If the theoretical prediction can't be calculated until the experiment is done that motivates the choices of what and what not to approximate, is it really a prediction?
Let me make that more meta.
If a theory is unable to predict a particular key value, is it still a theory?
This is not a hypothetical question. The theory being tested here is the Standard Model. The Standard Model in principle is entirely symmetric with regards to a whole variety of things that we don't see symmetry in. For example the relative mass of the electron and the proton.
But, you ask, how can it be that those things are different? Well, for the same reason that we find pencils lying on their side rather than perfectly balanced around the point of symmetry on the tip. Namely that the point of perfect symmetry is unstable, and there are fields setting the value of each asymmetry that we actually see. Each field is carried by a particle. Each particle's properties reflect the value of the field. And therefore the theory has a number of free parameters that can only be determined by experiment, not theory.
In fact there are 19 such parameters. https://en.wikipedia.org/wiki/Standard_Model#Theoretical_asp... has a table with the complete list. And for a measurement as precise as this experiment requires, the uncertainty of the values of those parameters is highly relevant to the measurement itself.
Let me make that more meta.
If a theory is unable to predict a particular key value, is it still a theory?
This is not a hypothetical question. The theory being tested here is the Standard Model. The Standard Model in principle is entirely symmetric with regards to a whole variety of things that we don't see symmetry in. For example the relative mass of the electron and the proton.
But, you ask, how can it be that those things are different? Well, for the same reason that we find pencils lying on their side rather than perfectly balanced around the point of symmetry on the tip. Namely that the point of perfect symmetry is unstable, and there are fields setting the value of each asymmetry that we actually see. Each field is carried by a particle. Each particle's properties reflect the value of the field. And therefore the theory has a number of free parameters that can only be determined by experiment, not theory.
In fact there are 19 such parameters. https://en.wikipedia.org/wiki/Standard_Model#Theoretical_asp... has a table with the complete list. And for a measurement as precise as this experiment requires, the uncertainty of the values of those parameters is highly relevant to the measurement itself.