On the low–energy behavior of the Adler function

The Adler function [1] plays a key role in particle physics. Specifically, theoretical description of some strong interaction processes (e.g., electron– positron annihilation into hadrons [2] and inclusive τ lepton decay [3,4]) is inherently based on this function. Besides, Adler function is essential for confronting the precise experimental measurements of some electroweak observables (e.g., muon anomalous magnetic moment [5] and shift of the electromagnetic fine structure constant [6]) with their theoretical predictions. In turn, the latter represents a decisive test of the Standard Model and imposes strict restrictions on possible “new physics” beyond it. Furthermore, Adler function plays a crucial role for the congruous analysis of spacelike and timelike experimental data. Indeed, since perturbation theory and renormalization group method are not applicable directly to the study of observables depending on the timelike kinematic variable, for the self–consistent description of the latter one has to relate the timelike experimental data with the spacelike perturbative results. Here, the required link between the experimentally measurable R–ratio of electron–positron annihilation into hadrons and theoretically computable Adler function D(Q) is represented by the dispersion relation [1]