Dmitri Diakonov - Research#

Prof. Dmitri Diakonov has made several pioneering contributions to the field of theoretical high energy physics and physics of elementary particles. He is a world expert in the very difficult field of quantum field theory which has played, and still does, the most prominent role in the field of theoretical particle physics.. In a nutshell, he is particularly famous for his work on representation of Wilson loops as functional integrals over a group, and on recognizing the role of instantons and other classical configurations in the problem of confinement in quantum chromodynamics which is the standard model of strong interactions.

More in detail:

1. In the 1970’s Quantum Chromodynamics (QCD) has been formulated as a candidate for the microscopic theory for strong (nuclear) interactions. However, at that time QCD seemed to contradict many experimental observations. For example. it predicted violations of Bjorken scaling in deep inelastic lepton scattering off nucleons, as well as the growth of transverse momenta of outgoing particles with the overall momentum transfer. Neither was observed in those early days.

Together with two graduate students Yu. Dokshitzer and S. Troian, Diakonov undertook a systematic study of `hard' processes at high energies, i.e. those characterized by high momentum transfer. Using clever tricks, they managed to sum up infinite series of Feynman graphs in QCD, dominating in hard hadronic processes. They compared their results with experiments, and proposed new experiments to check QCD directly. This was a pioneering contribution to now booming field called `perturbative QCD’, helping to establish the validity of QCD itself as the theory of strong interactions. This work enjoyes more than thousand citations and is still used today.

2. In the beginning of the 1980’s Diakonov was one of the first to move into then terra incognita of nonperturbative QCD. Most of physically important phenomena in strong interactions like confinement of quarks, spontaneous chiral symmetry breaking and breaking of the axial U(1) symmetry take place at strong coupling where perturbative methods fail, hence the need for nonperturbative approaches.

Together with V. Petrov, Diakonov developed a new variational method for gauge theories which they subsequently applied to build the `instanton liquid’ model of the QCD vacuum state. [Instantons are certain large nonperturbative fluctuations of the gluon field in the vacuum, of topological nature.] They obtained a self-consistent picture of a relatively dilute instanton ensemble, with all observables like the gluon condensate or the topological susceptibility calculated - via the `transmutation of dimensions' - through the basic Lambda parameter of QCD, and appearing in a fair agreement with the phenomenology.

A decade later, direct lattice simulations of the Yang-Mills vacuum have shown, after certain `smearing' procedure, a distribution of instantons and anti-instantons with the characteristics remarkably close to those variational estimates.

3. In 1984, Diakonov together with V. Petrov suggested a new microscopic mechanism of spontaneous breaking of chiral symmetry in QCD. This is one of the most, if not the most important phenomenon in strong interactions, manifesting itself, in particular, in the fact that nucleons are heavy whereas pions are light.

The new mechanism was due to `hopping' of originally massless or nearly massless quarks between instantons, or, to be more precise, as due to the delocalization of the would-be zero fermion modes of individual instantons, in the ensemble of randomly spaced and oriente instantons. Apart from being successful phenomenologically, this work laid base for the application of the Random Matrix Theory to spontaneous chiral symmetry breaking.

Diakonov’s papers on instantons have in total around two thousand citations.

4. In 1986 Diakonov and Petrov suggested a new field-theoretic model of baryons named `Chiral Quark--Soliton Model'. It was based on an earlier observation of Diakonov and Eides that integrating off quarks in the background pion field gave the Effective Chiral Lagrangian including the famous Wess – Zumino term and other four-derivatives terms which proved to desrcibe correctly the d-wave pion amplitudes and other observables. This is the effective theory to which full QCD is reduced at low momenta. The large number of colours N_c is a formal algebraic parameter justifying the use of a classical mean pion field in the baryon problem.

According to the model, baryons in the large-N_c limit can be viewed as N_c `valence' quarks bound by a self-consistent pion field whose energy is in fact coinciding with the aggregate energy of the Dirac sea of quarks. The model interpolates between the Skyrme model and the old non-relativistic quark models but contrary to the latter is field-theoretic and relativisticinvariant.

Therefore, it enables one to caclculate not only the static properties of baryons such as magnetic moments and axial constants but also the numerous parton distributions in nucleons at a low normalization point, which are totally nonperturbative.

Using the Chiral Quark – Soliton Model, Diakonov and collaborators from Ruhr-Universitaet Bochum calculated unpolarized and polarized quark and antiquark distributions in nucleons. These distributions satisfy all general requirements (positivity, sum rules constraints, etc.) and turn out to be in fair accordance with the phenomenology, without any `fitting' parameters whatsoever.

This cycle of papers has more than thousand citations.

5. Basing on the above model in 1997 Diakonov (with V. Petrov and M. Polyakov) predicted an existence of a relatively light and very narrow baryon resonance with quantum numbers that could be obtained only from four quarks and one antiquark – an exotic “pentaquark”, dubbed later on the Theta+ baryon by Diakonov.

This prediction stimulated a search of the Theta+ baryon by two independent experimental groups in Osaka in Moscow, and in the Autumn of 2002 both groups announced strong signals of the Theta+ precisely with the predicted mass, and very narrow. That was followed by a flow of a few dozen experiments at different installations worldwide, and many hundreds of theoretical papers.

Although the present experimental status of the Theta+ is still controversial, this work by Diakonov stimulated much activity in the study of hadron resonances and in the search of new ones, and played an important role in re-consideration of certain long-standing prejudices in the physics of strong interactions.

Recently, Diakonov gave a more intuitive explanation of the pentaquarks in terms of the mean-field approximation to baryon (justified theoretically at large N_c), and predicted a new type of pentaquarks containing heavy c or b quarks.

6. Quite recently Diakonov suggested a new microscopic mechanism of quark conferment and of the confinement-deconfinement phase transition at high temperatures, based on the idea of the dominance of monopole (dyon) configurations of the gluon field in the ground state. The quantum weight of dyons was computed for the first time by Diakonov and collaborators, which enabled him, together with Petrov, to build the statistical mechanics of the ensemble of interacting dyons, to which the Yang – Mills partition function reduces in the semiclassical approximation.

It was shown that the free energy of the quantum system of the Yang – Mills fields had the unique minimum corresponding to the zero average of the Polyakov line, which is one of the confinement criteria. All the other criteria – the area behaviour of large Wilson loops, the electric string appearing between static quarks, the disappearance of gluon degrees of freedom – where also demonstrated.

Furthermore, Diakonov showed that at higher temperatures, there is a competition between the dyons-induced nonperturbative free energy, and the perturbative one. At certain critical temperature T_c, the second prevails, and the system undergoes a phase transition to the deconfinement phase. The critical temperature computed in units of string tension turns out to be in remarkable agreement with lattice measurements of this quantity, where available.

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