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W+ decay modes neglect mass branching ratiosQ

  1. Mar 30, 2015 #1
    1. The problem statement, all variables and given/known data
    The question is that the decay modes for the ##W+## boson are , ##e^+ v_{e}, \mu^+ v_{\mu}, \tau^+ v_{\tau}, ud', cs' ##, where a ' denotes a anitquark, neglecting the masses of the decay products estimate the branching ratios of the ##W+##?

    2. Relevant equations

    N/A

    3. The attempt at a solution

    I know that the lepton decays differ to quark decays in the way that quarks come in 3 colours.

    I however thought that the quark decays would be reduced, as a pose to more likely, than the lepton decays by a factor of ##3##.

    My reasoning is that , (I believe you treat the 2 quark system as a meson and so the colours must add to neutral, I don't know whether the situation differs if the quarks are unbound or you should consider them unbound in this decay, if someone could answer this, thanks?) , if one of the quarks takes a particular colour, the colour of the other antiquark,say, is immediatey constrained by this as it must be of the same colour, so there is only a ##1/3## chance that it gets the right colour.

    Thanks.
     
  2. jcsd
  3. Mar 30, 2015 #2

    mfb

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    Staff: Mentor

    At this energy, the quarks can be considered as unbound. They will hadronize later, at a lower energy scale.

    You can treat the different quark colors as different particles. Then this constraint is equivalent to "if one particle is a positron, then the other particle has to be an electronneutrino" (as opposed to other neutrinos, or quarks, or whatever) - nothing that would make the decay less likely.
    The colors just give three different decay modes: u green d' antigreen, u red d' antired, u blue d' antiblue.
     
  4. Mar 30, 2015 #3
    Thanks. I see here as the W boson is colourless so the two quarks colour must sum to zero irrespective of whether it is a meson or not, in the general case of an unbound quark system the colour does not need to sum to zero?
     
  5. Mar 30, 2015 #4

    mfb

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    Staff: Mentor

    Right.

    Right. Gluon+gluon -> quark+antiquark can lead to different colors, for example.
     
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