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

1. Feb 15, 2012

### ndung200790

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$^{+}$e$^{-}$)=(1/2s)ImM(e$^{+}$e$^{-}$→e$^{+}$e$^{-}$).

We have:

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

I do not understand why they can write:

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

Where J$^{\mu}$ is the electromagnetic current of quarks.
Thank you very much for your kind helping.

2. Mar 2, 2012

### ndung200790

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?