How to Find Maximum and Minimum Photon Energies in D Meson Decay?

[bon]

Homework Statement

Ok so I am given the rest masses of D meson (1.86 GeV/c^2), pi meson (0.13 Gev/c^2) and K meson (0.5 Gev/c^2) and told that a D meson at rest decays into a K meson and pi meson. Told to calculate the energy and velocity of the pi meson..

Part (b) says the pi meson subsequently decays into a pair of photons. I'm asked to find the maximum and minimum energies of each photon in the D meson rest frame..

Homework Equations

The Attempt at a Solution

Ok so I think I did part (a) okay..found the energy of the pi meson to be 0.869 Gev/c^2...is this right?

I'm just not sure how to approach part (b)..

What does it mean by maximum and minimum energies of each photon? Won't the photons just move off in opposite directions with non equal momenta (depending on initial velocity of pi meson)?

 

[mark726]

Hello! Yes, your calculation for the energy of the pi meson in part (a) is correct.

For part (b), you are correct in saying that the photons will move off in opposite directions with non-equal momenta. However, the photons will have a range of possible energies, with a maximum and minimum value. This is due to the fact that the pi meson has a specific energy, but the decay into two photons is a random process, meaning the energies of the photons will vary within a certain range.

To calculate the maximum and minimum energies of the photons, you can use the conservation of energy and momentum. The total energy and momentum of the system (D meson and two photons) must be equal before and after the decay. You can set up equations using this principle and solve for the maximum and minimum energies of the photons.

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