The proton, at the heart of most visible matter

To answer many questions at the forefront of particle physics, atomic physics, and nuclear astrophysics, a precise quantitative knowledge of the strong interaction in the non-perturbative domain of Quantum Chromo Dynamics is crucial. 

In this talk, several examples of the state of our understanding of precision hadron physics will be surveyed. In the interplay with atomic physics, I will give an update on the proton radius puzzle and show how new measurements of polarizabilities, combined with more refined theoretical analyses, can importantly improve on the limiting factors in the interpretation of high precision tests of the Lamb shift in muonic atoms.

In improving the precision of proton elastic form factors, two-photon exchange (TPE) corrections between the lepton and hadron are at present understood as the largest source of hadronic uncertainty. I will review recent work  within a dispersion relation framework to estimate such TPE corrections both in elastic electron-proton and muon-proton scattering, which will be tested in a new generation of experiments.  

Furthermore I will show that the dilepton production process on a proton is a versatile new tool in the study of non-perturbative hadron physics. At low dilepton masses, it allows to access the real part of the forward Compton amplitude, which enters the  hadronic corrections in the Hydrogen atom Lamb shift, or the electromagnetic proton-neutron mass difference.  At dilepton masses in the J/Psi region, it allows to access the s-wave J/Psi-p scattering length, indicating whether J/Psi-nuclear bound states may exist. 

Finally, I will discuss how deep inelastic scattering processes allow to perform a tomographic image of the proton in terms of its constituent quarks and gluons in both coordinate and momentum space.