How to Calculate Energy and Velocity of Pi Meson in D Meson Decay?

[bon]

Homework Statement

Ok so I am given the masses of D meson, pi meson and K meson 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..

Homework Equations

The Attempt at a Solution

well i know you have to use conservation of 4 momentum..

so energy before = total energy after..and i know that the momenta of the pi and K meson after the collision are equal and opposite, but i can't see how to use this to get total energy of pi meson..:S

any tips?

 

[mgwasser]

I remember having this same question, confused me for a while as well.

Your right on the breaking it up into parts:

What is the energy of a D meson at rest? You might have to look this up online, when I solved it this information was supposed to be given (they didn't give the number, we had to look it up).
try using Einsteins Equation

Now After:
What is the rest energy of a K meson and Pi meson? This combined rest energy should be less than the einitial D meson energy. The difference in energy must have been converted to kinetic energy.

M(pi-meson)*V(Pi-Meson) = M(K-meson)*V(K-Meson)

 

[vela]

Do you know four-vectors?

 

[bon]

yes :)

what is the four vector method?

thanks

 

[vela]

Use conservation of energy and momentum to relate the four-momenta of the three particles. The trick is to isolate the four-momentum of the K meson on one side and then square the resulting equation. That will let you solve for the energy of the pion in terms of the masses. Once you know the energy, you can find the velocity.