Positronium atom is a sensitive probe of a "new" physics at long distance such as large extra dimensions, dark or mirror matter, hypothetical super-weakly interacting massless or fractionally charged particles, etc. Naturally, it is a subject of extensive experimental and theoretical research. Thanks to the smallness of the electron mass the strong and weak interaction effects are negligible and its properties can be calculated perturbatively in quantum electrodynamics (QED) as an expansion in Sommerfeld's fine structure constant $\alpha$ with very high precision only limited by the complexity of the calculations. We have evaluated the $\alpha^3\ln(alpha)$ corrections to the positronium HFS and decay rates which are necessary to confront the theoretical predictions and the current/future experimental measurements. The complete result for the ${\cal O}(\alpha^3)$ one-photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium is derived.
Quantum Hall and Josephson effects remain in the focus of experimental and theoretical research over decades. The study of the effects led to development of new fundamental physical concepts. At the same time they play a crucial role in metrology and determination of fundamental constants. We have discovered a deviation from the quantum mechanical prediction for the Hall conductivity and Josephson frequency-voltage relation due to radiative antiscreening of electric charge in an external magnetic field and predicted a weak dependence of the Josephson and von Klitzing constants on the magnetic field strength. This remarkable and unexpected manifestation of a fine nonlinear quantum field effect in a collective phenomenon in condensed matter is within the reach of the existing experimental techniques and merits a dedicated experimental analysis.
Bhabha scattering provides a very efficient tool for luminosity determination at electron-positron colliders and thus it is crucial for extracting physics from the experimental data. The two-loop corrections have to be incorporated into the theoretical analysis to match the demands of the present and future colliders. We have evaluated the two-loop photonic and heavy flavor corrections in the physical case of small electron mass by means of infrared subtraction method.
The advent of multi-TeV colliders like the LHC during the present decade or a future linear electron-positron collider will give access to a completely new energy domain to study the electroweak interactions. Once the characteristic energies $\sqrt{s}$ are far larger than the masses of the $W$- and $Z$-bosons, $M_{W,Z}$, exclusive reactions will receive virtual corrections enhanced by powers of the large electroweak logarithm $\ln\bigl({s/ M_{W,Z}^2}\bigr)$. The accuracy of the theoretical estimates necessary for the search of new physics beyond the standard model can be guaranteed only by including the logarithmic two-loop corrections. We have solved the problem for the electron-positron or quark-antiquark annihilation into a pair of fermions.
The theoretical study of nonrelativistic heavy quark-antiquark systems relies on the first principles of QCD and is based on the perturbative expansion. This makes heavy quark-antiquark systems an ideal laboratory to determine fundamental parameters of QCD, such as the strong coupling constant $\alpha_s$ and the heavy-quark masses $m_q$. However, the perturbative expansion for the basic heavy quarkonium parameters shows a rather bad convergence up to the next-to-next-to-leading (NNLO) order that makes the full NNNLO analysis mandatory. We have elaborated the general framework of the calculation [Nucl.Phys. B635 (2002) 357-383] based on potential NRQCD and the threshold expansion, and obtained a number of NNNLO results both for the quarkonium spectrum and production/annihilation rates.
In the observables used to extract the Cabibbo-Kobajashi-Maskawa (CKM) matrix elements and to gain deeper insight in the understanding of CP violation the bottom quark mass as well as the $B$ and $D$ meson leptonic decay constants enter as a crucial input parameters. A precise knowledge of them is mandatory for the interpretation of the experimental data. On the other hand, the top quark mass is one of the key parameters for precision tests of the standard model of the electroweak interactions at high energies and for the search of ``new physics'' at LHC and ILC. By evaluating the high order perturbative corrections within NRQCD and HQET framework we have obtained the most accurate estimates for these quantities.
Topantitop quark pair production close to the threshold will provide an integral part of the top quark physics program at the ILC. The theoretical interest in the topantitop threshold arises from the fact that the large top quark mass and width lead to a suppression of non-perturbative effects. This makes perturbative methods a reliable tool to describe the physics of non-relativistic top-antitop pairs, and allows for measurements of top quark properties directly at the parton level. From the resonance energy the top quark mass can be determined, whereas shape and height of the cross section near threshold are sensitive to the top quark width, the strong coupling constant and to the top Yukawa coupling. We have completed the NNLO analysis of the top-antitop threshold production.