Basic Questions on the Standard Model

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Discussion Overview

The discussion revolves around basic questions related to the Standard Model of particle physics, focusing on Feynman diagrams, cross-section calculations, background processes, and specific theoretical concepts such as technicolor. Participants seek clarification on various aspects of these topics, including computational methods and theoretical implications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that dominant contributions in Feynman diagrams correspond to those with greater amplitudes, while others express uncertainty about the existence of multiple dominant contributions for a single process.
  • There is a discussion on the complexity of computing cross-sections in terms of Mandelstam variables, with questions about the meaning of "average squared amplitude" and its relation to differential cross-sections.
  • Background processes are described as those that yield similar final state particles but are not the primary process of interest, with an example provided involving gluon fusion and Higgs production.
  • Participants inquire about the significance of higher order terms in amplitudes and their potential comparability to leading terms, particularly in the context of QCD.
  • Questions are raised about how to determine dominant processes at different energy levels, such as those at the LHC, and the methods for estimating expected outcomes.
  • Clarifications are sought regarding experimental signatures and the conditions under which processes are allowed at tree level in the Standard Model, including conservation laws related to leptonic, color, and flavor numbers.

Areas of Agreement / Disagreement

Participants express differing views on the nature of dominant contributions in Feynman diagrams and the implications of higher order terms. There is no consensus on the methods for computing cross-sections or the interpretation of experimental signatures, indicating multiple competing views and unresolved questions.

Contextual Notes

Limitations include the lack of clarity on specific definitions, the dependence of some claims on the context of energy levels, and unresolved mathematical steps in the computation of cross-sections and amplitudes.

Breo
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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.
 
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Breo said:
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).
Breo said:
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
 
mfb said:
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.

mfb said:
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?
 
Breo said:
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.

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

Wouldn't it violate the Standard Model...
 
ChrisVer said:
Wouldn't it violate the Standard Model...
Exactly.
 

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