# Why isn't a quark-antiquark loop included in the photon self-energy corrections?

In QED, the Lagrangian has a term $$\bar{\psi}A^\mu\psi$$, which gives a correction to the photon propagator, where the loop is made of a pair electron-positron, with the 1st order diagram:

In the Standard Model, there are also couplings such as $$\bar{u}A^\mu u$$ and $$\bar{d}A^\mu d$$, which would give rise to a similar correction (changing mass and dividing the coupling by 3). but I have never seen this discussion in a QFT textbook. Isn't this correction important? Wouldn't it change how we measure the vacuum polarization? The electron mass is $$\sim0.51$$MeV while the up quark mass is $$\sim2.2$$MeV, so it isn't heavy enough to be ignored.

One reason I thought could explain this is that the range of electromagnetic interactions is much larger than that of the strong force, so the quark-antiquark pair would hadronize before they could annihilate, but I'm not completely convinced this is true. Can anybody shed a light on this?

• Can you cite an example of a textbook that calculates the one-loop contribution to the photon propagator in the Standard Model without including quark loops? – Chiral Anomaly Nov 19 at 14:08