dhiginbotham/polynomialmagic

Using High Order Polynomials To Get Any Proton Radius

Polynomial Magic

Showing how to get whatever radius you like from a single set of charge form factor pseudo data.

Testing whether from a single randomly generated set of data one can always find the proton radius you want if you scan with high order polynomials. The radius is determined by taking the slope of the function at zero as it done with charge form factor data.

code outline

• generate ONE set of equal spaced random data with 1000 points from 0.01 to 10 fm$^{-2}$ using standard dipole and 0.003 random errors
• ask user to pick a proton radius from 0.70 to 0.92 fm
• loop over polynomial functions to see if we find the result we want
• it fails, drop one low q2 data point and try again
• repeat until we find at polynomial that will give the answer we want

bonus code

• float the normalizing of the "rejected" low q2 data and then show all the data now gives a great fit

Example Out

For the example figure, data is generated with standard dipole (0.81fm radius) and then a 0.90fm radius is requested. Using a high order polynomial and a floating normalization gives the requested radius.

As shown in the notebook, if one then fits the renormalized data with the high order polynomial it makes a beautiful fit of all 1000 points.