Energy levels of quantum electrodynamics (QED) bound states, which depend on a number of independent mass parameters, can be calculated as matrix elements of the QED energy-momentum tensor trace. As an example of such system we consider muonic hydrogen. The leading one-loop corrections to its energy levels depend on the electron and muon masses. These corrections are calculated as matrix elements of the energy-momentum tensor trace. Respective one-loop trace diagrams are different from the standard Lamb shift diagrams. We explain analytically and diagrammatically why two different sets of diagrams lead to the same results. Similar relationships should also hold beyond the one-loop approximation.

We calculate radiative-recoil contribution of order Z^2α(Zα)^5(m/M)^2m to the Lamb shift in muonium. This correction is due to insertion of radiative photons in the heavy line in the two-photon exchange diagrams. Our calculations are inspired by a new round of precise 1S-2S and 2S-2P experiments currently in progress.

Uncertainty of the theoretical prediction for the hyperfine splitting in the ground state of muonium is considered. It is compared with the respective discussion in the two most recent CODATA adjustments of the fundamental physical constants.

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.

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.

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.

We calculate hard spin-independent three-loop radiative corrections to energy levels in muonium and positronium which are due to radiative insertions in two-photon exchange diagrams. These corrections could be relevant for the new generation of precise $1S-2S$ and $2S-2P$ measurements in muonium and positronium.

An approach to the properties of the [Formula: see text] system developed to solve the famous [Formula: see text] problem is used to calculate the partial widths ratios to [Formula: see text] and [Formula: see text] in the [Formula: see text] and [Formula: see text] decays. We obtain the results in agreement with the experimental data.

We calculate spin-independent three-loop radiative-recoil corrections to energy levels in muonium due to polarization insertions in two-photon exchange diagrams. These corrections could be relevant for the new generation of precise $1S-2S$ and $2S-2P$ measurements in muonium.

An approach to the properties of the eta-eta' system developed to solve the famous U(1) problem is used to calculate the partial widths ratios to eta and eta' in the B-0 -> J/Psi eta(eta', pi(0)) and B-s -> J/Psi eta(eta') decays. We obtain the results in agreement with the experimental data.

Mikhail Borisovich Voloshin passed away unexpectedly in the 67th year of life. Voloshin was born on May 14, 1953 in Romania, where his father worked at that time. He went to the first specialized physical class of the famous 57th Moscow school, which he graduated from in 1970, and then entered, without exams, the Faculty of General and Applied Physics of the Moscow Institute of Physics and Technology (MIPT) as a winner of the International Physics Olympiad. Already in his student days, Voloshin's leadership among physicists of his generation became clearly pronounced. He studied at the department of elementary particle physics, whose head was Karen Avetovich Ter-Martirosyan. The institute associated with the department was the Institute for Theoretical and Experimental Physics (ITEP). When a thirdyear student, Voloshin passed the theoreticalminimum exams on quantum mechanics and quantum electrodynamics under Ter-Martirosyan and onGeneral Relativity (GR) under Igor' Yur'evich Kobzarev. Voloshin's academic advisor was Lev Borisovich Okun', who considered Voloshin his favorite student. The first paper by Voloshin, co-authored with Kobzarev and Okun', was devoted to the decay of a false vacuum. The results obtained there have been included in textbooks and are topical even now: the Higgs boson mass is such that our vacuum is at the stability boundary. The paper was published in the journal Yadernaya fizika (Nuclear Physics) (Vol. 20, p. 1229) in 1974. In about ten years, in a series of studies written by Voloshin together with K G Selivanov, he examined the processes of induced false vacuum decay with heavy-particle masses or colliding particle energies as inducing factors. It was revealed that the induced processes cannot be described by the perturbation theory on the background of a Euclidean solution, and the possibility of the disappearance of exponential suppression on the sphaleron energy scale was analyzed. This pioneering work opened new fields of research. In the autumn of 1974, the ``November revolution'' broke out: the groups of Ting in Brookhaven and Richter in Stanford discovered the J=C meson almost simultaneously. Voloshin and collaborators immediately joined the development of quarkonium theory; later, Voloshin without a doubt became the most prominent expert on heavy quark physics in the world. He made a fundamental contribution to the sum rule, the physics of hadrons containing heavy quarks, the basic elements of QCD, and the quark model. Based on the QCD sum rules, he predicted the Zc-meson mass that differed greatly from the experimental values available at the time. The uncertainty of that prediction was estimated, showing that the experimental value could not be valid. This prediction was confirmed by subsequent experiments. Together with M A Shifman, Voloshin found an elegant way to evaluate the matrix element of the Kobayashi±Maskawa matrix Vcb from exclusive semilepton B-meson decays. This method was used to seek manifestations of the new physics. Having graduated from MIPT in 1976, Voloshin began working at ITEP, and a year later defended his candidate thesis. Several years later, he defended his doctoral thesis devoted to the U-meson theory. Voloshin had a very wide spectrum of interests, not limited to heavy quark physics. He discovered the `custodial symmetry' of the electroweak theory relating the masses ofW and Z bosons. Voloshin, along with Okun' andM IVysotskii, proposed to measure time variations of neutrino fluxes associated with solar cycles as a method to discover the neutrino magnetic moment. These measurements have been carried out to date. Uspekhi Fizicheskikh Nauk 190 (5) 557 ± 558 (2020) Translated by M V Tsaplina PERSONALIA PACS number: 01.60.+q

New LHCb Collaboration results on pentaquarks with hidden charm1 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.

