Is the Pion Emitted by a High-Energy Nucleon Real or Virtual?

[malawi_glenn]

Homework Statement

Assume that a high-energy nucleon is emitting a pion, i.e. the process N→N+π. Is the pion real or virtual or both? Motivate your answer with a calculation or a good argument.

Homework Equations

Virtual particles does not obey energy (and momentum) conservation. The virtual particle never appears in the final state.

The Attempt at a Solution

I would say that the answer depends on the excitation energy of the nucleon and if the pi meson is reabsorbed. But I would spontaneous say that high - energy nucleon means energy is lower than the mass of delta (1232 MeV, mass of nucleon approx 940MeV, mass pion = 140MeV). Also I would think that the RHS is the final state, so that the pion is a real particle.

What do you guys think about that?

 

[pam]

Since the process cannot occur as an isolated process, at least one of the particles must be virtual.

 

[malawi_glenn]

okay, according to what argument?

 

[malawi_glenn]

Since the process cannot occur as an isolated process, at least one of the particles must be virtual.

what can I check to see if it can't occur as an isolated process?

Hint?

 

[pam]

what can I check to see if it can't occur as an isolated process?

Hint?

That's a better response, since we are not having an argument, but a discussion.
Use the invariant E^2-p^2. E^2-p^2=M^2 forthe proton.
For p plus pi, $$(E_p+E_\pi)^2-({\vec p}_p+{\vec p}_\pi)^2<br /> =M^2+m^2+2(E_p E_\pi-{\vec p}_p\cdot{\vec p}_\pi)$$,
which must be greater than M^2.

 

[malawi_glenn]

but the nucleon on the LHS is excited, so there is not the same $$E_{\text{p}}$$ on the RHS.

edit: my original post (which I can't edit), the process should be (if you have not read):

$$N^* \rightarrow N + \pi$$

the text is the same: "Assume that a high-energy nucleon is emitting a pion"

 

[pam]

It's a bit frustrating to give two answers to a question and find out four days later that the wrong question was asked.
If the original N is N*, an excited nucleon, everything is different.
In that case, the particiles may be real or vilrtual.
All known N* are more massive than M_p+m_pi.
If the process is an isolated N* decaying to N and p, then all particles are real.
If N*-->N + pi is part of a more complex perturbation diagram, then one or all could be virtual. Only if a particle is in the initial or final state of an interaction is the particle real.