2 -> 2 hadronic production cross section

In summary, the conversation is about calculating the hadronic production cross section for the process of p p > t t~ at tree level. The first problem encountered is a negative value for the matrix element amplitude and the Mandelstam variable. The variables are defined and the differential cross section formula is given. The speaker suggests that the calculations may have been done incorrectly and asks for suggestions or references for further understanding. The response advises to check the calculations and clarifies the notation used for the amplitude squared.
  • #1
Safinaz
258
8
Hi all,

Could anyone help for calculating the hadronc production cross section for example for
tree level : p p > t t~ process, I try to calculate, but the first problem I meet is a negative value of the matrix element amplitude (and so cross section ) and a negative ## \hat{t} ## Mandelstam variable :

I define ## \hat{t} ## : ## - \frac{\hat{s}}{2} (1 - \beta \cos \theta) + m^2_{t} ##
with: ## \beta =\sqrt{1- \frac{4m_{t}^2}{\hat{s}}} ##, ## \hat{s} = x1 x2 s \sim x^2 s (for x1=x2) ##, s = 14000^2 and ## ## tree level (partonic) diff. cross section :

## \frac{d\hat{\sigma}}{d\cos\theta} = \frac{\beta}{16\pi \hat{s}}~ | M|^2 ##So did I defined every thing consistently , any suggestions ..
Do you know any good refrence or exercises about that ..Regards,
Safinaz
 
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  • #2
of course you must be doing something wrong... Be careful, when you compute the amplitude squared, you write:
[itex]\left|M\right|^{2}= M^{+}M[/itex] with + I denote the dager/hermitian conjugate.
So it's practically impossible (even if you define something "wrong" in your procedure) to get negative value out of it...Something you are doing wrong in your calculations.

Also please give me to understand better what you did... Did you work with dirac spinors for example?
 

1. What is the 2 -> 2 hadronic production cross section?

The 2 -> 2 hadronic production cross section is a measure of the probability that a certain type of particle collision will occur and result in the production of two particles. This measurement is commonly used in high energy particle physics experiments to study the interactions of subatomic particles.

2. How is the 2 -> 2 hadronic production cross section calculated?

The 2 -> 2 hadronic production cross section is calculated by taking the number of observed events where two particles are produced and dividing it by the total number of collisions that occurred. This calculation is then adjusted for any experimental factors, such as detector efficiency, to obtain an accurate measurement.

3. What is the significance of the 2 -> 2 hadronic production cross section?

The 2 -> 2 hadronic production cross section is an important measurement in particle physics as it provides information about the strength of the interaction between particles. By studying this cross section, scientists can gain a better understanding of the fundamental forces that govern the behavior of particles.

4. How does the 2 -> 2 hadronic production cross section differ from other types of cross sections?

The 2 -> 2 hadronic production cross section is specific to the production of two particles and is different from other types of cross sections, such as the total cross section or the elastic cross section, which measure different aspects of particle collisions. The 2 -> 2 hadronic production cross section is also dependent on the energy of the collision and the types of particles involved.

5. What are some practical applications of studying the 2 -> 2 hadronic production cross section?

Studying the 2 -> 2 hadronic production cross section can have various practical applications. For example, it can help scientists understand the properties of new particles and their interactions, which can lead to the development of new technologies. Additionally, this cross section can also be used in the design of particle accelerators and detectors for high-energy experiments.

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