Constant in SET Definition

[elfmotat]

So I was looking through Wald when I noticed his definition of the stress-energy for an arbitrary matter field:

 

[math]T_{ab}=-\frac{\alpha_M}{8\pi} \frac{1}{ \sqrt{-g}} \frac{\delta S_M}{\delta g^{ab}}[/math]

 

where [math]S_M[/math] is the action for the particular type of matter field being considered, and [math]\alpha_M[/math] is some constant that determines the form of the Lagrangian for the coupled Einstein-matter field equations:

 

[math]\mathcal{L}=R\sqrt{-g}+\alpha_M \mathcal{L}_M[/math]

 

For example, for a Klein-Gordon field we take [math]\alpha_{KG}=16\pi [/math], and for an EM field we take [math]\alpha_{EM}=4[/math]. Now, my question is whether or not there is some prescription for finding the value of [math]\alpha_M[/math]. How do we know that the constant takes on those particular values? How could I go about finding [math]\alpha_{M}[/math] for an arbitrary [math]\mathcal{L}_M[/math]?