Toward ab initio determination of charge symmetry breaking strength of Skyrme functionals

We propose a new approach to determine the strength of the charge symmetry breaking (CSB) term in the framework of Skyrme density functional theory. It is shown that once textit{ab initio} calculations are available including accurate description of isospin symmetry breaking terms in medium and heavy nuclei, the mass difference of mirror nuclei as well as the neutron-skin thickness of doubly closed shell nuclei can be used to constrain the strength of CSB interaction with an uncertainty less than $ 6 , % $, separately from other isospin breaking forces. This method opens a new vista of textit{ab initio} nuclear energy density functionals.