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Why is hadronic vacum polarization to be a matrix element of product of currents?

  1. Feb 15, 2012 #1
    Please teach me this:
    In chapter 18.4 Peskin&Schoeder(QFT) they consider the annihilation of electron and positron to hadron.Ignoring the mass of the electron,we have:

    σ(e[itex]^{+}[/itex]e[itex]^{-}[/itex])=(1/2s)ImM(e[itex]^{+}[/itex]e[itex]^{-}[/itex]→e[itex]^{+}[/itex]e[itex]^{-}[/itex]).

    We have:

    iM=(-ie)[itex]^{2}[/itex]u[itex]^{-}[/itex](k)[itex]\gamma[/itex][itex]_{\mu}[/itex]v(k[itex]_{+}[/itex](-i/s)(i[itex]\Pi[/itex][itex]^{\mu\nu}_{h}[/itex](q))(-i/s)v[itex]^{-}[/itex](k[itex]_{+}[/itex][itex]\gamma[/itex][itex]_{\nu}[/itex]u(k).

    I do not understand why they can write:

    i∏[itex]^{\mu\nu}_{h}[/itex](q)=-e[itex]^{2}[/itex][itex]\int[/itex]d[itex]^{4}[/itex]xe[itex]^{iqx}[/itex]<T{J[itex]^{\mu}[/itex](x)J[itex]^{\nu}[/itex](0)>.

    Where J[itex]^{\mu}[/itex] is the electromagnetic current of quarks.
    Thank you very much for your kind helping.
     
  2. jcsd
  3. Mar 2, 2012 #2
    Now,I think that it is because the fluctuation of vacum(that is excited by virtue photon) making a loop that is product of two currents(not more complex including many hadronics).Is that correct?
     
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