The dynamics of baryon-antibaryon annihilation and reproduction ($B{bar B} leftrightarrow 3 M$) is studied within the Parton-Hadron-String Dynamics (PHSD) transport approach for Pb+Pb and Au+Au collisions as a function of centrality from lower Super Proton Synchrotron (SPS) up to Large Hadron Collider (LHC) energies on the basis of the quark rearrangement model (QRM). At Relativistic Heavy-Ion Collider (RHIC) energies we find a small net reduction of baryon-antibaryon ($B {bar B}$) pairs while for the LHC energy of $sqrt{s_{NN}}$ = 2.76 GeV a small net enhancement is found relative to calculations without annihilation (and reproduction) channels. Accordingly, the sizeable difference between data and statistical calculations in Pb+Pb collisions at $sqrt{s_{NN}}$= 2.76 TeV for proton and antiproton yields cite{53}, where a deviation of 2.7 $sigma$ was claimed by the ALICE Collaboration, should not be attributed to a net antiproton annihilation. This is in line with the observation that no substantial deviation between the data and statistical hadronization model (SHM) calculations is seen for antihyperons, since according to the PHSD analysis the antihyperons should be modified by the same amount as antiprotons. As the PHSD results for particle ratios are in line with the ALICE data (within error bars) this might point towards a deviation from statistical equilibrium in the hadronization (at least for protons/antiprotons). Furthermore, we find that the $B {bar B} leftrightarrow 3 M$ reactions are more effective at lower SPS energies where a net suppression for antiprotons and antihyperons up to a factor of 2 -- 2.5 can be extracted from the PHSD calculations for central Au+Au collisions.
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