A proton is a complex object. The perfect way to determine the size of a proton is by use of electromagnetic probes. The process of discovering the size of the proton can be traced back to some inventors. In 1909, Geiger-Marsden used particles to discover the nucleus, in 1956, Hofstadter and other researchers used proton scattering to prove that is a matter with size and finally in the late 1960s to early 1970s, Friedman Kendall used Inelastic Scattering to prove that proton has structure. To determine the size of a proton, it is procedural to first define the proton size. Proton has charged particles that move. Their root mean square radius is calculated. Proton radius is measured by electric and magnetic charge distribution and the slope determined. In measuring the size of the proton, there is a feature of curious discrepancy that gives rise to proton radius puzzle. The discrepancy could be caused by the problem of electronic extraction, the problem with muonic hydrogen theory or due to the new force that couples to muons but not electrons.
In providing a solution to the discrepancy in electronic extraction, it would be essential to try preventing Proton and Neutron from scattering. However, nobody knows the functional form of electronic and magnetic energies. The fact that the functional behaviour is unknown makes it difficult to know how many parameters are needed to fit the experimental data. Therefore to provide some constraints on their functional behaviour of the form factors, the z-expansion method is used which is based on the analysis of the properties of the form factor Gmp.This is done by first mapping the domain of the analyticity on the unit circle and defining a variable. The magnetic radius is extracted as well as the radius of the neutron which shows they are consistent with each other.
Neutrino physics requires precision for the future program. For precision, both form factors and nuclear effects need to be controlled. Literature focuses on nuclear models, but the biggest problem is the axial form factor. Everyone uses one parameter for axial form factor which is dipole model, but the dipole model is known to be inadequate for EM form factors. The experiment gives same results like other experiments, and it remains a question of what could be the source of discrepancies. Is it nuclear effects, form effects or both? Literature focuses on nuclear effects. When the z expansion is used with the axial form factor, it gives effective effects.
To resolve the proton radius puzzle, the z- expansion is used which disfavors the muonic hydrogen.Muonic hydrogen disagrees with that extracted from electronic hydrogen or electron-proton scattering. The two-photon exchange is testable in proton puzzle. There is need of polarizability effect on neutron, and then deuteron is used to determine the effect on neutron and then the other nuclei is predicted. This idea can explain the missing energy. Two photon exchanges can resolve the puzzle but the hydrogen cannot be described unless the structure uncertainty is larger than it is thought but that is an irritating uncertainty.
The first measurement of proton radius from muonic hydrogen was discovered to be away from hydrogen in 2010.The source of discrepancy is still not known. However, there are on-going intense developments by experts for future programs and experiments to come up with better results.