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

In summary, when two leptons annihilate into an elementary boson, the resulting particles can be either real or virtual depending on their role as force mediators. However, since gauge bosons are unstable, they are technically always off shell, but their 4-vector can still be calculated if enough information is known about the involved particles.
  • #1
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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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  • #2
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.
 
  • #3
Technically, since these gauge bosons are unstable (and what you actually detect are jets/leptons) all gauge bosons are off shell.
 

1. How do you determine if a particle is on shell?

To determine if a particle is on shell, one must consider its energy, momentum, and mass. If the energy and momentum of the particle satisfy the equation E^2 = p^2c^2 + m^2c^4, where c is the speed of light and m is the mass of the particle, then it is considered to be on shell.

2. What is the significance of a particle being on shell?

A particle being on shell means that it follows the fundamental laws of physics and is in accordance with the principles of conservation of energy and momentum. It also allows for easier calculations and predictions of its behavior in interactions with other particles.

3. Can a particle be both on and off shell?

Yes, a particle can exist in a superposition of on and off shell states. This is known as a virtual particle and it can briefly violate the energy-momentum relation described in question 1. However, these particles cannot be observed directly and are only detected through their effects on other particles.

4. How does the concept of on shell particles relate to quantum mechanics?

In quantum mechanics, particles are described by wave functions that can be on or off shell. The wave function of an on shell particle satisfies the Klein-Gordon equation, while an off shell particle does not. The concept of on shell particles is important in understanding the properties and behavior of particles at the quantum level.

5. Are all particles on shell?

No, not all particles are on shell. For example, virtual particles mentioned in question 3 are off shell. Additionally, particles in high energy environments such as particle accelerators may also temporarily exist in off shell states before quickly decaying back into on shell particles.

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