Atmospheric electron neutrinos

In summary, v50 said that the most probable time of decay is just after the particle exists at time 0.
  • #1
Zuzana
12
1
Hi,

I would like to ask question about atmospheric electron neutrinos.
It is known that atmospheric electron neutrinos originate from the decay of muon in the atmosphere, but we can also calculate that muon with energy more than 10 GeV is able to penetrate about 100 km, so it does not decay and no electron neutrino is produced. It means that electron neutrinos are produced from muons with energy < ~10 GeV and thus electron neutrino posses energies in this range (< ~ 10 GeV). Does it mean that we cannot detect atmospheric electron neutrinos with higher energies?

Thanks for the reply.
 
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  • #2
Zuzana said:
so it does not decay and no electron neutrino is produced.
How does that follow from
Zuzana said:
we can also calculate that muon with energy more than 10 GeV is able to penetrate about 100 km,
?
 
  • #3
Atmospheric muon with energy > 10 GeV can reach the Earth and can be detected, so electron neutrino won't be detected, since the muon did not decay in detector. Does it mean that only electron neutrinos, which come from decay of muon (energy < 10 GeV) can be detected at the Earth?
 
  • #4
Zuzana said:
Atmospheric muon with energy > 10 GeV can reach the Earth and can be detected
Huh? The atmospheric muon being detected or not is irrelevant. It is however true that high-energy muons will start reaching the Earth. Those will then be slowed down by scattering and decay with a lower energy than their original energy. This phenomenon is well known and does result in a predominantly muon neutrino flux at high energies. At low energies the muon-to-electron neutrino ratio is about 2. At higher energies it is predominantly muons from meson decays.

Zuzana said:
since the muon did not decay in detector
It has nothing to do with the muon being detected or not. It has to do with the muons reaching the Earth's surface and slowing down or not.

Zuzana said:
Does it mean that only electron neutrinos, which come from decay of muon (energy < 10 GeV) can be detected at the Earth?
No. Even at higher energies there will be some muons that decay. Decay is not a deterministic process. It becomes a game of rates whether the resulting higher energy neutrinos can be detected or not.
 
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  • #5
Muons can decay at any point in time, as mentioned. There is also the angle to consider: If you look closer to the horizon the muons had more time to decay before slowing down in the ground.
 
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  • #6
Orodruin said:
Huh? The atmospheric muon being detected or not is irrelevant. It is however true that high-energy muons will start reaching the Earth. Those will then be slowed down by scattering and decay with a lower energy than their original energy. This phenomenon is well known and does result in a predominantly muon neutrino flux at high energies. At low energies the muon-to-electron neutrino ratio is about 2. At higher energies it is predominantly muons from meson decays.It has nothing to do with the muon being detected or not. It has to do with the muons reaching the Earth's surface and slowing down or not.No. Even at higher energies there will be some muons that decay. Decay is not a deterministic process. It becomes a game of rates whether the resulting higher energy neutrinos can be detected or not.
Thank you very much for the explanation.
 
  • #7
mfb said:
Muons can decay at any point in time, as mentioned.
indeed, the most probable decay time is t = 0.
 
  • #8
Vanadium 50 said:
indeed, the most probable decay time is t = 0.
No time like the present …
 
  • #9
The survival probability is ##P_{\text{survival}}(t)=\exp(-\Gamma t)##, given that the particle exists at time ##t=0##. Correspondingly the probability for being decayed at time ##t## is ##P_{\text{decayed}}=1-\exp(-\Gamma t)##. It's not so clear, what you mean by the "most probable decay time". The average lifetime is ##1/\Gamma##.
 
  • #10
vanhees71 said:
The survival probability is ##P_{\text{survival}}(t)=\exp(-\Gamma t)##, given that the particle exists at time ##t=0##. Correspondingly the probability for being decayed at time ##t## is ##P_{\text{decayed}}=1-\exp(-\Gamma t)##. It's not so clear, what you mean by the "most probable decay time". The average lifetime is ##1/\Gamma##.
Those are the cdf for decay and 1-cdf for decay. For any given time, the pdf of the time of decay given it has not yet decayed is the largest at that time. Given that the particle exists at t=0, the most probable time of decay -as given by the pdf- is just after that.
 
  • #11
Ok, then you simply define it as the maximum of the probability density for decay, i.e., \dot{P}_{\text{dec}}=\Gamma \exp(-\Gamma t)##, and then it's of course at ##t=0##.
 
  • #12
vanhees71 said:
Ok, then you simply define it as the maximum of the probability density for decay, i.e., \dot{P}_{\text{dec}}=\Gamma \exp(-\Gamma t)##, and then it's of course at ##t=0##.
Well, it was v50 that said it, but that was my interpretation at least
 
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Related to Atmospheric electron neutrinos

1. What are atmospheric electron neutrinos?

Atmospheric electron neutrinos are subatomic particles that are produced by cosmic rays interacting with the Earth's atmosphere. They are part of the family of neutrinos, which are electrically neutral and have very little mass.

2. How are atmospheric electron neutrinos detected?

Atmospheric electron neutrinos are detected through large underground detectors, such as the Super-Kamiokande detector in Japan. When an electron neutrino interacts with the detector, it produces a faint flash of light that can be detected and measured.

3. What is the significance of studying atmospheric electron neutrinos?

Studying atmospheric electron neutrinos can provide insights into the behavior and properties of neutrinos, as well as the processes that occur in the Earth's atmosphere. It can also help us understand the origins and composition of cosmic rays.

4. How do atmospheric electron neutrinos differ from other types of neutrinos?

Atmospheric electron neutrinos are one of three types of neutrinos, along with muon neutrinos and tau neutrinos. They differ in their mass and their interactions with matter. Electron neutrinos are the lightest and most abundant of the three types.

5. What are the potential applications of atmospheric electron neutrinos?

The study of atmospheric electron neutrinos has potential applications in fields such as astrophysics, particle physics, and geology. It can also contribute to the development of new technologies, such as neutrino detectors and neutrino communication systems.

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