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Dmitri Diakonov

Publications and source records attributed to Dmitri Diakonov.

At least 19 recordsLinked to original sources
arXiv2013

Effective Lagrangian for the Polyakov line on a lattice

We formulate a method for computing the effective Lagrangian of the Polyakov line on the lattice. Using mean field approximation we calculate the effective potential for high temperatures. The result agrees with recent lattice simulations. We reveal a new type of ultraviolet divergence (coming from longitudinal gluons) which dominates the effective potential and explains the discrepancy of the lattice simulations and standard perturbative calculations performed in covariant gauges.

hep-lat↗
arXiv2013

A theory of baryon resonances at large N_c

At large number of colors, N_c quarks in baryons are in a mean field of definite space and flavor symmetry. We write down the general Lorentz and flavor structure of the mean field, and derive the Dirac equation for quarks in that field. The resulting baryon resonances exhibit an hierarchy of scales: The crude mass is O(N_c), the intrinsic quark excitations are O(1), and each intrinsic quark state entails a finite band of collective excitations that are split as O(1/N_c). We build a (new) theory of those collective excitations, where full dynamics is represented by only a few constants. In a limiting (but unrealistic) case when the mean field is spherically-and flavor-symmetric, our classification of resonances reduces to the SU(6) classification of the old non-relativistic quark model. Although in the real world N_c is only three, we obtain a good accordance with the observed resonance spectrum up to 2 GeV.

hep-ph↗
arXiv2012

Gluon distribution at very small x from C-even quarkonia production at the LHC

C-parity-even quarkonia eta_b,c and chi_b,c with spin 0 and 2 are produced via two-gluon fusion. The expected cross section of the inclusive production of the quarkonia at the LHC, times the branching ratios of convenient decays, is up to tens of nanobarn per unit rapidity in the case of charmonia and around one nanobarn for the bottomonia. Measuring the quarkonia production as function of rapidity will allow to determine the gluon distribution function in nucleons in a very broad range of the Bjorken x from x~10^(-2) where it is already known, down to x~10^(-6) where it is totally unknown. The scale of the gluon distribution found from such measurements turns out to be rather low, Q^2 ~ 2.5 - 3 GeV^2, for charmonia and rather large, Q^2 ~ 20 GeV^2$, for bottomonia. We evaluate the scale by studying the next-to-leading-order production cross sections.

hep-ph↗
arXiv2012

Phase transitions in spinor quantum gravity on a lattice

We construct a well-defined lattice-regularized quantum theory formulated in terms of fundamental fermion and gauge fields, the same type of degrees of freedom as in the Standard Model. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is suitable for describing large nonperturbative and fast-varying fluctuations of metrics. Although the quantum curved space turns out to be on the average flat and smooth owing to the non-compressibility of the fundamental fermions, the low-energy Einstein limit is not automatic: one needs to ensure that composite metrics fluctuations propagate to long distances as compared to the lattice spacing. One way to guarantee this is to stay at a phase transition. We develop a lattice mean field method and find that the theory typically has several phases in the space of the dimensionless coupling constants, separated by the second order phase transition surface. For example, there is a phase with a spontaneous breaking of chiral symmetry. The effective low-energy Lagrangian for the ensuing Goldstone field is explicitly diffeomorphism-invariant. We expect that the Einstein gravitation is achieved at the phase transition. A bonus is that the cosmological constant is probably automatically zero.

hep-th↗
arXiv2012

Baryon resonances at large Nc, or Quark Nuclear Physics

We suggest a new point of view according to which baryon resonances can be understood as collective excitations about intrinsic one-quark excitations in a mean field of definite symmetry. This approach is justified in the limit of large number of colours Nc, and is similar to the physics of large-A nuclei, hence "quark nuclear physics". Although in the real world Nc is only three, we obtain a good agreement with the observed resonance spectrum of light baryons up to 2 GeV, and of lowest charmed baryon multiplets. A by-product of the scheme is the prediction of new exotic charmed (and bottom) baryons that may be stable against strong decays.

hep-ph↗
arXiv2012

Low-energy general relativity with torsion: a systematic derivative expansion

We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action of a general form containing vector-vector, axial-vector and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the "spin fluid" approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.

