# Uncertainty principle and measurement of the mass of Virtual particles

1. We can have real photons as well as virtual photons. However, I think we can have only virtual weak gauge bosons $W^{\pm},Z$. Is that correct?

2. If virtual particles are just a manner of interpreting the S-matrix elements at various orders, why something as physical as energy-time uncertainty principle is invoked to explain their fleeting existence? The mathematics of quantum field theory, as far as I know, doesn't give any such picture to take seriously.

3. Since, the virtual particles do not obey dispersion relations, how justified is the measurement of Z-boson mass using the four-momentum conservation as explained in the maximum voted answer here?

• @AccidentalFourierTransform W or Z boson always appear in the propagator such as in the $e^+e^-\rightarrow \mu^+\mu^-$ scattering. Aren't they? And their masses are measured from such scattering events. Am I wrong?
– SRS
Dec 2, 2016 at 19:00
• @AccidentalFourierTransform- What do you think about the measurement of Z boson as answered in the link I have suggested? It appears to me that it assumes dispersion relation to be valid for the Virtual Z boson.
– SRS
Dec 2, 2016 at 19:03
• General comment: Since voting can at least in principle change the order of answers, it is preferred not to refer to SE answers by their popularity. Dec 2, 2016 at 19:16
• I think virtual refers to how closely a particle adheres to the mass-shell relation, i.e the longer it exists, the more it will tend to obey this relation. Dec 2, 2016 at 20:02

1. There are both virtual and real $W^{\pm}$, $Z$ bosons. Just as with photons (and for any other case), virtual $W^\pm$ and $Z$ bosons are some internal lines on Feynman diagrams and real $W^\pm$ and $Z$ bosons are some states of the electroweak theory.
3. The $Z$ boson mass was measured at LEP using electron-positron collisions. The cross section for the process that was used can be computed as a function of the center of mass energy $E$ of the final (or, equivalently, the initial) state. Around $E\sim M_Z$ this function has a bell shape peaked at $E=M_Z$ (in this kind of processes, the cross section is a Breit-Wigner distribution). By measuring many events at different $E$, the peak of the cross section can be found and the mass of the $Z$ boson is obtained.