## muon decay

how would we know that the muon is decay into electron antineutrino and muon neutrino to give the muon lifetime of about 2microsecond?
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 Recognitions: Science Advisor first of all, 2 microsec is a HUGE lifetime! remember that most muons we see are moving at relativistic speeds, so thanks to time dilation effects, the muon can travel a noticeable distance before it decays. So the muon decays into an electron and missing energy which we associate with the 2 neutrinos. As to what KIND of neutrinos it decays into: we don't really know, strictly speaking. It is not even obvious that these types of neutrinos/antineutrinos are different particles; that is an open question in neutrino research. But we assign neutrino flavors to force conservation laws to work. These conservation laws are consistent with other experiments and we have no reason to think that they would work there but not here. Hope that helps.
 The lifetime of both positive and negative muons at rest have been made at medium energy accelerators ever since the 1960's. Here is one recent positive muon lifetime measurement made at the Paul Scherrer Insttiute (PSI) in Switzerland. http://www.npl.illinois.edu/exp/mula...PRL_Submit.pdf The negative muon lifetime is shortened by the formation of muonic atoms, but in very low-Z targets, the effect is very small. Here is a listing of both positive and negative muon lifetime measurements: http://pdg.lbl.gov/2009/listings/rpp2009-list-muon.pdf The shape of the electron decay energy spectrum (Michel rho parameter) is consistent with the decay of the muon into an electron (or positron) and two neutrinos. http://cyclotron.tamu.edu/gagliardi/..._94_101805.pdf Bob S

## muon decay

does that mean the muon decay to electron antineutrino and muon neutrino have the same lifetime with it decay into electron neutrino and muon antineutrino...since we only detect the electron for the decay.....

Recognitions:
 Quote by thoms2543 does that mean the muon decay to electron antineutrino and muon neutrino have the same lifetime with it decay into electron neutrino and muon antineutrino...since we only detect the electron for the decay.....
in the standard model (ignoring neutrino mixing), one of those decays is impossible as it violates muon and electron numbers. Barring new physics (such as a Majorana mass for the neutrino) the only way the latter can happen is through mixing, which suppresses the width.
 if taken neutrino mixing into account, can it be possible to say that the muon decay lifetime 2microsecond is composed of the two type of decay....since they produce two type of neutrino...and we don't actually determine what type are them...

 Quote by thoms2543 if taken neutrino mixing into account, can it be possible to say that the muon decay lifetime 2microsecond is composed of the two type of decay....since they produce two type of neutrino...and we don't actually determine what type are them...
I think it is correct. If we denote neutrino mass eigenstates as vi, muon could decay into each vi with different lifetimes. But as neutrinos' masses are so small that present detectors can't distinguish the differences of each decay modes. So we measure the average decaying lifetime over all vi's. You can find some notes in a book "An introduction to the standard model of particle physics" by W. N. Cottingham and D. A. Greenwood. (P187)
 what i mean is, could muon life time be $$\tau\left(\mu^-\rightarrow e^-+\overline{\nu}\nu\right)=\tau\left(\mu^-\rightarrow e^- +\overline{\nu_e}\nu_\mu\right)+\tau\left(\mu^-\rightarrow e^-+\overline{\nu_\mu}\nu_e\right)$$

 Quote by thoms2543 what i mean is, could muon life time be $$\tau\left(\mu^-\rightarrow e^-+\overline{\nu}\nu\right)=\tau\left(\mu^-\rightarrow e^- +\overline{\nu_e}\nu_\mu\right)+\tau\left(\mu^-\rightarrow e^-+\overline{\nu_\mu}\nu_e\right)$$
No. If you really want to include mixing effects, you would need to sum over all possible combinations of flavors. Also, you should be summing decay widths, not lifetimes. But, it's pretty much a moot point, since the flavor preserving width will dominate the others by many orders of magnitude.
 because i notice the branching ratio of $$B\left(\mu^-\rightarrow e^-+\overline{\nu_\mu}\nu_e\right)$$ in the particle data booklet
 Mentor The answer is still no. I am trying to figure out what your question is, but it seems to be related to the question of whether the electron-ness is always associated with the antineutrino. The answer is yes.
 or i ask in another way. Is that all experiment in measuring the lifetime of muon decay proceed by detecting the electron only? does anyone doing the experiment by detecting the neutrino it produced? or how do we really know that the $$\overline{\nu_e},\nu_\mu$$are produced in the muon decay?Ignoring lepton number conservation.

 Quote by thoms2543 or i ask in another way. Is that all experiment in measuring the lifetime of muon decay proceed by detecting the electron only? does anyone doing the experiment by detecting the neutrino it produced? or how do we really know that the $$\overline{\nu_e},\nu_\mu$$are produced in the muon decay?Ignoring lepton number conservation.
We don't detect neutrinos because the cross section is very very small. It is easy to detect electrons as they have charges. But when dealing with neutrinos' oscillation, we have to detect neutrinos directly using for example inverse beta decays. What neutrinos are produced in the muon decay? Actually, as far as I know, it is just from the view of theory, namely, lepton number conservation.
 Muon decay experiments can only detect the electron. Neutrino detection is simply not possible on an event by event basis. That said, we know that neutrinos are produced in muon decay because of energy and momentum conservation. As measure in the muon's rest frame, the energy of the electron produced in the decay is not only different from the muon's rest energy, but also differs from event to event. This requires that the decay be to at least 3 bodies.
 The shape of the decay electron energy spectrum (known as the Michel parameter measurement) agrees with the emission of two different neutrinos. See http://cyclotron.tamu.edu/gagliardi/..._94_101805.pdf Bob S