Partial decay width in Mathematica

In summary, the conversation discusses integrating a partial decay width in Mathematica over two variables, q and theta. The individual has tried various methods such as defining a function and using NIntegrate, but has encountered errors. They are seeking help with this issue.
  • #1
Safinaz
259
8
Hi there,

I have a a partial decay width in form of ## \frac{d \Gamma}{d \cos{\theta}~ dq^2} = ## some terms functions in q and ## \theta ## variables.
How to integrate this decay width in Mathematica over this two variables ?

I tried some thing like
j[q_]:= ## \int_{1}^{-1} ## Gam[q, ## \theta ##] d Cos[## \theta ##]

then

## \int_{0}^{10} ## j[q] dq^2

But it gave me errors

Cos[## \theta ##] is not a valid variable.
Integrate::ilim: Invalid integration variable or limit(s) in {q^2,0,10}. >>

I also tried to use NIntegrate..

So any help in that ?

Cheers,
S.
 
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  • #2
##d \cos(\theta) = - \sin(\theta) d\theta## should help (don't forget the integration limits). Alternatively, express everything in terms of ##\cos(\theta)## and give this a new name.
 

1. What is the partial decay width in Mathematica?

The partial decay width in Mathematica is a function that calculates the probability of a particle decaying into a specific final state. It takes into account the mass of the decaying particle, the masses of the final state particles, and any coupling constants or other parameters that may affect the decay. The result is a numerical value representing the probability of the decay occurring.

2. How is the partial decay width calculated in Mathematica?

The partial decay width in Mathematica is calculated using the FeynCalc package, which allows for the automatic calculation of Feynman diagrams. The package uses standard Feynman rules and integrates over all possible phase space to determine the decay probability. It also takes into account any kinematic constraints and symmetry factors that may affect the decay width.

3. Can the partial decay width be calculated for any decay process?

Yes, the partial decay width can be calculated for any decay process as long as the Feynman diagram for the process is known. The FeynCalc package in Mathematica allows for the calculation of a wide range of decay processes, including both simple and complex decays involving multiple particles and interactions.

4. How accurate are the results obtained from the partial decay width function in Mathematica?

The accuracy of the results obtained from the partial decay width function in Mathematica depends on the accuracy of the input parameters and the complexity of the decay process. In general, for simple decays with well-known parameters, the results are highly accurate. However, for more complex decays with uncertain parameters, the accuracy may be lower.

5. Can the partial decay width in Mathematica be used for theoretical predictions?

Yes, the partial decay width in Mathematica can be used for theoretical predictions. It is often used in particle physics research to make predictions for decay processes that have not yet been observed experimentally. By inputting different values for the parameters, such as coupling constants or masses, the function can be used to study the behavior of a decay process and make predictions for its probability.

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