An approach to the properties of the η–η' system developed to solve the famous U(1) problem is used to calculate the partial widths ratios to η and η' in the B^0 → J/Ψ η(η', π^0) and B_s → J/Ψ η(η') decays. We obtain the results in agreement with the experimental data.

We consider decays of the hidden charm LHCb pentaquarks in the hadrocharmonium and molecular scenarios. In both pictures the LHCb pentaquarks are essentially nonrelativistic bound states. We develop a semirelativistic framework for calculation of the partial decay widths that allows the final particles to be relativistic. Using this approach we calculate the decay widths in the hadrocharmonium and molecular pictures. Molecular hidden charm pentaquarks are constructed as loosely bound states of charmed and anticharmed hadrons. Calculations show that molecular pentaquarks decay predominantly into states with open charm. Strong suppression of the molecular pentaquark decays into states with hidden charm is qualitatively explained by a relatively large size of the molecular pentaquark. The decay pattern of hadrocharmonium pentaquarks that are interpreted as loosely bound states of excited charmonium psi' and nucleons is quite different. This time dominate decays into states with hidden charm, but suppression of the decays with charm exchange is weaker than in the respective molecular case. The weaker suppression is explained by a larger binding energy and respectively smaller size of the hadrocharmonium pentaquarks. These results combined with the experimental data on partial decay widths could allow to figure out which of the two theoretical scenarios for pentaquarks (if either) is chosen by nature.

We consider hidden charm pentaquarks as hadroquarkonium states in a QCD inspired approach. Pentaquarks arise naturally as bound states of quarkonia excitations and ordinary baryons. The LHCb \(P_c(4450)\) pentaquark is interpreted as a \(\psi '\)-nucleon bound state with spin-parity \(J^P=3/2^-\). The partial decay width \(\varGamma (P_c(4450)\rightarrow J/\psi +N)\approx 11\) MeV is calculated and turned out to be in agreement with the experimental data for \(P_c(4450)\). The \(P_c(4450)\) pentaquark is predicted to be a member of one of the two almost degenerate hidden-charm baryon octets with spin-parities \(J^{P}=1/2^-,3/2^-\). The masses and decay widths of the octet pentaquarks are calculated. The widths are small and comparable with the width of the \(P_c(4450)\) pentaquark, and the masses of the octet pentaquarks satisfy the Gell-Mann–Okubo relation. Interpretation of pentaquarks as loosely bound \(\varSigma _c\bar{D}^*\) and \(\varSigma _c^*\bar{D}^*\) deuteronlike states is also considered. We determine quantum numbers of these bound states and calculate their masses in the one-pion exchange scenario. The hadroquarkonium and molecular approaches to exotic hadrons are compared and the relative advantages and drawbacks of each approach are discussed.

A hard three-loop correction to parapositronium energy levels of order m alpha(7) is calculated. This nonlogarithmic contribution is due to the insertions of one-loop photon propagator in the fermion lines in the diagrams with virtual two-photon annihilation. We obtained Delta E = 0.03297(2) (m alpha(7) / pi(3)) for this energy shift.

Calculation of hard three-loop corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium is reviewed. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.

We interpret the newly discovered pentaquark P-c(4450) as a bound state of charmonium psi(2S) and the nucleon. The binding potential is due to the charmonium-nucleon interaction that in the heavy quark approximation is proportional to the product of the charmonium chromoelectric polarizability and the nucleon energy-momentum distribution. We use the large N-c expansion to estimate the quarkonium polarizability and calculate the nucleon properties in the framework of the mean-field picture of light baryons. Two almost degenerate states J(P) = (1/2)(-) and J(P) = (3/2)(-) are predicted at the position of the P-c(4450) pentaquark. We find that the nucleon-psi(2S) bound state has a naturally narrow width in the range of tens of MeV. The unitary multiplet partners of the P-c(4450) pentaquark and the generalization to b (b) over bar -nucleon pentaquark bound states are discussed.

We consider hard three-loop nonlogarithmic corrections of order [Formula: see text] to hyperfine splitting in muonium and positronium. All these contributions are generated by the graphs with photon, electron and/or muon loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams.