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Abstract. In this work the behavior of power corrections to Adler function in operator product expansion (OPE) is studied, in particular the possible contribution of operator of dimension 2. The OPE terms of dimension 4 and 6 are taken into account. Various experimental data on reactions of e + e − -annihilation to pion channels (π + π − , 2π + 2π − , π + π − 2π 0 , 3π + 3π − , 2π + 2π − 2π 0 ) are used. The high-precision fits of the experimental data are obtained and used. The method based on Borel transformation of Adler function is applied. It is shown that the contribution of operator of dimension 2 is negative being compatible to zero at three standard deviations level. The strong (anti)correlation between short string and local gluon condensate is found.

We develop a new mathematical method of extraction of nonperturbative corrections in QCD. The main attention is directed to the study of dimension 2 operator and its properties. The ordinary perturbation theory (PT) and analytical perturbation theory (APT) are used. The D-function is explored in dependence on both Q2 and Borel parameter M2. It is shown that the C2 coeffcient of the dimension 2 operator is negative and its compatibility to zero depends on choice of PT or APT and can vary in chosen ranges of M2. The strong (anti)correlation between C2 and gluon condensate found previously is confirmed.

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We discuss recent progress in the development of the three-fluid hydrodynamics-based program THESEUS towards an event generator suitable for applications to heavy-ion collisions at the intermediate energies of the planned NICA and FAIR experiments. We follow the strategy that modifications of particle distributions at the freeze-out surface in the QCD phase diagram may be mapped directly to the observable ones within a sudden freeze-out scheme. We report first results of these investigations for the production of light clusters (deuterons and tritons) which can be compared to experimental data from the HADES and the NA49 experiment and for the interpretation of the "horn" effect observed in the collision energy dependence of the K + /π + ratio. Medium effects on light cluster production in the QCD phase diagram are negligible at the highest NICA energies but shall play a dominant role at the lowest energies. A sharp "horn"-type signal in the K + /π + ratio can be obtained when the onset of Bose condensation modelled by a pion chemical potential results in an enhancement of pions at low momenta (which is seen at LHC energies) and would occur already in the NICA energy range.