Probing new physics using Rydberg states of atomic hydrogen

We consider the role of high-lying Rydberg states of simple atomic systems such as $^1$H in setting constraints on physics beyond the Standard Model. We obtain highly accurate bound states energies for a hydrogen atom in the presence of an additional force carrier (the energy levels of the Hellmann potential). These results show that varying the size and shape of the Rydberg state by varying the quantum numbers provides a way to probe the range of new forces. By combining these results with the current state-of-the-art QED corrections, we determine a robust global constraint on new physics that includes all current spectroscopic data in hydrogen. Lastly we show that improved measurements that fully exploit modern cooling and trapping methods as well as higher-lying states could lead to a strong, statistically robust global constraint on new physics based on laboratory measurements only.