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Homework Help: Meson emission, real or virtual?

  1. Jan 2, 2008 #1

    malawi_glenn

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    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

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

    3. The attempt at a solution

    I would say that the answer depends on the excitation enrgy 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?
     
  2. jcsd
  3. Jan 4, 2008 #2

    pam

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    Since the process cannot occur as an isolated process, at least one of the particles must be virtual.
     
  4. Jan 4, 2008 #3

    malawi_glenn

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    okay, according to what argument?
     
  5. Jan 5, 2008 #4

    malawi_glenn

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    what can I check to see if it cant occur as an isolated process?

    Hint?
     
  6. Jan 5, 2008 #5

    pam

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    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, [tex](E_p+E_\pi)^2-({\vec p}_p+{\vec p}_\pi)^2
    =M^2+m^2+2(E_p E_\pi-{\vec p}_p\cdot{\vec p}_\pi)[/tex],
    which must be greater than M^2.
     
    Last edited: Jan 5, 2008
  7. Jan 6, 2008 #6

    malawi_glenn

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

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

    [tex] N^* \rightarrow N + \pi [/tex]

    the text is the same: "Assume that a high-energy nucleon is emitting a pion"
     
  8. Jan 7, 2008 #7

    pam

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    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.
     
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