ИСТИНА

Time-reversal invariance will be tested in proton-deuteron transmission experiment at COSY \cite{COSY}. The integrated cross section $\widetilde\sigma$ will be measured for transverse polarized proton beam ($p_y$) and tensor polarized deuterium target ($P_{xz}$). This observable provides a real null test of time invariance violating but P-parity conserving (TVPC) forces which do not arise in the standard model as a fundamental interaction. This signal is not affected by the initial and final state interaction and therefore its observation would directly indicate time-invariance violation, like in case of neutron EDM. To take under control background conditions of this experiment one has to know magnitudes of several T-even, P-even spin-observables in $pd$ scattering at energy of the planned experiment 100 - 200 MeV. In the present work the differential spin observables of the elastic $pd$ scattering and total $pd$ cross sections for polarized proton and deuteron are calculated within the Glauber theory. We use the formalism of \cite{PK} and develop it for inclusion of T-odd $pN$-scattering amplitudes. Furthermore, we properly modify the formalism of \cite{PK} to make a comparison with existing experimental data. The results of our calculations \cite{TUZYadfiz} for unpolarized differential cross section, vector $A_y$ and tensor $A_{ij}$ analyzing powers and spin correlation parameters $C_{ij}$, $C_{ij,k}$ of $pd$ elastic scattering %and spin-transfer coefficients $K_j^{i'}$ at 135 MeV (see Fig.\ref{figuz1}) and 250 MeV are in a reasonable agreement with the data \cite{Sekiguchi,Przewoski} in forward hemisphere. The total hadronic polarized cross sections $\sigma_1$, $\sigma_2$, $\sigma_3$ defined as in \cite{Uzikov2013} are calculated using the generalized optical theorem. In view of the planned accuracy of the $\widetilde\sigma$ measurement of about $10^{-6}$ \cite{COSY}, the obtained numerical result for $\sigma_1$ put a strong restriction on the magnitude of the possible false vector polarization of the deuteron ($P_y<10^{-6}$). Analytical formulas are derived for the $\widetilde\sigma$ observable and its energy dependence is calculated for several types of phenomenological TVPC $NN$-interactions. This dependence differs from that found in \cite{Beyer} where only a breakup mechanism was taken into account. We found that the TVPC $\rho$-meson exchange contribution to $\widetilde\sigma$ vanishes. Furthermore, we show that the Coulomb interaction does not lead to divergency of the $\widetilde\sigma$ observable. \bibitem{COSY} P.D.~Eversheim et al. , B.~Lorentz, Yu.~Valdau et al., COSY Proposal, N 215 (2012). \bibitem{PK} M.N.~Platonova, V.I.~Kukulin, Phys. Rev. {\bfseries C81}, 014004 (2010). % \bibitem{Sekiguchi} K.~Sekiguchi et al., Phys. Rev. {\bfseries C65}, 034003 (2002). % \bibitem{Przewoski} B.~von~Przewoski et al., Phys. Rev. {\bfseries C74}, 064003 (2006). % \bibitem{Uzikov2013} Yu.N.~Uzikov, J.~Haidenbauer, Phys. Rev. {\bfseries C87}, 054003 (2013). % \bibitem{Beyer} M.~Beyer, Nucl. Phys. {\bfseries A560} (1993) 895. % \bibitem{TUZYadfiz} A.A~Temerbaeyv, Yu.N.~Uzikov, Yad.Fiz. {\bf 78} (2015) (in press)