Basic Questions on the Standard Model

[Breo]

1) The Feynman Diagams which provide the dominant contributions are just those with the greater amplitudes? I have the doubt because I read could be more dominant contributions for a single process and I am not sure amplitude would be the same for them.

2) How to compute the cross section in terms of the Mandelstam variables? And the Average squared amplitude? I have just saw a couple of final computations which seems easy but it is like... I do not know what I should compute because in the formula appears the $F^2$ and I do not find how to compute this.

3) What means "background processes"?

4) Where can I find some info about technicolour gauge group $SU(4)_{TC}$, techniquarks $q_{TC}$, bound states technicolourless, gauge field transforming in the adjoint representation of the techniquark field transforming in the sextet representation, etc?

Answers (there are 3 basic questions I were carrying on, I know :s) would help me a lot to complete my knowledge.

 

[mfb]

1) The Feynman Diagams which provide the dominant contributions are just those with the greater amplitudes?

That is the meaning of "dominant", yes. If you look at the sum of 34528223 + 234 + 24, then the first summand is clearly dominant (even if we add complex phases to the numbers).

I have the doubt because I read could be more dominant contributions for a single process and I am not sure amplitude would be the same for them.

I don't understand that part.

2) Cross-section computations are complicated. A differential cross-section can be expressed as cross-section in terms of the Mandelstam variables. What do you mean with "average squared amplitude"? Average over what?

3) Processes that give the same particles in the final state (or particles similar enough to be mistaken), but without the real process you are interested in. gluon+gluon -> gluon -> b + bbar is a background for gluon-fusion -> Higgs -> b + bbar for example.

4) arXiv.org

 

[Breo]

I don't understand that part.

Because I have read there are some higher order terms which are not that smaller in comparison with the first terms on the amplitude.

What do you mean with "average squared amplitude"? Average over what?

I have saw it as $|F|^2$ and being expressed in terms of the Mandelstam variables, so the cross sections, and not only the differential cross sections, can be expressed with those terms, isn't it?
I have found it in the next equations:

$|F|^2 = |F_t|^2 + |F_u|^2 + F_tF_u* + F_uF_t*$ and

$\frac {d\theta}{d\Omega_{CM}} = \frac {1}{64\pi^2s} \frac {|P_j|}{|P_i|} |F|^2$Three more questions,

I suppose that the dominant processes can "change" given a $\sqrt{s}$ (in example higher energies in the LHC could produce Higgs bosons). How to compute that? For example for the LHC Higgs era with $\sqrt{s} = 8 \ TeV$ how to know what processes will happen more?

What is exactly the experimental signature?

In order to know if a process is allowed at tree level in the SM, could be enough to the leptonic, colour and flavour number to be conseved?

 

[mfb]

Because I have read there are some higher order terms which are not that smaller in comparison with the first terms on the amplitude.

That can happen, especially in QCD.

I suppose that the dominant processes can "change" given a $\sqrt{s}$ (in example higher energies in the LHC could produce Higgs bosons). How to compute that? For example for the LHC Higgs era with $\sqrt{s} = 8 \ TeV$ how to know what processes will happen more?

You calculate all up to some order and then you check their amplitude. Often you can get a rough estimate first to see what to expect.

What is exactly the experimental signature?

The experimental signature of what?

In order to know if a process is allowed at tree level in the SM, could be enough to the leptonic, colour and flavour number to be conseved?

Flavor does not have to be conserved (W boson), but charge has, and all vertices have to be allowed in the SM. You cannot couple a Z to a gluon, for example, it would not violate conservation laws but those particles just do not have a tree-level interaction.

 

[ChrisVer]

it would not violate conservation laws but those particles just do not have a tree-level interaction.

Wouldn't it violate the Standard Model...

 

[mfb]

Wouldn't it violate the Standard Model...

Exactly.