# 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 '16 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 '16 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. – Qmechanic Dec 2 '16 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. – kospall Dec 2 '16 at 20:02

## 1 Answer

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.

2. The time-energy uncertainty principle is a specially tricky version of the uncertainty principle (see this question, for example). Some people might use it to give intuition about virtual particles. This kind of analogies are not to be taken too seriously.

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.