Can anyone provide the formula for the differential cross section in square meters (sic) for Møller scattering? And maybe even give an authoritative reference?

I need the formula both for checking my math and for testing some computer programs.

I am interested in a formula which uses the International System of Units (SI) in general and m (meter), kg (kilogram), s (second) and A (Ampere) in particular.

Most sources can agree that the differential cross section in the Center of Mass (CM) coordinate system for a scattering angle $ \theta \in ( 0 , \pi ) $ and for incomming electrons which each have momentum $ p \in \mathbb{R}_+ $ is given by

\[ \frac { d \sigma } { d \Omega } = \beta \frac { 4 ( ( m c ) ^ 2 + 2 p ^ 2 ) ^ 2 + ( 4 p ^ 4 - 3 ( ( m c ) ^ 2 + 2 p ^ 2 ) ^ 2 ) ( \sin \theta ) ^ 2 + p ^ 4 ( \sin \theta ) ^ 4 } { p ^ 4 ( \sin \theta ) ^ 4 } \]

for some constant $ \beta \in \mathbb{R}_+ $ which is measured in square meters in the SI system. Unfortunately, the sources I have found are not very explicit about $ \beta $ and may even disagree with one another.

So the question is: can anyone provide a formula for $ \beta $ using the following physical constants?