Using Lanczos for nuclear corrections in muonic atoms and the proton radius puzzle

The most precise determination of the proton charge radius, from a novel muonic hydrogen spectroscopy experiment, disagrees with previous spectroscopy and scattering experiments done with electrons. 

This 7-sigma discrepancy is known as "proton radius puzzle", and may be the result of hitherto unknown physics. 

In order to investigate it, experiments with other muonic atoms have been conducted. 

These experiments rely on accurate theoretical predictions. 

In particular, their precision is limited by the nuclear corrections. 

We have calculated these corrections for muonic atoms with A=3,4 nucleons, for the first time using ab-initio methods and state-of-the-art nuclear potentials, significantly improving previous estimates, and contributed also to the A=2 case. 

This was achieved using a newly developed method, based on the Lanczos algorithm, for the calculation of energy-dependent sum-rules. 

Our new method and our results will be presented and discussed.