arXiv subjects

S. N. Nedelko

Publications and source records attributed to S. N. Nedelko.

14 recordsLinked to original sources

arXiv2010

Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory

Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon condensate is postulated. The minima are connected to each other by the parity transformations and Weyl group transformations associated with the color su(3) algebra. The presence of degenerated discrete minima in the effective potential leads to the solutions of the effective Euclidean equations of motion in the form of the kink-like gauge field configurations interpolating between different minima. Spectrum of charged scalar field in the kink background is discussed.

hep-ph↗

arXiv2006

Poincaré recurrence theorem and the strong CP-problem

The existence in the physical QCD vacuum of nonzero gluon condensates, such as $ $, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit ``topological charge'' $q$ characterising the fields approximating the gluon configurations which should dominate the QCD partition function. If $q$ is an irrational number then the critical values of the $θ$ parameter for which CP is spontaneously broken are dense in $\mathbb{R}$, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of $U_{\rm A}(1)$ symmetry. We present an explicit realisation of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.

hep-ph↗

arXiv2004

Realisation of chiral symmetry in the domain model of QCD

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background domain-like gluon field. Quark fluctuations satisfy a chirality violating boundary conditions parametrized by a random chiral angle $α_j$ on the $j-th$ domain. The free energy of an ensemble of $N\to\infty$ domains depends on $\{α_j, j=1... N\}$ through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial U(1) degeneracy in the ground state, leaving only a residual axial Z(2) symmetry. This discrete symmetry and flavour $SU(N_f)_L\times SU(N_f)_R$ chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of Dirac operator. In order to illustrate the splitting between the $η'$ from octet pseudoscalar mesons realised in the domain model, we estimate the masses of light pseudoscalar and vector mesons.

hep-ph↗

arXiv2003

Axial U(1) and spontaneous chiral symmetry breaking within a confining model of the QCD vacuum

A model for the QCD vacuum based on domain-like background gluon fields has previously been developed and demonstrated to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background gluon field. On the boundary of the j-th domain, quark fluctuations satisfy chirality violating boundary conditions parametrized by a chiral angle $α_j$ which is treated as a collective variable. The dependence of the free energy of an ensemble of $N\to\infty$ domains on $\{α_j, j=1... N\}$ is studied. For one massless flavour there are only two degenerate minima ($α_j=0,π$ $\forall j$) due to the contribution of the anomaly to the free energy, which suppresses the continuous U(1) degeneracy. The residual discrete symmetry is spontaneously broken with a quark condensate of $-(238 {\rm{MeV}})^3.$ For $N_f$ massless flavours a continuous $SU(N_f)_L\times SU(N_f)_R$ degeneracy appears, while the $U_A(1)$ direction remains suppressed.

hep-ph↗

arXiv2003

Quark determinant in domain-like gluon fields

We address the computation of the determinant for the Dirac operator corresponding to a quark propagating in a background gluon field of the following type: the gauge field is covariantly constant and self-dual inside a hypersphere and with quark fields satisfying bag-like (chiral-violating) boundary conditions at the surface of the hypersphere. We find that the parity odd part of the logarithm of the determinant corresponds to the Abelian anomaly. However the parity even part also depends on the chiral angle associated with the boundary. This unexpected dependence is discussed.

hep-ph↗

arXiv2002

Domains in the Nonperturbative QCD Vacuum

QCD vacuum gluon fields are modelled by hyperspherical domains of constant field strength. The pure glue theory confines static quarks. Solutions of the Dirac operator have chirality properties in agreement with lattice results.

hep-ph↗

arXiv2001

Confinement and chiral symmetry breaking via a domainlike mean field

Singular gauge fields in the partition function for QCD can lead to a domain-like picture for the QCD vacuum by virtue of constraints on quantum fluctuations at the singularities. With a simple model of hyperspherical domains with interiors of constant field strength we show that the main features of gluon condensation and an area law for static quarks can be realised.The Dirac operator in such a background is exactly soluble. Chirality properties of the solutions show agreement with recent lattice results.

