Calculating Cross Sections Using Intermediate Vector Boson Theory

In summary: However, I would recommend getting a more comprehensive textbook on the subject before attempting any calculations. In summary, the textbook "Introduction to Quantum Field Theory" by Donoghue, Golowich, and Holstein at Cambridge University Press goes into more detail about the IVB model and its high energy behavior. However, I think that a thicker textbook would be more beneficial before attempting any calculations.
  • #1
indigojoker
246
0
Would anyone know of any textbook that has explicit calculations of cross section using intermediate vector boson theory? I've looked in Perkins and Halzen+Martin but I do not see any in those texts.
 
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  • #2
I just looked into my Halzen & Martin, and I find there the muon decay rate calculated explicitely (just one example).

If Halzen & Martin's introductory textbook does not go deep enough, you probably need any textbook entitled "introduction to quantum field theory". Or "Dynamics of the Standard Model" (Donoghue, Golowich & Holstein @ Cambridge University Press) might do if you want phenomenology. If you are enclined towards theory, try Pokorsky's "Gauge Field Theories" @ same editor.
 
  • #3
In H+M, then give the amplitude using ivb theory (12.14) then they makes the approximation that [tex]q^2<<M_W^2[/tex] allowing the use of [tex]\frac{G}{\sqrt{2}}=\frac{g^2}{8M^2_W}[/tex] which then they eventually conclude with 12.35

Are there examples where they do not make this assumption?
 
  • #4
indigojoker said:
Are there examples where they do not make this assumption?
Later on when they talk about interferences in electron-positron annihilation for instance. But as you reach the end of this book, you probably need a thicker one :smile:

Therefore, congrats to you, because Halzen & Martin is a nice summary of basic particle physics.
 
  • #5
Correct me if I'm wrong, but calculating the cross section using IVB theory is very similar to using V-A theory. For example:

Say the cross section for some process is: [tex]\sigma = \frac{G^2 s}{\pi} [/tex] (H+M 12.60)

Then using IVB theory, we take out the [tex]\frac{G^2}{4}[/tex] constant when calculating the amplitude and replace it with [tex]\left(\frac{g^2}{M_W^2+q^2}\right)^2[/tex] so when all is said and done, we are left with the cross section as: [tex]\sigma=\left(\frac{g^2}{M_W^2+q^2}\right)^2 \frac{4s}{\pi}[/tex]

I think this makes sense because the first cross section allows [tex]\sigma[/tex] to go to infinity as s becomes large while using the IMV theory, the cross section is corrected at large s by the q^2 on the denominator, thus giving a finite total cross section.
 
  • #6
indigojoker said:
Correct me if I'm wrong, but calculating the cross section using IVB theory is very similar to using V-A theory. For example:

Say the cross section for some process is: [tex]\sigma = \frac{G^2 s}{\pi} [/tex] (H+M 12.60)

Then using IVB theory, we take out the [tex]\frac{G^2}{4}[/tex] constant when calculating the amplitude and replace it with [tex]\left(\frac{g^2}{M_W^2+q^2}\right)^2[/tex] so when all is said and done, we are left with the cross section as: [tex]\sigma=\left(\frac{g^2}{M_W^2+q^2}\right)^2 \frac{4s}{\pi}[/tex]

I think this makes sense because the first cross section allows [tex]\sigma[/tex] to go to infinity as s becomes large while using the IMV theory, the cross section is corrected at large s by the q^2 on the denominator, thus giving a finite total cross section.


Hi indigojoker,

It's definitely true that the IVB model improves greatly the high energy behavior.
It turns out, though, that it is nonrenormalizable if I recall correctly. I am not sure about this but I think that essentially, the difference between the IVB and the Standard Model weak interaction is that in the IVB model there is no relation between between the couplings to the charged and neutral carriers. In the weak interaction, there is of course a definite relation between them. Another difference (I think but am not sure) is that I think the original IVB model had only vector coupling ([tex] \gamma^\mu [/tex] ).

The book by Aitchison and Hey discusses a little bit the IVB model (Gauge theories in Particle Physics)
 

1. What is Intermediate Vector Boson (IVB) theory?

Intermediate Vector Boson (IVB) theory is a theoretical framework used to calculate cross sections in particle collisions. It describes the interactions between fundamental particles, such as protons and electrons, through the exchange of intermediate vector bosons, which are force-carrying particles.

2. How is IVB theory used to calculate cross sections?

IVB theory uses mathematical equations and principles of quantum field theory to calculate the probability of a specific particle interaction occurring in a collision. This probability is represented as the cross section, which is a measure of the effective area of the interaction.

3. What is the significance of calculating cross sections using IVB theory?

Calculating cross sections using IVB theory allows scientists to make predictions about the outcomes of particle collisions and to test the validity of the theory. It also helps to understand the fundamental structure of matter and the forces that govern its interactions.

4. What are some challenges in calculating cross sections using IVB theory?

One of the main challenges in calculating cross sections using IVB theory is the complexity of the mathematical equations involved. This requires advanced mathematical skills and computational resources. Additionally, uncertainties in the input parameters and experimental data can also affect the accuracy of the calculated cross sections.

5. How do scientists validate the results of cross section calculations using IVB theory?

Scientists validate the results of cross section calculations using IVB theory through experimental data from particle colliders, such as the Large Hadron Collider (LHC). By comparing the calculated cross sections to the measured cross sections, scientists can determine the accuracy of the theory and make improvements if necessary.

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