This question is motivated by sheer curiosity. I certainly do not expect that the free parameters we use in the standard model have changed in value since we started measuring them with a "modern" degree of accuracy.
It would seem to me however, that as our experimental data accumulates in both quality and quantity, that it is important to know the physical constant values we input into our models as precisely as we can.
My question is, as I know very little about experimental physics, (and to working physicists this is probably an obvious question I am asking), but is there a law of diminishing returns in knowing the value of say, the mass of an electron to the 21st decimal point?
Is it important to continually refine the constant values to make the most, for example, of seemingly minor discrepancies in the results from the Large Hadron Collider?
I hope I am making myself clear and I apologise if I am not.
My point is: if the LHC produces an unexpected, repeated but extremely subtle result in an experiment, are we confident enough in the correctness of our present measurements of physical constants that we can draw conclusions other than measurement errors in them?
I am pretty sure the answer is yes, and that perhaps some of the results from the LHC actually serve to refine the values of the constants to reduce the error bars of the current values even more.