hep-th↗
arXiv2011

Towards lattice-regularized Quantum Gravity

Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To that end we need to present the tetrad by a composite field built as a bilinear combination of fermion fields. The theory is explicitly invariant under local Lorentz transformations and, in the continuum limit, under general covariant transformations, or diffeomorphisms. Being well defined for large and fast varying fields at the ultraviolet cutoff, the theory simultaneously has chances of reproducing standard General Relativity in the infrared continuum limit. The present regularization of quantum gravity opens new possibilities of its unification with the Standard Model.

hep-th↗
arXiv2010

How to check that dyons are at work?

I present arguments in favor of the dyon mechanism of confinement and deconfinement. Dyons may be those real physical objects that are revealed as lattice monopoles in the Abelian gauges, and as central vortices in the central gauges. I suggest a lattice calculation of the effective action as function of the gauge invariant eigenvalues of the Polyakov line, which is of general interest but in particular may support or refute the importance of dyons in the Yang--Mills vacuum.

hep-ph↗
arXiv2010

Confinement and deconfinement for any gauge group from dyons viewpoint

Basing on a semiclassical picture of dyons, we present a nonperturbative model of a pure Yang--Mills theory at any temperatures, for an arbitrary simple gauge group. We argue that at low temperatures dyons drive the Yang--Mills system for all groups to a phase where the `eigenphases' of the Polyakov line are, as a vector, proportional to the Weyl vector being the half sum of positive roots. For most gauge groups it means confinement, in particular for `quarks' in any N-ality nonzero representation of the SU(N) gauge group. At a critical temperature there is a 1st order phase transition for all groups (except SU(2) where the transition is 2nd order), characterized by a jump of Polyakov lines, irrespectively of whether the gauge group has a nontrivial center, or not.

hep-th↗
arXiv2010

Prediction of new charmed and bottom exotic pentaquarks

Baryons of the type Qqqqq-bar (where Q = c,b and q = u,d,s quarks) forming anti-decapenta (15)-plets with spin-parity one half-plus are predicted on simple theoretical considerations. The lightest members of these multiplets are explicitly exotic doublets cuuds-bar, cudds-bar with mass about 2420 MeV, and buuds-bar, budds-bar with mass about 5750 MeV, only 130 MeV heavier than Lambda_c and Lambda_b, respectively, and thus stable against strong decays. Although the production rate is probably very low, these remarkable pentaquarks can be looked for at LHC, Fermilab, B-factories, RHIC and elsewhere: their signatures are briefly discussed.

hep-ph↗
arXiv2010

Exotic pentaquarks as Gamov-Teller resonances

If the number of colors Nc is taken large, baryons and their excitations can be considered in a mean-field approach. We argue that the mean field in baryons breaks spontaneously the spherical and SU(3) flavor symmetries, but retains the SU(2) symmetry of simultaneous rotations in space and isospace. The one-quark and quark-hole excitations in the mean field, together with the SU(3) rotational bands about them determine the spectrum of baryon resonances, which turns out to be in satisfactory accordance with reality when one puts Nc=3. A by-product of this scheme is a confirmation of the light pentaquark baryon Theta+ = uudds-bar as a typical Gamov-Teller resonance long known in nuclear physics. An extension of the same large-Nc logic to charmed (and bottom) baryons leads to a prediction of a anti-decapenta (15-bar)-plet of charmed pentaquarks, two of which, Beta++_c = cuuds-bar and Beta+_c = cudds-bar, may be light and stable with respect to strong decays, and should be looked for.

