CPT and Lorentz Tests in Hydrogen and Antihydrogen
  Signals for CPT and Lorentz violation at the Planck scale may arise in hydrogen and antihydrogen spectroscopy. We show that certain 1S-2S and hyperfine transitions can exhibit theoretically detectable effects unsuppressed by any power of the fine-structure constant. 
Robert Bluhm, Alan Kostelecky, Neil Russell