How to know if a particle is on shell in general?

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SUMMARY

The discussion addresses the criteria for determining whether an elementary boson, such as W±, Z°, or photons, is on-shell or off-shell. It establishes that while these bosons can act as force mediators, they are not always virtual; their status depends on the momenta of the involved particles. By calculating the 4-vector of the intermediate particle using the momenta of decay products, one can ascertain if the boson is approximately on-shell. Furthermore, it is noted that due to the instability of gauge bosons, what is detected are jets or leptons, which are inherently off-shell.

PREREQUISITES
  • Understanding of particle physics concepts, specifically elementary bosons.
  • Familiarity with the principles of on-shell and off-shell particles.
  • Knowledge of 4-vector calculations in relativistic physics.
  • Basic comprehension of decay processes and particle interactions.
NEXT STEPS
  • Study the properties of gauge bosons in particle physics.
  • Learn about the calculation of 4-vectors in relativistic kinematics.
  • Research the implications of virtual particles in quantum field theory.
  • Explore the methods for detecting jets and leptons in high-energy physics experiments.
USEFUL FOR

Particle physicists, students of quantum field theory, and researchers involved in high-energy physics experiments will benefit from this discussion.

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Is there a general way of knowing if an elementary boson for example is virtual or real?

So for example, two leptons annihilate into an elementary boson. Then you can get real photons, W+-/Z° bosons depending on the leptons.

However W+-/Z° and photons can also be virtual when acting as mediators of force.

Is this always the case? That whenever it's a force mediator it's going to be virtual and 100% off shell?
 
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There is no "100% off shell". If you know enough momenta of involved particles (e. g. all decay products), you can calculate the 4-vector of the intermediate particle, and see if it was (approximately) on-shell or not.
 
Technically, since these gauge bosons are unstable (and what you actually detect are jets/leptons) all gauge bosons are off shell.
 

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