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

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?

Lobzang Dojay

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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.

Lobzang Dojay and Tarlin
mfb
Mentor
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.

Dear mfb and The Duck-