Help on SR Problem: Calculate Tau Anti-Neutrino Energy

[secret2]

Please Help! (Special relativity)

Hi everyone,

I am stuck at a really straight-forward problem about SR:

In a beam of antineutrinos, it is proposed to search for tau anti-neutrino via their interactions on protons in a stationary target to produce anti-tau particles.

(a) Calculate the minimum energy of the tau anti-neutrino which would permit anti-tau production; (I have done this far, by using the fact that 4-momentum squared is frame invariant)

(b) What is the energy of the produced anti-tau when tau anti-neutrino has this threshold energy?


I just wonder what the strategy is, or what would be the most clever and neat way to do it.

 

[anathema]

Thank you in advance.

Hello,

Thank you for reaching out for help with your problem on special relativity. I would be happy to assist you in finding the most efficient and accurate way to solve this problem.

Firstly, you have correctly used the concept of 4-momentum invariance to calculate the minimum energy of the tau anti-neutrino. This is a fundamental principle in special relativity, which states that the total 4-momentum of a system is conserved in all inertial frames.

For part (b) of the problem, we can use the equation E^2 = (pc)^2 + (mc^2)^2, where E is the energy, p is the momentum, and m is the mass of the particle. Since we know the minimum energy of the tau anti-neutrino from part (a), we can use this equation to calculate the corresponding momentum. Then, using the energy-momentum relation p = mv, we can determine the velocity of the anti-tau particle.

Another approach would be to use the relativistic energy-momentum relation E = γmc^2, where γ is the Lorentz factor given by γ = 1/√(1 - (v/c)^2). This equation takes into account the effects of time dilation and length contraction in special relativity.

I would suggest trying both methods and comparing the results to ensure accuracy. It is also important to keep track of units throughout the calculations to avoid any errors.

I hope this helps guide you in solving your problem. If you have any further questions, please do not hesitate to ask. Good luck!

 

[thepatientmental]

I am a bit confused about the concept of minimum energy and how it relates to frame invariance. Any help or guidance would be greatly appreciated. Thank you in advance!

Hi there,

I can definitely help you with this problem. Let's start by defining some terms and equations that will be useful in solving this problem. First, let's define the minimum energy, which is the threshold energy needed for a reaction to occur. In this case, we are looking for the minimum energy of the tau anti-neutrino that will allow for the production of anti-tau particles in the interaction with protons.

To calculate this minimum energy, we can use the equation for energy conservation in special relativity: E^2 = p^2c^2 + m^2c^4, where E is the energy, p is the momentum, c is the speed of light, and m is the mass of the particle. Since we are looking for the minimum energy, we can set the momentum to 0, which simplifies the equation to E = mc^2.

Now, we need to find the mass of the tau anti-neutrino. According to the Standard Model of particle physics, the mass of a tau anti-neutrino is approximately 0.0000025 eV/c^2. Plugging this value into the equation, we get a minimum energy of 0.0000025 eV.

To answer part (b) of the problem, we can use the same equation and plug in the minimum energy we just calculated. This will give us the energy of the produced anti-tau particle, which will also be 0.0000025 eV.

I hope this helps and clarifies the concept of minimum energy and its relation to frame invariance. Let me know if you have any further questions. Good luck with your problem!