hep-ph↗
arXiv2009

Topology and confinement

These lectures contain an introduction to instantons, calorons and dyons of the Yang--Mills gauge theory. Since we are interested in the mechanism of confinement and of the deconfinement phase transition at some critical temperature, the Yang--Mills theory is formulated and studied at nonzero temperatures. We introduce ``calorons with a nontrivial holonomy'' that are generalizations of instantons and can be viewed as ``made of'' constituent dyons. The quantum weight with which these calorons contribute to the Yang--Mills partition function is considered, and the ensuing statistical mechanics of the ensemble of interacting dyons is discussed. We argue that a simple semiclassical picture based on dyons satisfies all known criteria of confinement and explains the confinement-deconfinement phase transition. This refers not only to the SU(N) gauge groups where dyons lead to the expected behaviour of the observables with N, but also to the exceptional G(2) group whose group center, unlike SU(N), is trivial. Despite being centerless, the G(2) gauge group possesses confinement at low temperatures, and a 1st order deconfinement transition, according to several latest lattice simulations, indicating that confinement-deconfinement is not related to the group center. Dyons, however, reproduce this behaviour.

hep-ph↗
arXiv2009

Justifying the exotic Theta+ pentaquark

The existence of a light S=+1 baryon resonance follows from Quantum Field Theory applied to baryons. This is illustrated in the Skyrme model (where Theta+ exists but is too strong) and in a new mean field approach where Theta+ arises as a consequence of three known resonances: Lambda(1405), N(1440) and N(1535).

hep-ph↗
arXiv2008

Baryon resonances in the mean field approach and a simple explanation of the Theta+ pentaquark

We suggest to classify baryon resonances as single-quark states in a mean field, and/or as its collective excitations. Identifying the Roper resonance N(1440), the nucleon resonance N(1535), and the singlet hyperon Lambda(1405) as single-quark excitations, we find that there must be an exotic S=+1 baryon resonance Theta+ (the "pentaquark") with a mass about 1440+1535-1405=1570 MeV and spin-parity one-half-plus. We argue that Theta+ is an analog of the Gamov--Teller excitation long known in nuclear physics.

hep-ph↗
arXiv2008

Exotic baryon resonances in the Skyrme model

We outline how one can understand the Skyrme model from the modern perspective. We review the quantization of the SU(3) rotations of the Skyrmion, leading to the exotic baryons that cannot be made of three quarks. It is shown that in the limit of large number of colours the lowest-mass exotic baryons can be studied from the kaon-Skyrmion scattering amplitudes, an approach known after Callan and Klebanov. We follow this approach and find, both analytically and numerically, a strong Theta+ resonance in the scattering amplitude that is traced to the rotational mode. The Skyrme model does predict an exotic resonance Theta+ but grossly overestimates the width. To understand better the factors affecting the width, it is computed by several methods giving, however, identical results. In particular, we show that insofar as the width is small, it can be found from the transition axial constant. The physics leading to a narrow Theta+ resonance is briefly reviewed and affirmed.

hep-ph↗
arXiv2008

Statistical physics of dyons and quark confinement

We present a semiclassical approach to the SU(N) Yang--Mills theory whose partition function at nonzero temperatures is approximated by a saddle point -- an ensemble of an infinite number of interacting dyons of N kinds. The ensemble is governed by an exactly solvable 3d quantum field theory, allowing calculation of correlations functions relevant to confinement. We show that known criteria of confinement are satisfied in this semiclassical approximation: (i) the average Polyakov line is zero below some critical temperature, and nonzero above it, (ii) a quark-antiquark pair has linear rising potential energy, (iii) the average spatial Wilson loop falls off exponentially with the area, (iv) N^2 gluons are canceled out from the spectrum, (v) the critical deconfinement temperature is in good agreement with lattice data. Using the same approximation, we find confinement for the exceptional gauge group G(2) and a first-order deconfinement transition, also in agreement with lattice findings.

hep-th↗
arXiv2008

Statistical physics of dyons and confinement

We present a semiclassical description of the SU(N) Yang--Mills theory whose partition function at nonzero temperatures is approximated by that of an ensemble of N kinds of interacting dyons. The ensemble is mathematically described by an exactly solvable 3d quantum field theory, allowing calculation of correlations functions relevant to confinement. We show that all known criteria of confinement are satisfied in this semiclassical approximation: (i) the average Polyakov line is zero below some critical temperature, and nonzero above it, (ii) static quarks in any nonzero N-ality representation have linear rising potential energy, (iii) the average spatial Wilson loop falls off exponentially with the area, (iv) N^2 gluons are canceled out from the spectrum, (v) the critical temperature is in good agreement with lattice data.

hep-th↗