My research interests can be roughly divided into two groups. The first is the phenomenology of various extensions of the Standard Model and possible applications to cosmology and astrophysics. The second is the semiclassical approach to quantum field theory and quantum mechanics, including instanton processes and processes with violation of fermion number.
Inflation with the Standard Model Higgs boson
Literature
- Standard Model Higgs boson mass from inflation. F. Bezrukov and M. Shaposhnikov. Phys.Lett.B659:703-706,2008. arXiv:0812.4950 [hep-ph]
- Standard Model Higgs boson mass from inflation. F. Bezrukov, A. Magnin, and M. Shaposhnikov. Phys.Lett.B675:88-92,2009, arXiv:0812.4950 [hep-ph]
- Standard Model Higgs boson mass from inflation: Two loop analysis. F. Bezrukov and M. Shaposhnikov. JHEP 0907:089,2009, arXiv:0904.1537 [hep-ph]
Cosmological inflation is possible just in the Standard Model, without adding any new fields and without modification of low energy physics. The only change is the introduction of a non-minimal coupling of the Higgs boson to gravity. The most interesting feature of this model is that there are essentially no free parameters, so definite predictions for many observables can be made. The model provides a framework to explain neutrino oscillations, Dark Matter, the baryon asymmetry of the Universe, and inflation. However, the parameters of the model are quite restricted. My current aim is to analyze all possible consequences of the proposed scenario for particle physics and cosmology.
A long-standing possibility here would be a detailed study of more generic theories with modified gravity and non-minimally coupled fields. Such theories may provide new insights into possible inflation mechanisms, and maybe also ways to explain the cosmological constant problem. Extensive research of even classical properties of such models is lacking at the moment. Analysis of quantum effects, though difficult, may provide important clues for the construction of future theories in particle physics and cosmology.
νMSM—Standard Model with 3 sterile neutrinos
At present there are several well-established experimental facts that require introduction of some new physics in addition to the Standard Model. Specifically, they are neutrino oscillations, the baryon asymmetry of the Universe, the presence of Dark Matter in the Universe, the inflationary stage of the Universe and the cosmological constant or Dark Energy. The first three effects can be nicely incorporated in a very simple extension of the Standard Model, called the νMSM. This model adds three right handed sterile neutrinos to the Standard Model, with one of these neutrinos providing a candidate for the Warm Dark matter, and makes possible to explain the baryon asymmetry of the Universe via some leptogenesis mechanism.
On the purely particle physics side, the importance of the analysis of experimental detection and analysis of right handed neutrinos in the νMSM is important. I analysed the neutrinoless double beta decay in the νMSM. The result is important for current experiments in measurement of the effective Majorana mass m0νββ for neutrinoless double beta decay. In all νMSM variations, m0νββ is smaller than 0.05 eV, such that measurement of larger m0νββ would forbid the model its the present form. An article on this topic is being prepared.
Another problem here is the generation of the correct Dark Matter neutrino abundance in the νMSM. The simplest mechanism, thermal production from oscillations of active neutrinos, is currently ruled out by simultaneous analysis of the astrophysical X-ray background and Lyman-α analysis. Other mechanisms are possible, but they lead either to nontrivial constraints on the sterile neutrino parameters, or they need further modifications of the theory, which introduce new particles that can be searched for experimentally. For example, one can produce the initial abundance of the sterile neutrino by inflaton decay, but the inflaton parameters turn out to be within experimental reach. Alternatively, one can analyse the possibilities of sterile neutrino creation in the models with modified gravity. Both of these problems are currently being worked on.
