Energy Conservation: Beta Ray & Neutrino

[fxdung]

Energy of beta ray and neutrino is equal Q=M(mass) of nucleous before-M of nucleous after,so it about 1Mev.But the mass of W boson is 80 MeV,so the least energy of electron and neutrino must be 80 MeV.
Why there is the difference?Why does it seem that energy were not conservation?

 

[bcrowell]

The W is a virtual particle. It's "off shell," so it doesn't have to have an energy and momentum that are consistent with its mass.

 

[jtbell]

Energy and momentum are both conserved at each vertex of a Feynman diagram, so one can calculate the energy and momentum of the virtual W from the energies and momenta of the outgoing (anti)neutrino and electron. However, because the W is virtual, $\sqrt{E^2 - (pc)^2}$ does not equal the mass of a real W. For a real W, $\sqrt{E^2 - (pc)^2} = m_W c^2$.

Particle physicists use the jargon that real (virtual) particles are "on (off) the mass shell," referring to the quantity $\sqrt{E^2 - (pc)^2}$. Or as Ben said, just "on (off) shell" for short.

 

[fxdung]

I can understand your teaching! Thanks very much!

 

[Orodruin]

Also, the mass of the W is 80 GeV.