# Diagrams Contributing to Electric Charge Correction (M. Schwartz)

In M. Schwartz's Quantum Field Theory and the Standard Model, he talks about the correction to the $g$-factor in Chapter 17. In Section 17.2 (Pg. 318), he is evaluating the diagram that gives the above correction.

However, he also mentions that there are three other diagrams at 1-loop which do not contribute to corrections of $g$. These are [Eq. (17.3) in the book]:

He goes on to say that these diagrams

can only give terms proportional to $\gamma^\mu$. This is easy to see because these graphs just correct the propagators for the corresponding particles. Thus, these graphs can only contribute to $F_1$ and have no effect on the magnetic moment.

(Emphasis mine.)

In the previous section, he had mentioned,

$F_1$ modifies the original $eA_{\mu}\bar{\psi}\gamma^{\mu}\psi$ coupling. This renormalizes the electric charge, as we saw from the vacuum polarization diagram.

My Question: Why do we calculate only the first diagram above while looking at charge renormalization, and not the other two? One would expect that all corrections to $F_1$ would reflect on the renormalized charge.

• There is also the vertex diagram that contributes to F1, and that cancels the last two diagrams at $Q^2=0$. That’s why you don’t need to calculate it. – QuantumDot Sep 10 '18 at 17:34
• Thanks @QuantumDot :) So, another way of looking at this would be to disregard these diagrams, and also redefine the corrections to $F_1$ by subtracting whatever correction comes from the vertex diagram at $Q^2=0$? – Sayan Mandal Sep 10 '18 at 18:16