High Precision Calculations in Quantum Field Theory

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Over the last few years the Large Hadron Collider (LHC) has transformed from a raw discovery into a high-precision machine. Despite many expectations no direct signal of new phenomena such as the extra space dimensions, supersymmetry, low-scale gravity etc. has been detected so far. Thus the "new physics" is likely to show up only as a tiny deviation of the experimental data from the theoretical predictions based on the standard model of particle interactions. At the same time the increasing accuracy of the low-energy experiments allows for a very accurate determination of the fundamental parameters of particle physics and becomes competitive in probing  physics beyond the standard model. Hence, the theoretical analysis which is able to provide the required precision becomes ultimately important.  The main aim of the project is the calculation of the high-order perturbative corrections in a wide class of the quantum field theory problems ranging from nonrelativistic threshold to ultrarelativistic Regge and Sudakov limit, which are of primary phenomenological importance for current and future experiments. One of the most interesting  field of the proposed research is related to the Higgs boson physics program at the LHC. It includes the perturbative analysis of  two main channels for the production of the Higgs boson or a pair of the Higgs bosons via gluon and electroweak gauge boson fusion. During the last two decades the methods and techniques of the perturbative quantum field theory reached an unprecedented level. The next-to-next-to-next-to-leading results have been obtained in quantum chromodynamics  for a number of the key processes such as Drell-Yan and the Higgs boson production at the LHC and the top quark-antiquark pair threshold production at a future linear collider. However, many of the pending problems  are still beyond the reach of available techniques for a direct calculation or go beyond any finite order of perturbation theory. These problems require a development of the new theoretical and computational tools, which are closely related to the fundamental concepts of the quantum field theory such as the effective field theory approach, renormalization group, asymptotic expansions, etc. Deeper understanding and development of these concepts are also among the aims of the project. The use of the ideas inherited from quantum field theory has become one of the main trends in the modern condensed matter physics. Such concepts as Majorana fermions, magnetic monopoles, supersymmetry etc., which are yet to be discovered at fundamental level in particle physics, are effectively realized in various condensed matter systems. This gives a significant boost to the application of the quantum field theory methods to condensed matter. I plan to continue the study of physical phenomena at the interface between the quantum fields and condensed matter and to develop and apply the advanced perturbative methods in this context.