Toward a global search for new physics with isotope shifts

Isotope shifts have emerged as a sensitive probe of new bosons that couple to electrons and neutrons, and of nuclear structure. The recent Hz- or even sub-Hz-level isotope shift measurements across different elements call for a global assessment of all available data. In this work, we present the fit framework that enables a combined analysis of isotope shift data from several elements, taking into account correlations. We provide a thorough comparison of analytical methods and the fit to analyze linear and nonlinear King plots and quantify their uncertainties. Finally, we provide recommendations for future measurements that could enhance the sensitivity to new physics and offer new insights into nuclear structure.