# Decay of a particle of mass M into two particles

• Forco
In summary, the conversation discusses the decay of a particle of mass M and 4-moment P into two particles of masses m1 and m2. The total energy of each particle (lab frame) is found by setting the equation E1+E2=Mc^2, and the kinetic energy T1 of the first particle in the same reference frame can be expressed as T1=ΔM(1- m1/M - ΔM/2M). The conversation also mentions the decay of a pion (M=139.6 MeV) into a muon (m=105.7 MeV) and a neutrino (m=0). Finding the kinetic energy of the muon and the neutrino in both
Forco

## Homework Statement

A particle of mass M and 4-moment P decays into two particles of masses m1 and m2
1) Find the total energy of each particle (lab frame).
2) Show that the kinetic energy T1 of the first particle in the same reference frame is given by
$$T_1= \Delta M (1 - \frac{m_1}{M} - \frac{\Delta M}{2M})$$
3) A pion (M= 139.6 MeV) decays into a muon (m=105,7 MeV) and a neutrino (m=0). Find the kinetic energy of the muon and the neutrino (pion rest frame and lab frame).

## Homework Equations

$$E_1+E_2 = Mc^2$$
$$E_{1}^{2} +\frac{p^2}{c^2} = m_{1}^{2} c^4$$
$$E_{2}^{2} +\frac{p^2}{c^2} = m_{2}^{2} c^4$$

## The Attempt at a Solution

I was able to do the first one, since it was really simple, I only needed to set

$$E_{1}^{2} - m_{1}^{2} c^4 = E_{2}^{2} - m_{2}^{2} c^4$$
And since $$E_1+E_2 = Mc^2$$, it was easy to find that
$$E_1 = \frac{M^2+m_{1}^{2}-m_{2}^{2}}{2M}$$
Which is the correct expression for the energy. I'm having some trouble with the other two though. Especially the second one.
Any help is appreciated.

Forco said:
I was able to do the first one, since it was really simple, I only needed to set

$$E_{1}^{2} - m_{1}^{2} c^4 = E_{2}^{2} - m_{2}^{2} c^4$$
And since $$E_1+E_2 = Mc^2$$, it was easy to find that
$$E_1 = \frac{M^2+m_{1}^{2}-m_{2}^{2}}{2M}$$
Which is the correct expression for the energy.

Are you sure? I don't see how you can justify equations you started with in the lab frame.

## 1. What is the decay process of a particle of mass M into two particles?

The decay process of a particle of mass M into two particles involves the breaking down of the original particle into two smaller particles, often through the emission of other particles such as photons or neutrinos.

## 2. What is the significance of the mass M in the decay process?

The mass M represents the initial energy of the decaying particle, which is conserved throughout the decay process. It determines the energy and mass of the resulting particles.

## 3. What factors influence the probability of a particle decaying into two particles?

The probability of a particle decaying into two particles is influenced by several factors, including the mass difference between the original particle and the resulting particles, the available energy for the decay process, and the strength of the interaction between the particles involved.

## 4. Can the decay process of a particle be reversed?

In most cases, the decay process of a particle cannot be reversed. Once a particle has decayed into two or more particles, it is not possible for those particles to merge back together to form the original particle.

## 5. How is the decay process of a particle predicted and studied?

The decay process of a particle can be predicted and studied through the use of mathematical models and experiments, such as particle accelerators. These tools allow scientists to observe and measure the properties of the particles involved in the decay process and make predictions about their behavior.

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