# Another question on rates, propagators, etc

• vertices
In summary, the ratio rate for the two decays in the files "Feynman.pdf" and "rate.pdf" is shown to be proportional to the fourth power of the coupling constant due to the amplitude being squared. However, there may also be a strong dependence on the mass ratio k/pi and the W propagator is not taken into account in the ratio calculation.
vertices
Please take a look at the file "Feynman.pdf". The ratio rate for the two decays is shown in the second file, "rate.pdf".

I understand it takes that form because the usW vertex is Carribbo supressed relative to the udW vertex. My concern is that the ratio is only squared.

Rate is proportional to the amplitude *squared*. And the amplitude is proportional to the square of the coupling constant (multiplied by the propagator). So the transition rate must be proportional to the fourth power of the coupling constant, right?

Is the expression in rate.pdf wrong?

#### Attachments

• Feynman.pdf
58.4 KB · Views: 283
• Rate.pdf
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The W-mu-nu coupling is the same for each so the amplitude is proportional to the first power of each g.
However, I would also expect a strong dependence on the mass ratio k/pi because the muon
has to have positive helicity for this decay.

Additionally, the ratio can't be right because it completely ignores the W propagator: there's 10 times as much Q in the kaon decay.

## 1. What is the purpose of rates and propagators in scientific research?

Rates and propagators are commonly used in scientific research to describe the behavior and interactions of various systems or processes. Rates refer to the speed or frequency of a certain change or event, while propagators describe the propagation or spread of a certain phenomenon. Together, they provide valuable insights and understanding of complex systems.

## 2. How are rates and propagators calculated or determined?

Rates and propagators can be calculated using mathematical equations and models that take into account various factors such as time, distance, and initial conditions. These calculations are often based on experimental data or theoretical predictions and can be further refined through further research and analysis.

## 3. What are some real-world applications of rates and propagators?

Rates and propagators have a wide range of applications in various fields of science, including physics, chemistry, biology, and engineering. They are commonly used to study and predict the behavior of physical and chemical reactions, population dynamics, disease spread, and many other phenomena.

## 4. Can rates and propagators be used to predict future events?

While rates and propagators can provide valuable insights and predictions about certain systems or processes, they are not always accurate in predicting future events. This is because they are often based on simplified models and assumptions, and real-world systems can be highly complex and unpredictable.

## 5. How can rates and propagators be manipulated or controlled in experiments?

In experiments, rates and propagators can be manipulated or controlled by changing various parameters, such as temperature, pressure, or concentration. This allows scientists to study the effects of these factors on the behavior of a system and potentially optimize or control the rates and propagators for a desired outcome.

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