Standard model describes three interactions (strong, weak, electromagnetic) of elementary particles. Coupling strengths are free parameters.
There are several arbitrary parameters in the scalar sector, which are:
1. Symmetry breaking SU(2)xU(1) .--> U(1) proceeds through the VEV of the Higgs scalar =v. This is a free parameter.
2. Higgs field interacts with fermions through trilinear Yukawa couplins of the form fermion-fermion-scalar. There are, six quarks and three leptons, consequently there are nine Yukawa couplings.
3. Higgs self interaction strength is a free parameter.
4. Cabbibo-Kobayashi-Maskawa mixing matrix has three angles and a phase, giving four parameters.
Furthermore there is an unknown theta term in QCD Lagrangian giving rise to strong CP problem.
In total there are nineteen of them. Except four parameters of CKM sector, the remaining fifteen parameters are complex.
Because these parameters are fixed by experiments, one thinks that there is a strong motivation for carrying out studies beyond the standard model in a direction which will have more predictive power and fewer free parameters.
Excellent,,,,,,, We know that the parameters are nothing but a a tool that describes a particle. First of all particle should exist then only we can predict(Or rediscover it by experiment) What ever methodology you have written( in terms of Quantum mechanics)is one way of describing a particle. But is it only way to discover or predict the particles? If particles exist beyond this parameters , we can not say that such particle are non existent.---------- In some other way if we predict a particle(a particle made up of space time....here space time is also a type of material forms mass--- this particle can be described by quantum mechanics parameters. But quantum mechanics denies the space time described by General relativity within the measure of elementary particle....Thus in my opinion Higgs mechanism to describe basic building block of mass. Actual basic building block of mass is material made up of space time...
Thank you for your interest in describing parameters in depth subject