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Mass not conserved?

  1. Oct 20, 2012 #1
    Hi, this may be a stupid and obvious question but its my first post so allow me to ask:

    Why is mass not conserved in most weak quark interactions e.g : d → u + W-
    the mass of the down quark is about 4.8 MeV
    and the up quark is about 2.4 MeV
    and the W- mass is 80.4 GeV!
    And even accounting for the constituent quark mass the equation doesn't add up,
    could someone clear this up for me? Thanks.
  2. jcsd
  3. Oct 20, 2012 #2


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    2017 Award

    Staff: Mentor

    There is no mass conservation.
    There is energy conservation - and your process cannot produce a real W-boson for that reason. It can, however, produce a virtual W-boson (that can violate the energy-momentum relation for the W) which quickly decays into other particles.
  4. Oct 20, 2012 #3
    okay thanks for clearing that up for me :)
  5. Oct 20, 2012 #4


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    Science Advisor

    look at the simple example

    [tex]e^+ + e^- \to 2\gamma[/tex]

    Energy E and momentum p are conserved. The invariant mass m is conserved, too:

    [tex]E = E_{e^+} + E_{e^-}[/tex]
    [tex]p = p_{e^+} + p_{e^-}[/tex]
    [tex]m^2 = E^2 - p^2[/tex]


    [tex]E' = E'_{\gamma_1} + E'_{\gamma_2}[/tex]
    [tex]p' = p'_{\gamma_1} + p'_{\gamma_2}[/tex]
    [tex]m'^2 = E'^2 - p'^2[/tex]


    [tex]m = m'[/tex]

    But of course the sum of the rest masses is not conserved

    [tex]m_{e^+} +m_{e^-} \neq 2 m_{\gamma}[/tex]
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