Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why is this tau decay not allowed?

  1. Apr 12, 2015 #1
    Why is the decay ##\tau^{-} \rightarrow \mu^+ + \mu^- + \mu^-## not allowed?

    Charge, lepton number are conserved. I have a feeling it is something really basic. I'm thinking in weak interactions you only go from a ##l^- \rightarrow \nu_{l}## and not 'hop' from one muon to another non-neutrino muon.
     
  2. jcsd
  3. Apr 12, 2015 #2
    In the standard model, electron number, muon number, and tau number are each separately conserved, except for very small effects coming from neutrino mixing.

    One way of searching for physics beyond the standard model is to look for processes like ##\mu^- \to e^- + \gamma## that violate these individual lepton flavor numbers and so are negligibly rare in the SM. So a detection of a process like this would signal new physics.
     
  4. Apr 12, 2015 #3
    Got it. So lepton numbers must be separate, unlike hadronic numbers.
     
  5. Apr 12, 2015 #4

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Lepton number is not conserved in this decay. The lepton numbers associated with the three lepton flavors are conserved separately in these interactions.
     
  6. Apr 13, 2015 #5

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Even with neutrino mixing, this process is incredibly unlikely, with a branching fraction somewhere in the range of 10-50 to 10-60, completely undetectable. Comment from a theorist: "We didn't bother to make a more precise estimate".
    Only new physics could lead to a detectable branching fraction.
     
  7. Apr 14, 2015 #6

    ChrisVer

    User Avatar
    Gold Member

    How would the neutrinos or/and their mixing have something to do with these processes? :rolleyes: or are you talking about neutrinos changing their flavor (and so the conservation of each individual flavor's lepton number)?
     
  8. Apr 14, 2015 #7

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Neutrino mixing means charged lepton number is only approximately conserved, but approximately means, as mentioned above, "good to a part in 1050".
     
  9. Apr 14, 2015 #8

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Neutrino mixing is exactly the process of neutrinos changing their flavor.
    That is frequent when the neutrinos can fly hundreds of kilometers or more, but as virtual particles within a decay process (necessary for tau -> 3 mu) it is extremely unlikely.
     
  10. Apr 14, 2015 #9

    ChrisVer

    User Avatar
    Gold Member

    that's what I meant :) So the SM process would be like [itex]\tau \rightarrow \nu_\tau W \rightarrow \nu_\mu \bar{\nu}_\mu \mu \rightarrow Z \mu \rightarrow \mu \mu \mu^+[/itex]?
     
  11. Apr 14, 2015 #10

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I doubt that diagram would be dominant. You can draw a box-like diagram with two W and two neutrinos forming the box, where one neutrino changes its flavor in between.
     
  12. Apr 14, 2015 #11

    ChrisVer

    User Avatar
    Gold Member

    would that really give 3 muons?
    I think the best in odds [but only one muon as a product] would be a single loop, with the W in one (below) half and a changing tau neutrino to muon on the other (top) half...
    this would lead to [itex] \tau \rightarrow \mu [/itex].
     
  13. Apr 14, 2015 #12

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Sure, that would give three muons.

    ##\tau \rightarrow \mu## is forbidden by energy/momentum conservation. You would need an additional photon, for example.
     
  14. Apr 15, 2015 #13
    And, I think lepton number is not conserved in neutrino oscillations.
     
  15. Apr 15, 2015 #14

    ChrisVer

    User Avatar
    Gold Member

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Why is this tau decay not allowed?
Loading...