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

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Homework Help Overview

The discussion revolves around the calculation of the invariant mass of an electron and an electron antineutrino resulting from the decay of a neutron into a proton, an electron, and an electron antineutrino. Participants are exploring concepts related to conservation laws and the properties of four-momentum in the context of particle physics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to interpret the problem, questioning whether the invariant mass refers to the sum of the masses of the electron and antineutrino or the invariant mass of the system comprising both particles. There are discussions about the correct application of four-momentum and its definition in relation to invariant mass.

Discussion Status

Some participants have provided clarifications on the interpretation of the problem, suggesting that the invariant mass refers to the system of the two particles rather than their individual masses. There is an ongoing exploration of the definitions and calculations involved, with some participants expressing uncertainty about their understanding of four-momentum.

Contextual Notes

Participants are working from first principles and expressing doubts about their interpretations and calculations. There is a recognition of the need to revisit definitions related to invariant mass and four-momentum.

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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 known2. 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.
 
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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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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...
 
Last edited:
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.
 

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