Rare Decays
Another approach to new physics searches follows the opposite logic: instead of constructing a very constrained theory and looking for experimental predictions, one can construct a very general extension of the Standard Model and try to derive experimental constraints on the parameters of such a model, and later compare specific theories with the obtained constraints. My work on CP violation in rare kaon or pion decays follows this logic. We analysed the possible contributions from the most generic two Higgs doublet model to CP-odd observables in kaon decays, for example to transverse lepton polarisation in K→μνγ, K→πμν, and similar decays. These observables are insensitive to CP-violation in CKM matrix and are promising for discovery of CP-violating new physics. This work (with the paper being currently prepared) is encouraging for the rare kaon decay experiments, as it shows that the parameter region accessible in kaon decay experiments is complementary to the one explored in high precision measurements at high energy accelerators.
Nonperurbative effects
In a more field theoretical front, I am working on applications
of semiclassical methods in field theory. The original problem of
this type was the calculation of the probability of baryon number
violating processes in the electroweak sector of the Standard Model
in particle collisions at high energy that are accompanied by a
change of the topological number of the vacuum. At low energies such
processes are described by instantons, and are exponentially
suppressed via the small electroweak coupling constant, being
practically unobservable. The situation may change at high energies,
comparable to the energy of the sphaleron
—a static solution
of the equations of motion with minimal energy required to cross the
barrier between the adjacent topologically different vacua. However,
the problem of tunneling in high energy particle collisions is more
difficult than the problem of temperature tunnelling, because the
two-particle initial state is significantly different from the
sphaleron configuration. For calculation of the cross sections of
processes with a change of topological number, a semiclassical
method was developed, based on solution of a boundary problem for
the classical field equations in complex time with nontrivial
boundary conditions. The solution of this boundary problem turnes
out to be quite a nontrivial computational task, due to the peculiar
form of the field equations in complex time and the large size of
the system required to obtain a reliable solution. A numerical
solution, performed by me using this method on a parallel
supercomputer, gave a strict bound on the probability of such
processes up to very high energies (250 TeV). The suppression
at high energies arises precisely from the need to rearrange the
two-particle initial state into a state close to the sphaleron.
Currently, we are interested in analysis of topological processes in theories with extra dimensions. The question appears when the effective theory with reduced extra dimensions (the theory on the brane) has nontrivial topological properties. One may expect that the naïve description in the effective theory might not coincide with the exact treatment from the underlying theory with extra dimensions, since the topological properties of the latter are generally quite different. Solutions of the strong CP problem in this style were recently proposed. However, no analysis of a realistic theory, or even a full toy model in a smaller number of dimensions, has been made up to this point.
Theories with chiral fermions may have problems when a nontrivial topological structure is present. It is known that in models with instantons and with only one chiral fermion of matter, instanton processes are accompanied by a change of fermion number of one, i.e. creation of just one fermion. In four dimensions such models suffer from the global Witten anomaly, and are internally inconsistent. But in two dimensions the global anomaly is absent, and such process may happen. Models of this type appear, for example, in superconductors. We calculated the probability of such process in two dimensions, and verified that it does not lead to any mathematical inconsistencies. It is planned to analyse how anomalies of this type may manifest themselves in theories with extra dimensions, where the full theory is anomaly free, but the effective theory is naïvely anomalous.
Teaching interests
I was involved in the teaching process at the Moscow State University, where I gave a course on Supersymmetric theories in particle physics for the 4th year students over a period of several years. Also, I participated in giving a course on classical gauge theory for 3rd and 4th year students there, both in the lecture part of the course, and in leading the exercise sessions. In EPFL I led exercise sessions for the Quantum field theory course, and participated the supervision of reading courses of students studying gauge theory and cosmology.
I was supervisor of the master thesis of R. Chicheportiche
(in the EPFL) on the topic of Constraining the Transverse Muon
Polarization in K+→γμ+ν in the Framework
of a General Two Higgs Doublet Model
. An article is being
prepared as a continuation of this work.
I am interested in leading courses in topics like quantum field
theory and supersymmetry. Another idea for the course of
Additional chapters of quantum mechanics
appeared during our
work in semiclassical tunneling, which used some path integral and
coherent state techniques that are usually missed out in standard
courses on quantum mechanics. Other topics connected with cosmology
and particle physics phenomenology may also be of interest.
