Dmitri Diakonov

Nucleon mass and nucleon sigma term

The nucleon mass MN and the nucleaon σ-term σ = 〈|muu + mddd|N〉 are calculated from a low momenta QCD effective larangian involving dynamically massive quarks interacting with the pion field. Minimizing the aggregate energy of the quark Dirac sea plus the energy of an extra bound-state level for valence quarks, we find MN = 1207 MeV. Introducing non-zero current quark masses we calculate the value of the σ-term: σ = 54 MeV.

Yang-Mills theory in three dimensions as a quantum gravity theory

We perform the dual transformation of theYang-Mills theory in three dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but which is embedded into a flat 6-dimensional space [for the SU(2) gauge group]. In the continuum limit, the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual-color space. The Yang-Mills theory can also be rewritten as a quantum gravity theory with the Einstein-Hilbert action but with a purely imaginary Newton constant plus a homogeneous “ether” term. The theory can be formulated in a gauge-invariant and local form without explicit color degrees of freedom.

Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory

A bstractWe present a study of the free energy of parameterized Polyakov loops P in SU(2) and SU(3) lattice gauge theory as a function of the parameters that characterize P. We explore temperatures below and above the deconfinement transition, and for our highest temperatures T > 5 Tc we compare the free energy to perturbative results.

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

A bstractC-parity-even quarkonia ηb,c and χb,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, Q2 ≃ 2.5 − 3 GeV2, for charmonia and rather large, Q2 ≃ 20 GeV2, for bottomonia. We evaluate the scale by studying the next-to-leading-order production cross sections.

Non-Abelian Stokes theorems in the Yang-Mills and gravity theories

We discuss the interpretation of the non-Abelian Stokes theorem or the Wilson loop in the Yang-Mills theory. For the “gravitational Wilson loops,” i.e., holonomies in curved d=2, 3, 4 spaces, we then derive “ non-Abelian Stokes theorems” that are similar to our formula in the Yang-Mills theory. In particular, we derive an elegant formula for the holonomy in the case of a constant-curvature background in three dimensions and a formula for small-area loops in any number of dimensions.

Instability of finite baryon densities and baryon number non-conservation at high energies

Abstract We show that a state with a finite density of baryons and/or leptons is unstable under tunneling to a state with no fermions but many W and Higgs bosons. The decay rate increases rapidly with the baryon density, and at densities corresponding to the Fermi momentum μ crit = 2πm w α≈16 TeV it becomes unsuppressed. We present arguments that the high-density problem is equivalent to that of the accelerator baryon number violation at TeV energies and explain how to solve both problems non-perturbatively. We show that the total baryon number violation cross-section becomes exponentially unsuppressed at s =2μ crit ≈32 TeV , irrespectively of the Higgs mass.

Effective Lagrangian for the Polyakov line on a lattice

A bstractWe 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.

Diffeomorphism-invariant lattice actions

We present a lattice-discretization procedure which is based on the simplicial lattice preserves diffeomorphism invariance. The presented procedure is the straightforward generalization for the procedure used for discretization of the spinor gravity [7]. As a stable way to guarantee the removing of the lattice regularization, i.e. the continuum limit, for lattice diffeomorphism invariant theories, we propose to tune the system to point of the phase transition. We expect that the Einstein gravitation is achieved at this point.

Screening of fractional charges in (2+1)-dimensional QED

We show that the logarithmically rising static potential between opposite-charged sources in two dimensions is screened by dynamical fields even if the probe charges are fractional, in units of the charge of the dynamical fields. The effect is due to quantum mechanics: the wave functions of the screening charges are superpositions of two bumps localized both near the opposite- and the same-charge sources, so that each of them gets exactly screened.

Strange quarks in semibosonized SU(3) Nambu-Jona-Lasinio Model

In a semibosonized SU(3) Nambu-Jona-Lasinio model explicit symmetry breaking mass terms are introduced. The soliton solution corresponding to an isospin embedding of the SU(2) hedgehog in the SU(3) group is studied. The hyperon splittings and the hadronic part of the isospin mass differences are calculated and a good agreement with experiment is found.