Why Mass Not Conserved in Weak Quark Interactions?

[potatobabe]

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.

 

[mfb]

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.

 

[potatobabe]

okay thanks for clearing that up for me :)

 

[tom.stoer]

look at the simple example

e^+ + e^- \to 2\gamma

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

E = E_{e^+} + E_{e^-}
p = p_{e^+} + p_{e^-}
m^2 = E^2 - p^2

and

E' = E'_{\gamma_1} + E'_{\gamma_2}
p' = p'_{\gamma_1} + p'_{\gamma_2}
m'^2 = E'^2 - p'^2

with

m = m'

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

m_{e^+} +m_{e^-} \neq 2 m_{\gamma}