Critical Comments on the T-Null Theorem and New Approach to Searches for T-Invariance Violation in Quantum Systems

Abstract

for nuclear reactions that are two-body ones in the initial and final channels and which involve polarized particles, the T-null theorem stating the absence of vanishing observables in such reactions was proven in a number of studies by means of concepts of reaction \({\cal T}\) matrices that take into account general conservation laws along with T-invariance conditions in the “dynamically independent” approach. Not only does this approach focus on known mechanisms of such reactions, but it may also be applicable to their as-yet unknown mechanisms. By employing T-invariance conditions, the selection rules for specific mechanisms that make it possible to describe observables of a → b many-particle multistep nuclear reactions involving polarized particles are analyzed in the present study. It is shown that, in the differential cross sections for the initial nuclear reactions a → b and for \(\overline b \to \overline a \) reactions that are time-reversed with respect to them, the components characterized by specific P and T parities and related by T-invariance conditions are associated with unified mechanisms of their appearance and can be expressed in terms of unified scalar functions differing for a → b and \(\overline b \to \overline a \) reactions by the interchange of the channels and by the sign reversal for the momenta and spins of particles involved in these reactions. First, this permits selecting only one mechanism among all possible T-invariant mechanisms that describes simultaneously the features of the components considered for a → b and \(\overline b \to \overline a \) reactions and discarding all of the remaining mechanisms. Second, this enables one to obtain, in a number of cases, zero values for some components of the differential cross sections for the reactions in question. The latter constrains the applicability region of the aforementioned T-null theorem and makes it possible to use these components in the cross section for the initial reaction a → b to study the nature of T-noninvariant interactions.