Estimation of antihydrogen properties in experiments with small signal deficit

For a class of precision CPT-invariance test measurements using antihydrogen, a deficit in the data indicates the presence of the signal. The construction of classical confidence intervals for the properties of the antiatoms from measurements may pose a challenge due to the limited statistics experimentally available. We use the Feldman-Cousins (Feldman and Cousins, Phys. Rev. D, 57, 3873. (doi:10.1103/PhysRevD.57.3873)) method to estimate model parameters for such a low count rate measurement. First, we construct confidence intervals for the Poisson process with a known background and an unknown signal deficit. Then the generalized Monte Carlo version of the method is applied to the use case of the hyperfine transition frequency measurement of the ground-state antihydrogen atom, where the expected double-dip resonance line shape and the mean background is assumed to be known. We find that confidence intervals of the antihydrogen properties could be obtained already from low statistics data. We also discuss how the method may be extended to allow estimation of additional model parameters.