Is the finestructure constant a parameter of the standard model?
Your guess is correct. After electroweak symmetry breaking, the coupling constant for the residual $U(1)_\textrm{EM}$ gauge group can be written as a function of the couplings of the broken $SU(2)_L \times U(1)_\textrm{Y}$ gauge groups: $$ \alpha = \frac{1}{4\pi}\frac{g^2 g\prime^2}{g^2+g\prime^2} = \frac{e^2}{4\pi} $$
These couplings, however, are running parameters, defined at a particular energy scale. In your table, the energy scale is $\mu=M_Z$. If you plugged in the numbers from your table, you would calculate $\alpha$ at $\mu=M_Z$, which is $\alpha(\mu=M_Z) \approx 1/128$.
The finestructure constant is usually considered to be the IR fixedpoint of $\alpha$, which is $\alpha(\mu = m_e) = 1/137$, i.e., $\alpha$ at low energy. To calculate this from your table, you would have to run $e$ to a lower energy scale, with the $\beta$function: $$ \frac{\partial e(\mu)}{\partial \log \mu} \equiv \beta(e) = \frac{e(\mu)^3}{12\pi^2} $$ With this, and your knowledge of $\alpha(\mu=M_Z)$, you could recover $\alpha(\mu = m_e)= 1/137$.
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Peter de Rivaz 5 months
According to the wikipedia entry on the finestructure constant:
In fact, α is one of the about 20 empirical parameters in the Standard Model of particle physics, whose value is not determined within the Standard Model.
but, the wikipedia list of parameters does not mention α:
me Electron mass 511 keV mμ Muon mass 105.7 MeV mτ Tau mass 1.78 GeV mu Up quark mass μMS = 2 GeV 1.9 MeV md Down quark mass μMS = 2 GeV 4.4 MeV ms Strange quark mass μMS = 2 GeV 87 MeV mc Charm quark mass μMS = mc 1.32 GeV mb Bottom quark mass μMS = mb 4.24 GeV mt Top quark mass Onshell scheme 172.7 GeV θ12 CKM 12mixing angle 13.1° θ23 CKM 23mixing angle 2.4° θ13 CKM 13mixing angle 0.2° δ CKM CPviolating Phase 0.995 g1 or g' U(1) gauge coupling μMS = mZ 0.357 g2 or g SU(2) gauge coupling μMS = mZ 0.652 g3 or gs SU(3) gauge coupling μMS = mZ 1.221 θQCD QCD vacuum angle ~0 v Higgs vacuum expectation value 246 GeV mH Higgs mass ~ 125 GeV (tentative)
Is α one of the basic parameters of the Standard Model?
If not, then is there a simple formula for α in terms of these other parameters?
(My guess is that α can be derived from g1/g2/g3. However, I have been unable to find an explicit formula so far.)

Peter de Rivaz over 9 yearsThanks, this is exactly what I've been searching for! Do you happen to have a link to a web page where I should have been able to find these formulae myself?

innisfree over 9 yearsA nice fist course on the Standard Model, arxiv.org/abs/hepph/0001283, which will contain the first equation (p65), but it won't cover the $\beta$functions. For that you will need a course on QFT, see p395 of web.physics.ucsb.edu/~mark/qft.html, but that reference is quite advanced...