu- h

While the opposite of the "$" syntax is the decay chain syntax so the opposite of
generate p p > w+ b j $t
is
generate p p > t j, t > w+ b

(which are safer for gauge invariance)

Cheers,

Olivier

Yes. I just found out that the command
generate mu+ mu- > z > mu+ mu- h

produces only the s-channel diagrams. But generate mu+ mu- > mu+ mu- h $$z generates only the t-channel diagrams. Is there any other way to generate only the t-channel diagrams other than this?

Also how breaking the gauge-invariance will affect the cross-section?

I couldn't find the resources that you mentioned there.

Here is the most complete answer on how to do diagram filtering.

For the gauge invariance, it means that the reported cross-section depends on arbitrary parameter.
In EW process, the gauge invariance is canceling the energy growing of the amplitude (such that the process is unitary)
So if you break such gauge invariance, what you obserce is that cross-section is typically enhanced at high energy (and can break unitary bound). On the other hand, the gauge fixing term are sometimes also used to cancel some specific contribution, so if you keep only that contribution, then the result can be zero.

So in summary, the result of a computation without gauge invariance can vary from zero to infinity. And the result makes sense only if you sum up all the configuration to form a gauge invariant subset.

Cheers,

Olivier
FAQ #3322: “How to select of subset of diagram for LO computation?”.