# ''Invariant mass of the electron and electron antineutrino''

• Coffee_
The invariant mass of a system consisting of two particles is the norm of the four-momentum of that system.

#### Coffee_

1. A neutron decays into a proton, an electron and an electron antineutrino. In the frame of the neutron, the proton is in rest after decay. Calculate the ''invariant mass of the electron and electron antineutrino together''. The rest masses of the proton and neutrno are known

2. Conservation of energy, momentum and conservation of four momentum.

3. The problem is that I don't understand what is asked of me, are they asking for ##m_{e} + m_{v}##? If so, I start like this in natural units (h bar = 1 , c=1)

##m_{n}=m_{p} + E_{e} + E_{v}##

Plugging in the relativistic formulas for energy, and knowing that since the proton has no momentum the momenta of the electron and antineutrino have to be equal in size:

##\sqrt{p^{2}+m_{e}^{2}}+\sqrt{p^{2}+m_{v}^{2}}=m_{n}-m_{p}##

Seems like not enough info, hence I'm doubting I'm correctly interpreting the question.

They are asking for the "invariant mass of the electron and electron antineutrino together". That is, they are asking the invariant mass of a system consisting of those two particles. That is not the same thing as asking for the sum of the invariant mass of the electron of the electron anti-neutrino.

jbriggs444 said:
They are asking for the "invariant mass of the electron and electron antineutrino together". That is, they are asking the invariant mass of a system consisting of those two particles. That is not the same thing as asking for the sum of the invariant mass of the electron of the electron anti-neutrino.

Is ## \sqrt{ (p_{e} + p_{v})^{2}}## the correct interpretation then? Where ##p_{e}## and ##p_{v}## represent the four momenta of the particles?

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jbriggs444
When it comes to four-momentum, I am out of my depth, and am working from first principles. But no, that does not appear to be the correct interpretation.

Edit: It looks correct now.

Go back to definitions. What is the definition of invariant mass of X? The norm of the four-momentum of X, right? So if X is a system consisting of two particles...

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jbriggs444 said:
When it comes to four-momentum, I am out of my depth, and am working from first principles. But no, that does not appear to be the correct interpretation.

Go back to definitions. What is the definition of invariant mass of X? The norm of the four-momentum of X, right? So if X is a system consisting of two particles...

Oh damn I messed up my squares being too qucik, here I fixed it. What about now?

Yes, that works.