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Energy levels of hydrogen are calculated as one-loop matrix elements of the QED energy-momentum tensor trace in the external field approximation. An explicit connection established between the one-loop trace diagrams and the standard Lamb shift one-loop diagrams. Our calculations provide an argument against inclusion of the anomalous trace contribution as a separate term in the decomposition of the QED quantum field Hamiltonian and serve as an illustration how the trace anomaly is realized in the bound state QED. 

We calculate hard spin-independent contributions to energy levels in muonium and positronium which are due to radiatively corrected electron factor insertion in two-photon exchange diagrams. Calculation of these corrections is motivated by the new round of precise measurements of spin-independent transition frequencies in muonium and positronium. 

Abstract Electron mass is considered as a matrix element of the energy–momentum trace in the rest frame. The one-loop diagrams for this matrix element are different from the textbook diagrams for the electron mass renormalization. We clarify connection between the two sets of diagrams and explain analytically and diagrammatically why the results of both calculations coincide. 

New LHCb Collaboration results on pentaquarks with hidden charm 1 are discussed. These results fit nicely in the hadrocharmonium pentaquark scenario.[Formula: see text] In the new data the old LHCb pentaquark [Formula: see text] splits into two states [Formula: see text] and [Formula: see text]. We interpret these two almost degenerated hadrocharmonium states with [Formula: see text] and [Formula: see text], as a result of hyperfine splitting between hadrocharmonium states predicted in Ref. 2. It arises due to QCD multipole interaction between color-singlet hadrocharmonium constituents. We improve the theoretical estimate of hyperfine splitting[Formula: see text] that is compatible with the experimental data. The new [Formula: see text] state finds a natural explanation as a bound state of [Formula: see text] and a nucleon, with [Formula: see text], [Formula: see text] and binding energy 42 MeV. As a bound state of a spin-[Formula: see text] meson and a nucleon, hadrocharmonium pentaquark [Formula: see text] does not experience hyperfine splitting. We find a series of hadrocharmonium states in the vicinity of the wide [Formula: see text] pentaquark that can explain its apparently large decay width. We compare the hadrocharmonium and molecular pentaquark scenarios and discuss their relative advantages and drawbacks.