# Tau lepton decay problem - weird answer?

• jeebs
In summary, the conversation discusses the decay of a tauon into a charged pion and a neutrino. The maximum energy the pion can have after the decay is determined by retaining all of the tauon's momentum. However, the rest of the tauon's energy is carried away by the neutrino, which has a small mass and therefore a large kinetic energy. This explains why the final energy after the decay is much less than the initial energy of the tauon.
jeebs
Hi,
I've got a tauon weak-decaying into a charged pion and a neutrino. The tauon has total energy $$\ E_{\tau} = 2.5GeV$$, rest mass $$\ m_{\tau} = 1.777GeV/c^2$$, and the pion has rest mass $$\ m_{\pi} = 0.1396GeV/c^2$$.
This is everything I am told.
I have to find the maximum energy the pion can have after the decay.

So, what I said was that the pion will get the most energy by retaining all of the tauon's momentum, ie.

$$\ p_{\tau} = \sqrt{E_{\tau}^2 - m_{\tau}^2} = p_{\pi} = 1.758GeV/c$$

and so $$\ E_{\pi} = \sqrt{p_{\pi}^2 + m_{\pi}^2}$$

This gives me the result that $$\ E_{\pi} = 1.764GeV$$.
However, the neutrino that is also produced has a tiny mass and I have assumed it to have zero momentum, so where has most of the 2.5GeV tauon energy gone?

I had 2.5GeV before the decay, but now I have not much more than 1.764GeV after the decay, so where has the rest of this energy magically disappeared to?

Thanks.

The rest of the energy is carried away by the neutrino. Since the neutrino has such a small mass, almost all of its energy is in its kinetic energy. The neutrino's momentum is equal to the difference between the initial tauon's momentum and the final pion's momentum, so it can take away quite a bit of energy.

## 1. What is the "Tau lepton decay problem"?

The "Tau lepton decay problem" refers to an inconsistency in the expected decay rates of tau particles in particle physics. According to the Standard Model of particle physics, the decay rates of tau particles should be equal to those of their lighter counterparts, the muon and electron. However, experimental measurements have shown a discrepancy between the predicted and observed decay rates.

## 2. What is the "weird answer" to the Tau lepton decay problem?

The "weird answer" refers to the possible solution to the Tau lepton decay problem proposed by a team of researchers in 2019. They suggested that the discrepancy in decay rates could be explained by the existence of a new, undiscovered particle, which they called the "leptonic dark force". This particle would interact with both tau and muon particles, causing the observed difference in decay rates.

## 3. How does the "leptonic dark force" solve the Tau lepton decay problem?

The "leptonic dark force" theory proposes that the new particle would interact with the tau and muon particles in a similar way to the well-known weak nuclear force. This interaction would cause the observed difference in decay rates, providing a possible explanation for the Tau lepton decay problem.

## 4. What evidence supports the existence of the "leptonic dark force"?

While the existence of the "leptonic dark force" has not been directly observed, there is some indirect evidence that supports its existence. The researchers behind the theory used data from previous experiments on tau particle decays to calculate the properties of the proposed particle. If the "leptonic dark force" does exist, it should be possible to detect it in future experiments specifically designed to search for it.

## 5. What are the implications of the "leptonic dark force" theory for particle physics?

If the "leptonic dark force" theory is confirmed, it could have significant implications for our understanding of particle physics and the Standard Model. The existence of a new force and particle would challenge current theories and require further research and experimentation to fully understand its properties. It could also have implications for our understanding of dark matter and the fundamental forces of the universe.

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