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How can a tiny neutrino produce massive W+ and electron?

by a dull boy
Tags: electron, massive, neutrino, produce, tiny
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a dull boy
Jul23-14, 11:39 AM
P: 33
A charged lepton can absorb a W+ boson and be converted into a neutrino, and visa versa. The neutrino has such small rest mass, how can it produce these large particles/be produced by them?
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Jul23-14, 12:44 PM
P: 874
The energy of the neutrino matters more than its rest mass. Consider the reaction

##\bar \nu_e + p \to e^+ + n##

that is: an electron-antineutrino hits a proton and in the process of the collision the proton turns into a neutron and the antineutrino turns into a positron. This happens via the exchange of a W boson between the antineutrino and the proton.

You are right that a lepton like a positron is much heavier than a neutrino. Also, a neutron is heavier than a proton. The extra rest-mass energy is supplied by the kinetic energy of the initial particles. Therefore this reaction can only happen if the antineutrino has enough kinetic energy to supply the missing rest-mass energy needed to make the final-state particles.
Jul23-14, 12:49 PM
P: 12,023
The W+ boson is often a virtual particle - "its energy" (note: this is not really a well-defined value here) can be below the W mass.
To produce positrons or other reaction products, it needs enough kinetic energy.

a dull boy
Jul24-14, 09:18 AM
P: 33
How can a tiny neutrino produce massive W+ and electron?

Dear mfb and The Duck-
Thanks very much for your answers - I understand!
Best, Mark
Jul25-14, 08:39 PM
P: 1,008
Also a single neutrino (alone), cannot decay to another particle because of energy conservation...

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