When was the phrase "beta function" of renormalization first used? My question is a historical one: when was the phrase "beta function", as it pertains to the renormalization-group equations, used in physics? I am talking about this beta function:
$$\beta_g\equiv \frac{\partial g}{\partial \log \mu}$$
In fact some of the early seminal papers on this subject (as it pertains to quantum field theory) only use the phrase "renormalization-group equations" [Gell-Mann, Low; 1954] [Callan; 1970], so I am led to believe the terminology was adopted much later.
I am interested because I believe the other "beta function", i.e. the Euler integral of the first kind, is actually quite commonly used in physics (especially in QFT, when calculating physics beta-functions!), so I find it a little surprising that the slightly conflicting terminology was adopted. 
I understand that questions on terminology and/or etymology are usually off-topic here, but I fear this question may be too technical to ask on the History of Science and Mathematics stack exchange site.
 A: I've seen references specifically to the "Callan-Symanzik beta function", so I don't think it was much later. (Curt Callan and Kurt Symanzik independently discovered their equation in 1970.)
Although the notation of Callan (1970) is unclear to me, Symanzik (1970) implicitly defined $\beta(g)$ [Eq. (I.13)] Then, Symanzik (1971) clearly defined $\beta(g)$ as a derivative [Eq. (I.13b)] and discussed some of its properties. Symanzik simply named different coefficients $\alpha,\beta,\gamma$, so the notation itself is rather natural.
The earliest published instances I'm aware of where the function was referred to by the phrase (as opposed to "$\beta(g)$", "the function $\beta$", or similar) are from a couple years later. Politzer (1973) stated that the notation was already common "the coefficient function in the Callan-Symanzik equations commonly called $\beta(g)$...", and proceeded to explicitly write "$\beta$ functions". Later the same year, Weinberg (1973) did use "beta function" in text form. I cannot rule out someone else using the phrase earlier, but it nevertheless appears to be during the early 70s.
