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Homework Help: Z-particle creation with relativistic e-beams

  1. Jan 30, 2007 #1
    1. The problem statement, all variables and given/known data
    The aim in a particle scattering event is to let an electron and a positron collide and annihilate each other to form a Z-particle. The (rest) masses of these particles are given by:
    [tex]m_e- c^2 = m_e+ c^2 = 0.511 MeV[/tex]
    [tex]m_Z c^2 = 91.187GeV[/tex]

    There are two ways the experiment could be done. One way is to take a beam of positrons and fire these at a target containing (almost) stationary electrons. The other is to take a beam of positrons and a beam of electrons moving with equal speeds in opposite directions.

    Determine the energies required in the two different processes.

    2. Relevant equations

    Given in accompanying notes:

    [tex]\\mathbb{P}_1 \\cdot \\mathbb{P}_1 = -(m_i c)^2
    =(\\mathbb{P}_3 - \\mathbb{P}_2) \\cdot ( \\mathbb{P}_3 - \\mathbb{P}_2)
    =-(m_3 c)^2 - (m_2 c)^2 + 2 m_3 c E_2 / c[/tex]

    This formula replaces one P term of the final term with E2/c - which is fair enough, makes sense. To solve for a target case, there's a little jigging about but the method is essentially the same.

    The problem I have is that using this method - taking conservation of momentum and ensuring that the zero 3-momentum term of the electron's 4-momentum cancels in the dot product, I can't see why one cannot solve this equation in exactly the same way for the electron and the positron, thus giving the same answer.

    3. The attempt at a solution

    See above - it's the given formula I have a problem with, not the method itself. I'd like to use what i've been given if at all possible.
  2. jcsd
  3. Jan 30, 2007 #2


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    Homework Helper

    Your tex didn't come out so well. But the thing to remember is that M_Z*c^2 worth of mass energy in the center of mass frame in each case.
  4. Jan 30, 2007 #3
    Gah. I can never get the hand of tex.

    Nevermind. I've sorted this out now, problem solved.
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