# Mass not conserved?

1. Oct 20, 2012

### 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.

2. Oct 20, 2012

### 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.

3. Oct 20, 2012

### potatobabe

okay thanks for clearing that up for me :)

4. Oct 20, 2012

### 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

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