Statistical Biases in the UCNtau Experiment

Statistical biases come to the fore as the UCNtau experiment pushes the uncertainty of neutron lifetime measurements toward $0.01$\% precision. In UCNtau, we store ultracold neutrons (UCN) in a lossless magneto-gravitational trap and count the surviving neutrons after various storage times. The reduction of the UCN population is described by the exponential radioactive decay law; the observed decay constant is the inverse of the neutron lifetime. The Poisson statistics of particle counting -- due to its asymmetric distribution -- leads to varying degrees of bias in the extracted lifetime, depending upon the treatment and combination of individual measurement cycles. I will explain how these biases manifest in the context of the multi-step neutron counting scheme used in UCNtau. These effects must be quantified to control the systematic shift that results from the phase-space evolution of neutrons stored in the trap.