Calculating Energy, Momentum & Mass for Neutral Pion Decay

[h.a.y.l.e.y]

Hi first time user here.
I was hoping someone could please help me with the following question:

A moving neutral pion is observed to decay into 2 photons each with energy 80MeV, there being an angle 120deg between their trajectories.Calc
i)The total energy of the meson
ii)The momentum of the meson
iii)The rest mass of the meson

I am aware one must use the realtivistic formula for energy etc, but it is the business of the angle that confuses me.

Thanks for your time...

 

[marlon]

Hi first time user here.
I was hoping someone could please help me with the following question:

A moving neutral pion is observed to decay into 2 photons each with energy 80MeV, there being an angle 120deg between their trajectories.Calc
i)The total energy of the meson
ii)The momentum of the meson
iii)The rest mass of the meson

I am aware one must use the realtivistic formula for energy etc, but it is the business of the angle that confuses me.

Thanks for your time...

Maybe this will help,

http://www.hep.princeton.edu/~mcdonald/examples/piondecay.pdf

regards
marlon

 

[Astronuc]

In the pion's rest frame, each photon would be moving away in the opposite direction from the other. The 120° angle means 60° from the trajectory of the pion (symmetrical), and 30° from the normal to that trajectory.

Each photon has energy and momentum, and the pion has energy, rest mass and momentum. Momentum (velocity) are vector quantities, while energy and mass are scalar.

We know the \pi^o rest mass is about 135 MeV, so one has to use relativistic kinematics.

 

[Meir Achuz]

Your problem is easy if you don't get scared by the angle.
i) Conservation of energy gives E=80+80=160MeV.
ii) Conservation of momentum gives p=80\cos 60^\circ<br /> + 80\cos 60^\circ=160\sqrt{3} MeV.
iii) The invariant mass of the meson =\sqrt{E^2-p^2}=80 MeV.
The meson could not be a pion. You have discovered a new particle!

 

[h.a.y.l.e.y]

Thank you all for you responses.
Very kind and helpful!