hep-ph↗

arXiv2001

On Domain-like Structures in the QCD Vacuum

We suggest that clusters or domains of topological charge and action density occur in the QCD vacuum as an effect of singularities in gauge fields and can simultaneously lead to confinement and chiral symmetry breaking. The string constant, condensates and topological susceptibility are estimated within a simplified model of hyperspherical domains with interiors of constant field strength with reasonable values obtained. Propagators of dynamical quarks and gluons have compact support in configuration space, thus having entire Fourier transforms, which gives rise to their confinement.

hep-ph↗

arXiv2001

Domain-like Structures in the QCD Vacuum, Confinement and Chiral Symmetry Breaking

We discuss how the inclusion of singular gauge fields in the partition function for QCD can lead to a domain-like picture for the QCD vacuum by virtue of specific conditions on quantum fluctuations at the singularities. With a simplified model of hyperspherical domain regions with interiors of constant field strength we calculate the basic parameters of the QCD vacuum, the gluon condensate, topological susceptibility, string constant and quark condensate, and briefly discuss confinement of dynamical quarks and gluons.

hep-ph↗

arXiv1998

(Anti-)self-dual homogeneous gluon field and axial anomaly in QCD

The transition form factor, decay width and charge form factor of pion are calculated within the model of induced nonlocal quark currents based on the assumption that the nonperturbative QCD vacuum can be characterized by a homogeneous (anti-)self-dual gluon field. It is shown that the interaction of the quark spin with the vacuum gluon field, being responsible in the model for the chiral symmetry breaking and the spectrum of light mesons, can also play the decisive role in forming the transition form factor and two-photon decay width. Asymptotic behavior of quark loops in the presence of the background gluon field for large momentum transfer is discussed.

hep-ph↗

arXiv1998

Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory

We examine in non-Abelian gauge theory the heavy quark limit in the presence of the (anti-)self-dual homogeneous background field and see that a confining potential emerges, consistent with the Wilson criterion, although the potential is quadratic and not linear in the quark separation. This builds upon the well-known feature that propagators in such a background field are entire functions. The way in which deconfinement can occur at finite temperature is then studied in the static temporal gauge by calculation of the effective potential at high temperature. Finally we discuss the problems to be surmounted in setting up the calculation of the effective potential nonperturbatively on the lattice.

hep-th↗

arXiv1998

Self-dual homogeneous gluon field and electromagnetic structure of pion

hep-ph↗

arXiv1996

(Anti-)self-dual homogeneous vacuum gluon field as an origin of confinement and $SU_L(N_F)\times SU_R(N_F)$ symmetry breaking in QCD

It is shown that an (anti-)self-dual homogeneous vacuum gluon field appears in a natural way within the problem of calculation of the QCD partition function in the form of Euclidean functional integral with periodic boundary conditions. There is no violation of cluster property within this formulation, nor are parity, color and rotational symmetries broken explicitly. The massless limit of the product of the quark masses and condensates, $m_f \langle \barψ_f ψ_f \rangle$, is calculated to all loop orders. This quantity does not vanish and is proportional to the gluon condensate appearing due to the nonzero strength of the vacuum gluon field. We conclude that the gluon condensate can be considered as an order parameter both for confinement and chiral symmetry breaking.

hep-ph↗

arXiv1996

Meson masses within the model of induced nonlocal quark currents

The model of induced quark currents formulated in our recent paper (Phys. Rev. D51, 176) is developed. The model being a kind of nonlocal extension of the bosonization procedure is based on the hypothesis that the QCD vacuum is realized by the (anti-)self-dual homogeneous gluon field. This vacuum field provides the analytical quark confinement. It is shown that a particular form of nonlocality of the quark and gluon propagators determined by the vacuum field, an interaction of quark spin with the vacuum gluon field and a localization of meson field at the center of masses of two quarks can explain the distinctive features of meson spectrum: Regge trajectories of radial and orbital excitations, mass splitting between pseudoscalar and vector mesons, the asymptotic mass formulas in the heavy quark limit: $M_{Q\bar Q}\to 2m_Q$ for quarkonia and $M_{Q\bar q}\to m_Q$ for heavy-light mesons. With a minimal set of parameters (quark masses, vacuum field strength and the quark-gluon coupling constant) the model describes to within ten percent inaccuracy the masses and weak decay constants of mesons from all qualitatively different regions of the spectrum.

hep-ph↗