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indigojoker
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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.
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 oneindigojoker said:Are there examples where they do not make this assumption?
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.
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.
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.
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.
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.
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.