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I understand that the Weak interaction is mediated by the $W$ and $Z$ bosons, and that their huge masses are the reason for the Weak interaction's short range.

However, I cannot find an explanation for why they are created. As they are such massive particles, $\geq$80 times the rest mass of a proton, I assume their creation requires a lot of energy, where does this energy come from?

Qmechanic
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Connor
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    Take my comment with a grain of salt since I am no expert in QFT, but it should be allowed by the uncertainty principle as long as it happens in a short time since $\Delta t \Delta E \geq \frac{\hbar}{2}$ and that's why interactions mediated by heavier particles have a shorter range. – Andrea May 06 '22 at 14:56
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    Even though, as you say, weak interactions are mediated by $W$ and $Z$ bosons, they are not necessarily created on-shell, thus not requiring energies comparable to their mass - e.g. beta-decays are mediated by virtual $W$s for which the square of the four-momentum does not obey $p_\mu^2 = m^2$, while in e.g. top quark decays $t \rightarrow Wb$, the $W$ are on-mass. – Vangi May 06 '22 at 15:06
  • I never really considered this, thank you both for your answers! That's so interesting that particles can form "off mass", do you know of any references where I can learn more about this? – Connor May 06 '22 at 15:22
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    There are a few questions on this forum related to on-shell and off-shell (virtual) particles, with links to other questions and sources. Try this link and the links/sources therein. – Vangi May 06 '22 at 15:32
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    see virtual particles http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/expar.html and my answer here https://physics.stackexchange.com/questions/90928/virtual-higgs-boson/90973#90973 – anna v May 06 '22 at 16:33

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