Feynman loop diagrams

Question

I am learning about Feynman diagrams, and I have trouble interpreting loop diagrams. The picture below shows a loop-induced decay of the neutral pion. $\pi^0 \rightarrow e^+ + e^-$.

I understand that $\pi^0$ has to decay into two photons in order to conserve momentum and angular momentum. I do not understand, however, what the vertical line in this diagram means.

My guess would be that each photon annihilates into a position electron pair, and the vertical line represents a positron and electron annihilating, thus leaving only one electron positron pair as the final products.

However, if that was to be the case, the reaction would be $\pi^0 \rightarrow e^+ + e^- + \gamma$. Can anyone explain the physics represented by this vertical line?

Answer 1

You have to realize that Feynman diagrams are one to one recipes for integrals built up within a quantum field theory. There are rules with one to one correspondence to the integral represented. They are used in order to evaluate crossections and lifetimes and to compare calculations to experiment.

There are internal lines and external lines, whether going along the x axis or the y axis.

External line in your diagram is the pi0 and external lines are the two e+ e- lines on the far right. These are real particles i.e. they have a real four momentum vector and carry the momentum and energy of the interaction.

The loop is a loop of virtual particles which live only within the integral . Virtual means that the four vectors repesenting them in the integral are off mass shell, in this case not on the mass of the electron and photon, but vary within the integral. See the answer here for a simplified explanation.

So in the case above, the two photons are virtual and are represented in the integral with a photon propagator, and the inernal electron line is represented with an electron propagator. Conservations of charge and lepton number defines the integral.

My guess would be that each photon annihilates into a position electron pair, and the vertical line represents a positron and electron annihilating, thus leaving only one electron positron pair as the final products.

This is virtually true, at each point of the integration, because the four vectors of the virtual lines are under the integration continually variable. The line carry the name "photon" and|"electron" "positron" so as to keep quantum numbers correct between input and output external lines. The internal lines are keeping count of these quantum numbers and thus are identified with the particles, and also the propagators have the mass of the named particle. This is just a useful mathematical tool.