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

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Homework Help Overview

The discussion revolves around a problem in particle physics concerning the decay of a D meson at rest into a K meson and a pi meson. Participants are tasked with calculating the energy and velocity of the pi meson using principles of conservation of momentum and energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of conservation of four-momentum and energy, with one noting the need to consider the rest energies of the mesons involved. Questions about the four-vector method and its application arise, as well as the relationship between the momenta of the decay products.

Discussion Status

The discussion is active, with participants sharing insights and asking questions about the methods to approach the problem. Some guidance has been offered regarding the use of Einstein's equation and the conservation laws, but no consensus has been reached on a specific method or solution.

Contextual Notes

Participants note the potential need for additional information, such as the rest energy of the D meson, which may not have been provided in the problem statement. There is also an emphasis on ensuring that the combined rest energy of the decay products is less than that of the initial D meson.

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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?
 
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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)
 
Do you know four-vectors?
 
yes :)

what is the four vector method?

thanks
 
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.
 

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