# Calculating Energy, Momentum & Mass for Neutral Pion Decay

• h.a.y.l.e.y
In summary, the pion decays into two photons with energy 160MeV, each moving at an angle of 30° away from the original pion's trajectory.
h.a.y.l.e.y
Hi first time user here.

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.

h.a.y.l.e.y said:
Hi first time user here.

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.

Maybe this will help,

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

regards
marlon

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.

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 $p=80\cos 60^\circ + 80\cos 60^\circ=160\sqrt{3}$ 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!

Thank you all for you responses.

## 1. How is energy calculated for neutral pion decay?

The energy of a neutral pion can be calculated using the formula E=mc², where E is energy, m is mass, and c is the speed of light. The mass of a neutral pion is approximately 135 MeV/c², so the energy would be 135 MeV.

## 2. What is momentum and how is it calculated for neutral pion decay?

Momentum is a measure of an object's motion and is calculated using the formula p=mv, where p is momentum, m is mass, and v is velocity. For neutral pion decay, the momentum can be calculated by dividing the energy by the speed of light, since the speed of light is the velocity of the pion.

## 3. How is mass calculated for neutral pion decay?

The mass of a neutral pion is a constant value of approximately 135 MeV/c². This value can be found in particle data tables or calculated from other properties of the pion, such as its energy and momentum.

## 4. What is the relationship between energy, momentum, and mass in neutral pion decay?

In neutral pion decay, energy and momentum are conserved quantities. This means that the total energy and momentum of the pion before and after decay must be equal. The mass of the pion also remains constant throughout the decay process.

## 5. Can the calculations for neutral pion decay be applied to other particles?

Yes, the calculations for energy, momentum, and mass can be applied to other particles as well. However, the values will vary depending on the specific properties of the particle. It is important to consult particle data tables or other reliable sources when working with different particles.

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