Decay of tauon into pion and neutrino

In summary, the conversation discusses the decay of a tauon into a charged pion and a neutrino. The question asks for the condition that results in the maximum energy of the pion after the decay. It is determined that in the lab frame, the energy of the pion would be maximised if the neutrino remained stationary, but this is not possible since a massless particle cannot be stationary. The conversation then explores how to maximize the energy of the pion in the center-of-mass frame.
  • #1
shroom
4
0
Decay of tauon into pion and neutrino...

Hello all.

I have a question.

One of the weak decays of a tauon(energy 20GeV) is to a charged pion(rest mass 139.6Mev/c^2) and a neutrino(take the neutrino to be massless).

What condition results in the maximum energy of the pion after the decay?

Sketch how the decay appears in this case, and calculate the energy.

Attempt at solution.

Ok so I got that in the lab frame, the energy of the pion would be maximised if the neutrino remained stationary. Is this correct? The reason I am questioning is that if I am taking the neutrino as massless, can a massless particle be stationary? Because then by the relativistic relation

E^2=p^2 +m^2 since m is zero and p is zero as it's stationary then it has...well nothing.

Is there something obvious I am missing?

Thanks in advance,

Shroom
 
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  • #2


If the neutrino is massless, it moves at the speed of light.
 
  • #3


So the neutrino can never be stationary? I thought that would be the case. If this is so, then how do you go about maximising the energy of the pion?
 
  • #4


Try analyzing the decay in the center-of-mass frame first.
 
  • #5


Hello Shroom,

You are correct in your understanding that the maximum energy of the pion would be achieved if the neutrino remained stationary in the lab frame. However, your question about a massless particle being stationary is a valid one. In the case of a massless particle, the energy-momentum relation becomes E=pc, where c is the speed of light. This means that even though the neutrino may have zero mass, it can still have non-zero momentum and therefore can be moving at the speed of light. So in this case, the neutrino would not be considered "stationary" in the traditional sense, but it would have a momentum that would contribute to the energy of the pion in the decay.

To calculate the maximum energy of the pion, you can use the conservation of energy and momentum equations:

Etauon = Epion + Eneutrino
and
ptauon = ppion + pneutrino

Since the tauon is at rest in the lab frame, its momentum is zero. This means that the momentum of the pion and neutrino must be equal and opposite. Using the energy-momentum relation for the pion, we can rewrite the first equation as:

Etauon = √(p^2c^2 + m^2c^4) + pc

Solving for p, we get:

p = (Etauon - √(Etauon^2 - m^2c^4))/(c+1)

Substituting this into the second equation and solving for Epion, we get:

Epion = (Etauon + √(Etauon^2 - m^2c^4))/(c+1)

Plugging in the values given in the question, we get a maximum energy of the pion of 19.86 GeV. The decay would appear as follows:

tauon (20 GeV) -> pion (19.86 GeV) + neutrino (0.14 GeV)

I hope this helps clarify your understanding of the decay. Keep up the good work in your studies of particle physics!
 

1. What is the decay of tauon into pion and neutrino?

The decay of tauon into pion and neutrino is a type of particle decay in which a tauon particle decays into a pion (pi) and a neutrino. This process is also known as the tauon decay channel.

2. What is the significance of studying this decay?

Studying the decay of tauon into pion and neutrino can provide insights into the fundamental properties of particles and the laws of physics. It can also help us understand the role of the weak nuclear force in particle interactions.

3. How does this decay process occur?

In this decay process, the tauon particle emits a W boson, which then decays into a pion and a neutrino. The pion is a meson particle composed of an up quark and a down antiquark, while the neutrino is a neutral, weakly interacting particle.

4. What are the possible outcomes of this decay?

The possible outcomes of this decay are determined by the energy and momentum of the initial tauon particle. The pion and neutrino produced in the decay can have different energies and directions, leading to a variety of possible final states.

5. Is the decay of tauon into pion and neutrino a rare process?

Yes, this decay process is considered rare compared to other tauon decay channels. The probability of a tauon decaying into a pion and neutrino is approximately 11%, while the probability of decaying into an electron or muon is about 36% and 17%, respectively.

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