In the Standard Model, we have these free parameters:
6 quark masses
6 lepton masses
3 coupling constants
4 CKM parameters
4 PMNS parameters
QCD vacuum angle
That's 26 in total. For gravity, we also need the cosmological constant $\Lambda$.
So that would make... 27 parameters.
Is that all? I'm assuming quantum theory + Poincarè invariance + $U(1) \times SU(2) \times SU(3)$ gauge symmetry + general covariance on a 4-dimensional Lorentzian manifold.
Does string theory reduce this number? What about loop quantum gravity? Do we have any theory which reduces it?
What about strong constraints on some of these parameters determined by some others?