How can I calculate the decay rate for the K_e3 semileptonic decay process?

[bgy]

Homework Statement

I have to calculate the decay rate of the following process:

K^{+} ---> pion^{0}+e^{+}+neutrino

Homework Equations

the differential decay rate for this process is

2(p*p_neutrino)(p*p_electron)-(p_neutrino*p_electron)(p^2) * diracdelta(p_kaon - p_pion - p_electron - p_neutrino) * [d^3p_pion/E_pion]*[d^3p_electron/E_electron]*[d^3p_neutrino/E_neutrino] ,

where p=p_kaon+p_pion

The Attempt at a Solution

I think it would be better calculate in the rest frame of kaon...or not?

So, the exercise is: I have to integrate this rate for the final state of the particles, but how it goes?

thanks

 

[Jhero]

To calculate the decay rate for this process, you will need to use the equation provided in the homework section. As you correctly mentioned, it would be easier to calculate in the rest frame of the kaon. This is because in the rest frame, the momentum of the kaon is zero, making it easier to integrate the equation.

To integrate the equation, you will need to take into account the energy and momentum of each of the particles in the final state (pion, electron, and neutrino). You can use the energy-momentum relation to calculate the energy of each particle given its momentum. Once you have the energies, you can then integrate the equation over the 3-dimensional momentum space of each particle.

I hope this helps. Let me know if you have any further questions.