New method for data treatment in polarization measurements

Precise formulae are obtained for the expectation values E(ξ), E(η) and variances V(ξ), V(η) of random variables ξ, η describing the spin asymmetry in the same reaction when a background process contribution is zero and appreciable, respectively. The variances of ξ and η are proved to be finite. It is shown that E(ξ) is equal to the physical asymmetry. This property of ξ and the finiteness of V(ξ) allows to find the asymmetry from experimental data without studying in detail the detector efficiency as a function of all kinematic variables essential for a process under investigation. This is the base of the proposed method of data treatment which is illustrated by Monte Carlo calculations. The formula for E(η) can be used to estimate the systematic uncertainty of the obtained asymmetry due to the background contribution. The high statistics limits for E(η) and V(η) are also considered for a nonzero value of the signal-to-background ratio.